Macroeconomics 10th Ed Andrew Abel, Bernanke, Croushore Solution Manual

Type:

Solution Manual

Resource:

Macroeconomics

Edition:

10th Edition

Author(s):

Andrew B. Abel Ben S. Bernanke Dean Croushore

Contents Chapter 1

Introduction to Macroeconomics .............................................................................

1

Chapter 2

The Measurement and Structure of the National Economy .......................................

16

Chapter 3

Productivity, Output, and Employment ....................................................................

39

Chapter 4

Consumption, Saving, and Investment .....................................................................

69

Chapter 5

Saving and Investment in the Open Economy ..........................................................

109

Chapter 6

Long-Run Economic Growth ..................................................................................

133

Chapter 7

The Asset Market, Money, and Prices .....................................................................

156

Chapter 8

Business Cycles ......................................................................................................

177

Chapter 9

The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis ................................................................

198

Classical Business Cycle Analysis: Market-Clearing Macroeconomics...........................................................................

229

Keynesianism: The Macroeconomics of Wage and Price Rigidity .....................................................................................

260

Chapter 12

Unemployment and Inflation ...................................................................................

296

Chapter 13

Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy .........................................................

324

Chapter 14

Monetary Policy and the Federal Reserve System....................................................

368

Chapter 15

Government Spending and Its Financing .................................................................

393

Chapter 10 Chapter 11

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Chapter 1 Introduction to Macroeconomics n

Learning Objectives

I.

Goals of Part I A. Introduce students to the main concepts in macroeconomics (Ch. 1) B. Introduce national income accounting and major economic magnitudes (Ch. 2)

II. Section Goals A. Summarize the primary issues addressed in macroeconomics (Sec. 1.1) B. Describe the activities and objectives of macroeconomists (Sec. 1.2) C. Differentiate between the classical and Keynesian approaches to macroeconomics (Sec. 1.3) III. Notes to Ninth Edition Users: This chapter is little changed; the data were updated.

©2020 Pearson Education, Inc.

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Teaching Notes

I.

What Macroeconomics Is About (Sec. 1.1) Macroeconomics: the study of structure and performance of national economies and government policies that affect economic performance. Macroeconomists study: A. Long-run economic growth 1. Growth of output in United States over time a. Text Fig. 1.1: Output of United States since 1869 b. Note decline in output during recessions; increase in output during some wars 2. Sources of growth—population, average labor productivity growth This may be a good place to introduce students to the calculation of a growth rate, which is used throughout the textbook. You can write it first in general terms, as %DX = [(Xt+1 - Xt)/Xt] ´ 100% = [(Xt+1/Xt) - 1] ´ 100%.

Then you might use an example with something you’re talking about, such as real GDP growth over the past year, or the inflation rate.

Throughout the text, students may come across mathematical calculations that are unfamiliar to them. The appendix to the textbook contains some helpful basic guidance to mathematical topics, including discussions of functions and graphs, slopes of functions, elasticities, functions of several variables, shifts of a curve, exponents, and growth-rate formulas.

3. Average labor productivity a. Average labor productivity: output produced per employed worker b. Text Fig. 1.2: Average labor productivity of United States since 1900 c. Average labor productivity growth: (1) 2.6% per year from 1949 to 1973 (2) 1.1% per year from 1973 to 1995 (3) 1.9% per year from 1995 to 2007 (4) 0.9% per year from 2007 to 2017 Working with Macroeconomic Data Problem 1 gives students practice in calculating average labor productivity and dealing with growth rates.

B. Business cycles 1. Business cycle: short-run contractions and expansions in economic activity 2. Downward phase is called recession C. Unemployment 1. Unemployment: the number of people who are available for work and actively seeking work but cannot find jobs 2. U.S. experience shown in text Fig. 1.3, showing unemployment rate (unemployment as a percent of labor force) 3. Recessions cause unemployment rate to rise Analytical Problem 1 asks students to think about average labor productivity and unemployment and their relationship to output. Working with Macroeconomic Data Problem 2 has students examine data on the unemployment rate and to see how it behaves in recessions.

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Chapter 1 Introduction to Macroeconomics

D. Inflation Analytical Problem 2 asks students to think about the welfare consequences of having a higher price level.

1. U.S. experience shown in text Fig. 1.4 2. Deflation: when prices of most goods and services decline 3. Inflation rate: the percentage increase in the level of prices 4. Hyperinflation: an extremely high rate of inflation You may wish to discuss how to calculate the inflation rate, which is just the growth rate of the price level. It can be expressed as p = [(Pt+1/Pt) - 1] ´ 100%. Numerical Problem 1 gives students practice calculating growth rates, including the growth rate of average labor productivity and the inflation rate. Working with Macroeconomic Data Problem 3 requires students to examine and analyze historical movements in inflation.

E. The international economy 1. Open vs. closed economies a. Open economy: an economy that has extensive trading and financial relationships with other national economies b. Closed economy: an economy that does not interact economically with the rest of the world Working with Macroeconomic Data Problem 4 requires students to compare GDP growth rates across countries.

F.

2. Trade imbalances a. U.S. experience shown in text Fig. 1.5 b. Trade surplus: exports exceed imports c. Trade deficit: imports exceed exports Macroeconomic policy 1. Fiscal policy: government spending and taxation a. Effects of changes in federal budget b. U.S. experience in text Fig. 1.6 c. Relation to trade deficit?

Numerical Problem 2 serves two purposes: (1) to get students to look at some real data on the economy and (2) to give them some idea about how large the trade deficit and government budget deficit are. Working with Macroeconomic Data Problem 5 has students look at the ratio of federal government debt to GDP and to think about what causes it to rise.

2. Monetary policy: growth of money supply; determined by central bank; the Fed in United States

G. Aggregation 1. Aggregation: summing individual economic variables to obtain economywide totals 2. Distinguishes microeconomics (disaggregated) from macroeconomics (aggregated)

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II.

What Macroeconomists Do (Sec. 1.2) A. Macroeconomic forecasting 1. Relatively few economists make forecasts

Data Application There are many firms that provide forecasts for some macroeconomic variables, but only a few firms have complete, large-scale macroeconomic models that include details on every sector of the economy. The main forecasting firms in the United States are Macroeconomic Advisers and IHS Global Insight. These firms produce new forecasts every month and analyze the current economic situation.

You do not have to subscribe to one of these services to keep up-to-date on forecasts. There are several surveys of forecasters available to the general public, including the Blue Chip survey, the NABE (National Association of Business Economists) survey, a survey run by the Wall Street Journal, the Livingston survey, and the Survey of Professional Forecasters. (The latter two are free of charge and run by the Federal Reserve Bank of Philadelphia.) However, these surveys will not give you the level of detail that the large forecasting firms provide.

2. Forecasting is very difficult

Data Application Alan Meltzer gives a graphic example of how difficult it is to forecast the macroeconomy in his article, “Limits of Short-Run Stabilization Policy,” Economic Inquiry, January 1987, pp. 1–14. He shows that the forecast errors for real output made at the beginning of the quarter are very large, making it almost impossible to use the forecasts to make policy. However, he looked only at the volatile time period from mid-1980 to early 1985. More recent current-quarter forecasts seem to be better.

B. Macroeconomic analysis 1. Private and public sector economists—analyze current conditions

Data Application Wall Street hires a large number of economists, most of whom are engaged in data analysis on a daily basis. Their job is to tell traders what newly released economic data mean for financial markets in general, as well as for the prices of individual assets. Many Wall Street economists also make their own detailed forecasts of the economy.

2. Public sector employs many macroeconomic analysts who provide policy advice C. Macroeconomic research 1. Goal: to make general statements about how the economy works 2. Theoretical and empirical research are necessary for forecasting and economic analysis 3. Economic theory: a set of ideas about the economy, organized in a logical framework 4. Economic model: a simplified description of some aspect of the economy This is a good point for you to talk about your own research interests. Students are very interested in learning about the kinds of research their professors do. You may want to talk about your research later, when you come to a section of the textbook that discusses the topic on which you do your research.

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Chapter 1 Introduction to Macroeconomics

5. Usefulness of economic theory or models depends on reasonableness of assumptions, possibility of being applied to real problems, empirically testable implications, and theoretical results consistent with real-world data 6. In Touch with Data and Research: Developing and Testing an Economic Theory a. Step 1: State the research question b. Step 2: Make provisional assumptions c. Step 3: Work out the implications of the theory d. Step 4: Conduct an empirical analysis to compare the implications of the theory with the data e. Step 5: Evaluate the results of your comparisons

Theoretical Application The classic discussion of research issues by Milton Friedman is, “The Methodology of Positive Economics,” Essays in Positive Economics, Chicago: University of Chicago Press, 1953.

Analytical Problem 3 is an exercise in how to formulate and test a theory.

D. Data development—very important for making data more useful

Data Application As head of the Council of Economic Advisers in the Bush presidency, Michael Boskin led an effort to get more accurate and timely statistics in the United States. See “Improving the Quality of Economic Statistics” in the Economic Report of the President, 1990.

A good example of data development came in early 1994, when the Commerce Department revised its questionnaire for the Current Population Survey. This survey determines the unemployment rate. Prior to 1994 the survey did not do a good job of distinguishing between people who were unemployed and looking for a job but spending most of their week doing work at home, and those who were out of the labor force and not even looking for a job. As a result of the change in the survey, there is a one-time jump in the unemployment rate in January 1994, not because of any change in the macroeconomy, but just because the more accurate questionnaire found that more people were unemployed than in the previous survey.

In 1996 the national income accounts underwent a major revision, changing how its price indexes are calculated (moving to a chain-weighted index) and changing how government purchases are measured (accounting more accurately for government capital formation).

Also in 1996, a major controversy arose over the calculation of the consumer price index (CPI). Economists argued that the CPI was biased upward significantly, so that inflation as measured by the CPI was about one percentage point greater than the true increase in the cost of living. This topic is also discussed in Chapter 2.

Data must change to keep up with technology. In October 1999, the national income accounts were revised in a significant way by treating computer software as an investment. This change raised the measured growth rate of the economy in the late 1990s. In 2013, the government began to explicitly recognize intangible investment, again leading to higher measured levels of GDP than before.

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Policy Application In a speech discussing what economists have learned from the financial crisis in 2008, Fed Chairman Ben Bernanke suggested that the financial crisis was the result of a failure of economic engineering or economic management, rather than economic science (“On the Implications of the Financial Crisis for Economics,” at Princeton University, September 24, 2010). Economic science encompasses academic research and the development of theory and empirical estimation.

Economic engineering is the development of frameworks that apply economic theory, such as banks’ risk-management systems and the methods used by bank regulators, which clearly failed, leading to the crisis. Economic management is the operation of economic frameworks in practice, which also failed in the case of banks and investment firms, who failed to understand the risks they were taking, and of bank supervisors, who also failed to understand the risks that banks were taking. The crisis was thus less a problem with economic theory, but with how it was put into practice.

III. Why Macroeconomists Disagree (Sec. 1.3) A. Positive vs. normative analysis 1. Positive analysis: examines the economic consequences of a policy 2. Normative analysis: determines whether a policy should be used Analytical Problem 4 gives students practice in distinguishing positive from normative analysis.

B. Classicals vs. Keynesians 1. The classical approach a. The economy works well on its own b. The “invisible hand”: the idea that if there are free markets and individuals conduct their economic affairs in their own best interests, the overall economy will work well c. Wages and prices adjust rapidly to get to equilibrium (1) Equilibrium: a situation in which the quantities demanded and supplied are equal (2) Changes in wages and prices are signals that coordinate people’s actions d. Result: Government should have only a limited role in the economy

Theoretical Application At this point in the discussion, you may want to talk about philosophies of economics. Students are often fascinated by how philosophical differences arise and what they mean, especially for policy. This helps to reinforce the idea that the Keynesian and classical models are very different in their implications. You might suggest the idea that economists who are skeptical of the government’s role in the economy are more likely to believe in a classical model, while those who believe the government can do good are more likely to become Keynesians. You can point out, however, that things are changing; some New Keynesians seem skeptical of government intervention.

2. The Keynesian approach a. The Great Depression: Classical theory failed because high unemployment was persistent

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Chapter 1 Introduction to Macroeconomics

b. Keynes: Persistent unemployment occurs because wages and prices adjust slowly, so markets remain out of equilibrium for long periods c. Conclusion: Government should intervene to restore full employment Analytical Problem 5 asks students to distinguish between how a classical economist and a Keynesian economist would think about the same issue.

3. The evolution of the classical–Keynesian debate a. Keynesians dominated from World War II to 1970 b. Stagflation led to a classical comeback in the 1970s c. Last 30 years: excellent research with both approaches

Theoretical Application You may wish to add a discussion of the recent progression of research. You could start by a brief overview of how the failure of Keynesian models in the stagflation of the 1970s led to the growth of rational-expectations modeling, with its focus on the importance of microfoundations. Then you could discuss New Keynesian macroeconomics (discussed in greater detail in Chapter 11) and its attempts to provide some microfoundations for wage and price stickiness in Keynesian models.

Although the textbook presents just a few versions of classical models and Keynesian models, it is difficult to find a prototypical classical or Keynesian economist who believes fully in that particular model. The lack of convincing evidence on which model is correct has led macroeconomists to be eclectic, so they often hedge their bets. As a result, a one-armed macroeconomist is hard to find; analysis tends to be of the “on the one hand, on the other hand” variety. And of course that means that if you laid all the macroeconomists on the earth end to end, they still wouldn’t reach a conclusion!

C. A unified approach to macroeconomics 1. Textbook uses a single model to present both classical and Keynesian ideas 2. Three markets: goods, assets, labor 3. Model starts with microfoundations: individual behavior 4. Long run: wages and prices are perfectly flexible 5. Short run: Classical case—flexible wages and prices; Keynesian case—wages and prices are slow to adjust

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Additional Issues for Classroom Discussion

1.

What Are Society’s Major Economic Problems Today?

In the first class session, it may be interesting to discuss students’ perceptions of the major economic problems facing the economy today. Public-opinion polls show that Americans’ views on the importance of different issues vary sharply over the business cycle. In recessions, people perceive unemployment and economic growth as the main problems. When inflation is high, reducing it is a high priority.

You may wish to ask your students to rank the importance to them of the following economic issues: (1) unemployment; (2) inflation; (3) economic growth; (4) stagnant incomes; (5) the trade deficit; (6) Social Security; (7) the government budget; and (8) income inequality. Some discussion of all these topics is covered later in the text.

2.

Let’s Forecast!

Here’s an exercise that will surprise both you and your students. On the first day of class, before they even know much about the macroeconomic variables that will be studied in the course, ask them to forecast such things as inflation, unemployment, the growth rate of output, and interest rates. You can give them a handout of the current values of key variables. (By the way, it is easy to get the data online; the easiest way is to use the Federal Reserve Bank of St. Louis FRED database at fred.stlouisfed.org.)

Some of your students will have outrageously high forecasts for some variables, but others will be really low. If you calculate the median forecast, you and your students may be amazed at how close it is to the median forecast of the Survey of Professional Forecasters or one of the other macroeconomic surveys.

And at the end of the semester, you may be surprised at how accurate your students’ forecasts were.

3.

Formulating a Model

Here is an exercise in formulating an economic model that will help students learn how to think about economic issues and how to model them. The idea is for you (or them) to pick a current topic like CPI bias, the basis of the business cycle, the effect of government deficits, the effect of trade deficits, or something else. It is useful to do this now, before they have learned much about the topic. Follow the steps outlined in the textbook for developing and testing an economic theory. This exercise will help them get an idea of how research is actually done, starting from a point when you do not know much about the answer to a question. It is especially important to emphasize how you could conduct an empirical analysis to test the theory. You can also spend some time talking about what key assumptions you need to make to simplify the theory.

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Answers to Textbook Problems

Review Questions 1. Both total output and output per worker have risen strongly over time in the United States. Output itself has grown by a factor of 150 in the last 148 years. Output per worker is more than 7 times what it was in 1900. These changes have led to a much higher standard of living today.

2. The business cycle refers to the short-run movements (expansions and recessions) of economic activity. The unemployment rate rises in recessions and declines in expansions. The unemployment rate never reaches zero, even at the peak of an expansion.

3. A period of inflation is one in which prices (on average) are rising over time. Deflation occurs when prices are falling on average over time. Before World War II, prices tended to rise during war periods and fall after the wars ended; over the long run, the price level remained fairly constant. Since World War II, however, prices have risen fairly steadily.

4. The budget deficit is the annual excess of government spending over tax collections. The U.S. federal government has been most likely to run deficits during wars or recessions. From the early 1980s to the mid-1990s, deficits were very large, even without a major war. The U.S. government ran surpluses for several years, from 1998 to 2001. But the deficit became enormous from 2008 to 2010 because of the depth of the recession caused by the financial crisis.

5. The trade deficit is the amount by which imports exceed exports; the trade surplus is the amount by which exports exceed imports, so it is the negative of the trade deficit. In recent years, the United States has had huge trade deficits. But from 1900 to 1970, the United States mostly had trade surpluses.

6. Macroeconomists engage in forecasting, macroeconomic analysis, macroeconomic research, and data development. Macroeconomic research can be useful in investigating forecasting models to improve forecasts, in providing more information on how the economy works to help macroeconomic analysts, and in telling data developers what types of data should be collected. Research provides the basis (results and ideas) for forecasting, analysis, and data development.

7. These are the steps in developing and testing an economic model or theory: (1) state the research question; (2) make provisional assumptions that describe the economic setting and the behavior of the economic actors; (3) work out the implications of the theory; (4) conduct an empirical analysis to compare the implications of the theory with the data; and (5) evaluate the results of your comparisons. The criteria for a useful theory or model are that (1) it has reasonable and realistic assumptions; (2) it is understandable and manageable enough for studying real problems; (3) its implications can be tested empirically using real-world data; and (4) its implications are consistent with the data.

8. Yes, it is possible for economists to agree about the effects of a policy (that is, to agree on the positive analysis of the policy), but to disagree about the policy’s desirability (normative analysis). For example, suppose economists agreed that reducing inflation to zero within the next year would cause a recession (positive analysis). Some economists might argue that inflation should be reduced, because they prefer low inflation even at the cost of higher unemployment. Others would argue that inflation is not as harmful to people as unemployment is, and would oppose such a policy. This is normative analysis, as it involves a value judgment about what policy should be.

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9. Classicals see wage and price adjustment occurring rapidly, while Keynesians think that wages and prices adjust only slowly when the economy is out of equilibrium. The classical theory implies that unemployment will not persist because wages and prices adjust to bring the economy rapidly back to equilibrium. But if Keynesian theory is correct, then the slow response of wages and prices means that unemployment may persist for long periods of time unless the government intervenes.

10. Stagflation was a combination of stagnation (high unemployment) and inflation in the 1970s. It changed economists’ views because the Keynesian approach could not explain stagflation satisfactorily.

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Numerical Problems 1. (a) Average labor productivity is output divided by employment: 2017: 12,000 tons of potatoes divided by 1000 workers = 12 tons of potatoes per worker 2018: 14,300 tons of potatoes divided by 1100 workers = 13 tons of potatoes per worker (b) The growth rate of average labor productivity is [(13/12) - 1] ´ 100% = 8.33%. (c) The unemployment rate is: 2017: (100 unemployed/1100 workers) ´ 100% = 9.1% 2018: (50 unemployed/1150 workers) ´ 100% = 4.3% (d) The inflation rate is [(2.5/2) - 1] ´ 100% = 25%.

2. The answers to this problem will vary depending on the current date. The answers here are based on the data as of July 2018. Numbers are at annual rates in billions of dollars. There does not appear to be a trend in the data; all the ratios are fairly stable.

2015

2016

2017

GDP

18120.71 18624.48 19390.61

Exports

2264.916 2214.566 2343.988

Imports

2788.958 2735.805 2915.551

Receipts

3441.392 3452.073 3588.048

Expenditures

4028.044 4149.351 4252.472

a.

Exports/GDP

12.5%

11.9%

12.1%

Imports/GDP

15.4%

14.7%

15.0%

Trade Imbalance/GDP

-2.9%

-2.8%

-2.9%

Receipts/GDP

19.0%

18.5%

18.5%

Expenditures/GDP

22.2%

22.3%

21.9%

Deficit/GDP

-3.2%

-3.7%

-3.4%

b.

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Analytical Problems 1. Yes, average labor productivity can fall even when total output is rising. Average labor productivity is total output divided by employment. So average labor productivity can fall if output and employment are both rising but employment is rising faster.

Yes, the unemployment rate can also rise even though total output is rising. This can occur in a number of different ways. For example, average labor productivity might be rising with employment constant, so that output is rising; but the labor force may be increasing as well, so that the unemployment rate is rising. Or average labor productivity might be constant, and both employment and unemployment could rise at the same time because of an increase in the labor force, with the number of unemployed rising by a greater percentage.

2. Just because prices were lower in 1890 than they are in 2018 does not mean that people were better off back then. People’s incomes have risen much faster than prices have risen over the last 100 years, so they are better off today in terms of real income.

3. There are many possible theories. One possibility is that people whose last names begin with the letters A through M vote Democratic, while those whose names begin with the letters N through Z vote Republican. You could test this theory by taking exit polls or checking the lists of registered voters by party. However, this theory fails the criterion of being reasonable, since there is no good reason to expect the first letters of people’s last names to matter for their political preferences.

A better theory might be one based on income. For example, you might make the assumption that the Republican Party promotes business interests, while the Democratic Party is more interested in redistributing income. Then you might expect people with higher incomes to vote Republican and people with lower incomes to vote Democratic. Taking a survey of people as they left the polls could test this. In this case the assumptions of the theory seem reasonable and realistic, and the model is simple enough to understand and to apply. So it is potentially a useful model.

4. (a) Positive. This statement tells what will happen, not what should happen. (b) Positive. Even though it is about income-distribution issues, it is a statement of fact, not opinion.

If the statement said “The payroll tax should be reduced because it . . . ,” then it would be a normative statement. (c) Normative. Saying taxes are too high suggests that they should be lower. (d) Positive. Says what will happen as a consequence of an action, not what should be done. (e) Normative. This is a statement of preference about policies.

5. A classical economist might argue that the economy would work more efficiently without the government trying to influence trade. The imposition of tariffs increases trade barriers, interfering with the invisible hand. The tariffs simply protect an industry that is failing to operate efficiently and is not competitive internationally.

A Keynesian economist might be more sympathetic to concerns about the steel industry. Keynesians might argue that there may need to be a long-run adjustment in the steel industry, but would want to prevent workers in the steel industry from becoming unemployed in the short run.

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Chapter 1 Introduction to Macroeconomics

Working with Macroeconomic Data 1. The data as they existed in July 2018 were as follows: Year 1949 1959 1969 1979 1989 1999 2009

GDPC1

PAYEMS

2,004.7 3,055.1 4,715.5 6,503.9 8,850.2 12,323.3 14,541.9

43,517 54,175 71,240 90,673 108,849 130,789 129,781

Based on these data, average labor productivity at the end of each decade is as follows: Year

Average Labor Productivity

1949 1959 1969 1979 1989 1999 2009

46.1 56.4 66.2 71.7 81.3 94.2 112.0

The growth rate of average labor productivity in each decade is as follows: Year

1950s 1960s 1970s 1980s 1990s 2000s a. b.

Average Labor Productivity Growth Rate 2.0% 1.6% 0.8% 1.3% 1.5% 1.7%

Using these data, labor productivity grew the most quickly in the 1950s and most slowly in the 1970s.

Annual growth rates are:

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Year

2010 2011 2012 2013 2014 2015 2016 2017

Labor Productivity Growth Rate 1.9% 0.1% -0.3% 2.5% 2.5% 1.9% 1.7% 2.3%

The average annual growth rate from 2010-2017 is 1.6%, which is just a bit above the average of all the decades from the 1950s to the 2000s.

2. The rise in the unemployment rate was greatest during the 2007–2009 recession compared with earlier recessions. The unemployment rate took longer to decline in the recoveries in the 2000s and 2010s compared with earlier recessions.

3. The inflation rate was highest in the 1970s. The inflation rate was the most stable in the 1990s.

4. Based on the data as of July 2018, Mexico grew the fastest from 2013-2018 and Japan grew the slowest.

Year US Japan Mexico 2013 1.7 2.0 1.4 2014 2.6 0.4 2.8 2015 2.9 1.4 3.3 2016 1.5 1.0 2.9 2017 2.3 1.7 2.0 avg 2.2 1.3 2.5

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5. Here is a plot of the data as of July 2018:

Prolonged declines in the debt/GDP ratio occurred from the mid-1940s to the early 1970s, and in the late 1990s. The ratio rose most rapidly in the early 1940s and in the period during and following the Great Recession from 2008 to 2013. The rise in the 1940s was caused by government military spending to fight World War II. The rise in the Great Recession was caused by a sharp decline in tax revenues as incomes declined, combined with a rise of government expenditures, as the government tried to stimulate the economy.

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Chapter 2 The Measurement and Structure of the National Economy n

Learning Objectives

I.

Section Goals A. Differentiate among the three approaches to national income accounting (Sec. 2.1) B. Explain how GDP is measured (Sec. 2.2) C. Discuss the measurement of aggregate saving and its relation to wealth (Sec. 2.3) D. Explain the calculations of real GDP, price indexes, and inflation (Sec. 2.4) E. Define real and nominal interest rates (Sec. 2.5)

II.

Notes to Ninth Edition Users A. In the In Touch box on the National Income and Product Accounts, we added more description of how often the data are revised.

B. In Section 2.4, we added some details on how GDP growth rates are calculated, in terms of quarterly data at annualized growth rates. We also added a discussion of seasonal adjustment of data. Finally, we added a graph showing the annual quarterly GDP growth rate.

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Teaching Notes

I.

National Income Accounting: The Measurement of Production, Income, and Expenditure (Sec. 2.1) A. National income accounts: an accounting framework used in measuring current economic activity B. Three alternative approaches give the same measurements 1. Product approach: the amount of output produced 2. Income approach: the incomes generated by production 3. Expenditure approach: the amount of spending by purchasers C. Juice business example shows that all three approaches are equal

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1. Important concept in product approach: value added = value of output minus value of inputs purchased from other producers D. Why are the three approaches equivalent?

1. They must be, by definition 2. Any output produced (product approach) is purchased by someone (expenditure approach) and results in income to someone (income approach) 3. The fundamental identity of national income accounting: total production = total income = total expenditure

(2.1)

II. Gross Domestic Product (Sec. 2.2) A. The product approach to measuring GDP 1. GDP (gross domestic product) is the market value of final goods and services newly produced within a nation during a fixed period of time

Data Application The period referred to here is either a quarter or a year. You may want to show students what some of the tables from the National Income and Product Accounts, most easily accessible on the Internet at www.bea.gov.

Students are also interested in seeing what happens in the financial markets and to public opinion on the day a new GDP report comes out.

2. Market value: allows adding together unlike items by valuing them at their market prices a. Problem: misses nonmarket items such as homemaking, the value of environmental quality, and natural resource depletion Analytical Problems 1 and 3 both discuss difficulties in counting nonmarket items for GDP, including the important idea that GDP is not the same as welfare. b. There is some adjustment to reflect the underground economy c. Government services (that aren’t sold in markets) are valued at their cost of production 3. Newly produced: counts only things produced in the given period; excludes things produced earlier 4. Final goods and services

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a. Don’t count intermediate goods and services (those used up in the production of other goods and services in the same period that they themselves were produced) b. Final goods & services are those that are not intermediate c. Capital goods (goods used to produce other goods) are final goods since they aren’t used up in the same period that they are produced d. Inventory investment (the amount that inventories of unsold finished goods, goods in process, and raw materials have changed during the period) is also treated as a final good e. Adding up value added works well, since it automatically excludes intermediate goods 5. GNP vs. GDP a. GNP (gross national product) = output produced by domestically owned factors of production GDP = output produced within a nation b. GDP = GNP - NFP (net factor payments from abroad) (2.2) c. NFP = payments to domestically owned factors located abroad minus payments to foreign factors located domestically

Data Application Prior to December 1991, the United States used GNP as its main measure of production; after that, GDP became the main concept. The main reasons for the switch were that GDP is more relevant to production in an open economy (though GNP is more relevant for income), and GDP is more precise than GNP in the advance estimate, since net factor payments are difficult to measure quickly. See Survey of Current Business, November 1991, for a discussion of the switch. d. Example: Engineering revenues for a road built by a U.S. company in Saudi Arabia is part of U.S. GNP (built by a U.S. factor of production), not U.S. GDP, and is part of Saudi GDP (built in Saudi Arabia), not Saudi GNP e. Difference between GNP and GDP is small for the United States, about 0.2%, but higher for countries that have many citizens working abroad

Data Application The timeline for national income and product account releases is generally: Advance estimate Last week of month following end of quarter Second estimate Last week of second following month Third estimate Last week of third following month Revisions occur every July for the following three years. Each new release contains either additional new data that was not available before, or a change in seasonal factors, or a correction of errors made previously. Periodically, the annual revision in July contains significant changes in the method used to produce the data; these revisions can dramatically change the data going far back in time. [Note: This structure is different now than it was before: Prior to 2009, the first three releases were known as advance, preliminary, and final, and major changes in the methods used to create the data were saved up for a benchmark revision, which took place about every 5 years, instead of being incorporated into the annual release.]

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B. The expenditure approach to measuring GDP 1. Measures total spending on final goods and services produced within a nation during a specified period of time 2. Four main categories of spending: consumption (C), investment (I ), government purchases of goods and services (G), and net exports (NX) 3. Y = C + I + G + NX, the income–expenditure identity (2.3) 4. Consumption: spending by domestic households on final goods and services (including those produced abroad) a. About 2/3 of U.S. GDP b. Three categories (1) Consumer durables (examples: cars, TV sets, furniture, and major appliances) (2) Nondurable goods (examples: food, clothing, fuel) (3) Services (examples: education, health care, financial services, and transportation)

Data Application Note that the consumption category in the national income and product accounts does not correspond to economists’ concept of consumption, because it includes the full value of durable goods. When economists study consumption behavior, they must account for this; one way to do so is to assume that durable goods provide services that are proportional to their existing stock.

Total consumption is this fraction of the stock of consumer durables, plus nondurables and services.

5. Investment: spending for new capital goods (fixed investment) plus inventory investment a. Volatile, with fixed investment about 13% to 20% of U.S. GDP b. Business (or nonresidential) fixed investment: spending by businesses on structures, equipment, and intellectual property products, such as software, research and development, or artistic originals c. Residential fixed investment: spending on the construction of houses and apartment buildings d. Inventory investment: increases in firms’ inventory holdings

Data Application A major change in the National Income and Product Accounts came in July 2013, when the accounts were changed to include intellectual property products, which are treated as capital. Until then, artwork, such as movies, was treated as adding to GDP only in the year it was created. But much artwork continues to have value long after it was created, so it makes sense to treat it as capital. As a result of this change, real GDP and investment were revised up significantly.

6. Government purchases of goods and services: spending by the government on goods or services a. About 1/6 of U.S. GDP b. Most by state and local governments, not federal government c. Not all government expenditures are purchases of goods and services (1) Some are payments that are not made in exchange for current goods and services (2) One type is transfers, including Social Security payments, welfare, and unemployment benefits

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(3) Another type is interest payments on the government debt d. Some government spending is for capital goods that add to the nation’s capital stock, such as highways, airports, bridges, and water and sewer systems

Data Application People often don’t realize how large transfer programs are relative to federal government consumption expenditures. For example, in 2017, transfer payments were $2.7 trillion, while government consumption expenditures were only $1.0 trillion. Gross investment by the federal government ($0.3 trillion) was about the same as depreciation ($0.3 trillion), so net investment was close to zero.

7. Net exports: exports minus imports a. Exports: goods produced in the country that are purchased by foreigners b. Imports: goods produced abroad that are purchased by residents in the country c. Imports are subtracted from GDP, as they represent goods produced abroad, and were included in consumption, investment, and government purchases

Data Application Behind the scenes at the Bureau of Economic Analysis (BEA), a major change took place in the 2000s concerning the national income accounts and the data on GDP. Because the types of goods and services people buy changed so much over time, the BEA decided to modify how it categorizes industries when it collects data on production. The new system was known as NAICS: the North American Industry Classification System; it replaced a system called SIC: Standard Industrial Classification. NAICS differs from SIC in both principle and in practice.

The key principle governing NAICS is that firms that use similar production processes will be classified in the same industry, which was not true under SIC. The result is that the number of firms in different industries changed; for example, the manufacturing industry is different under NAICS than under SIC. One of the main reasons for the switch from SIC to NAICS is the growth of service industries and computer-related industries. In the previous 70 years, manufacturing output had declined from 54% of GDP to 38%, while the output of service industries had increased from 35% of GDP to 54%. The SIC had not been updated to reflect the changes in the economy. NAICS improved the compatibility of U.S. statistics with those in other countries.

The disadvantage of the switch from SIC to NAICS is that data from today based on NAICS is not strictly comparable to data from the past based on SIC. But the BEA believed that the improved quality of the data justified the loss of historical comparability. In addition, NAICS has the advantage of being very adaptable when industries change; for example, its information sector includes such categories as Internet publishing and broadcasting. Adding new categories will not be difficult as technology changes further and new industries evolve.

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C. The income approach to measuring GDP 1. Adds up income generated by production (including profits and taxes paid to the government) a. National income = compensation of employees (including benefits) + proprietors’ income + rental income of persons + corporate profits + net interest + taxes on production and imports + business current transfer payments + current surplus of government enterprises b. National income + statistical discrepancy = net national product c. Net national product + depreciation (the value of capital that wears out in the period) = gross national product (GNP) d. GNP - net factor payments (NFP) = GDP 2. Private sector and government sector income a. Private disposable income = income of the private sector = private sector income earned at home (Y or GDP) and abroad (NFP) + payments from the government sector (transfers, TR, and interest on government debt, INT) - taxes paid to government private disposable income = Y + NFP + TR + INT - T b. Government’s net income = taxes - transfers - interest payments = T - TR - INT c. Private disposable income + government’s net income = GDP + NFP = GNP

(2.4) (2.5)

Numerical Problems 1, 2, 3, 4, and 5 provide practice in working with the national income and product accounts.

III. Saving and Wealth (Sec. 2.3) A. Wealth 1. Household wealth = a household’s assets minus its liabilities 2. National wealth = sum of all households’, firms’, and governments’ wealth within the nation 3. Savings by individuals, businesses, and government determine wealth B. Measures of aggregate saving 1. Saving = current income - current spending 2. Saving rate = saving/current income 3. Private saving = private disposable income - consumption Spvt = (Y + NFP + TR + INT - T) - C

(2.6)

4. Government saving = net government income - government purchases of goods and services Sgovt = (T - TR - INT) - G

(2.7)

a. Government saving = government budget surplus = government receipts - government outlays b. Government receipts = tax revenue (T) c. Government outlays = government purchases of goods and services (G) + transfers (TR) + interest payments on government debt (INT) d. Government budget deficit = -Sgovt e. Despite the BEA’s change in methods that explicitly recognize government investment, the text simplifies matters by counting government investment as government purchases, .

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not investment. This avoids complications when the concepts are introduced and can be modified for further analysis later.

5. National saving a. National saving = private saving + government saving b. S = Spvt + Sgovt = [Y + NFP + TR + INT - C - T] + [T - TR - INT - G] (2.8) = Y + NFP - C - G = GNP - C - G c. Text Fig. 2.1: plots national saving, private saving, and government saving relative to GDP; note trend decline in ratio of national saving to GDP matches trend decline in government saving relative to GDP C. The uses of private saving 1. S = I + (NX + NFP) S = I + CA Derived from S = Y + NFP - C - G and Y = C + I + G + NX CA = NX + NFP = current account balance 2. Spvt = I + (-Sgovt ) + CA {using S = Spvt + Sgovt} The uses-of-saving identity—saving is used in three ways: a. investment (I ) b. government budget deficit (-Sgovt) c. current account balance (CA)

(2.9) (2.10)

(2.11)

3. Text Fig. 2.2: shows uses-of-savings identity a.

Private saving, gross private domestic investment, government budget deficit, and current account balance, each as a percentage of GDP b.

Since early 1990s, current account balance has been negative c.

Foreigners buying U.S. assets d.

In some crisis periods, we observe large increases in the government budget deficit accompanied by sharp declines in gross private domestic investment and increases in private saving e.

In periods of strong growth, we observe a decline in private saving and the government budget deficit, along with a rise in investment Analytical Problem 4 has students examine how the uses-of-savings identity would change if we redefined government saving so that government investment was separate from government consumption expenditures, so that G = GCE + GI and Sgovt = (T - TR - INT ) - GCE. D. Relating saving and wealth 1. Stocks and flows a. Flow variables: measured per unit of time (GDP, income, saving, investment) b. Stock variables: measured at a point in time (quantity of money, value of houses, capital stock) c. Flow variables often equal rates of change of stock variables 2. Wealth and saving as stock and flow (wealth is a stock, saving is a flow)

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3. National wealth: domestic physical assets + net foreign assets a. Country’s domestic physical assets (capital goods and land) b. Country’s net foreign assets = foreign assets (foreign stocks, bonds, and capital goods owned by domestic residents) minus foreign liabilities (domestic stocks, bonds, and capital goods owned by foreigners) c. Wealth matters because the economic well-being of a country depends on it d. Changes in national wealth (1) Change in value of existing assets and liabilities (change in price of financial assets, or depreciation of capital goods) (2) National saving (S = I + CA) raises wealth e. Comparison of U.S. saving and investment with other countries (1) The United States is a low-saving country; Japan is a high-saving country (2) U.S. investment exceeds U.S. saving, so we have a negative current-account balance IV. Real GDP, Price Indexes, and Inflation (Sec. 2.4) A. Real GDP 1. Nominal variables are those in dollar terms 2. Problem: do changes in nominal values reflect changes in prices or quantities?

3. Real variables: adjust for price changes; reflect only quantity changes 4. Example of computers and bicycles 5. Nominal GDP is the dollar value of an economy’s final output measured at current market prices 6. Real GDP is an estimate of the value of an economy’s final output, adjusting for changes in the overall price level 7. Quarterly annualized growth rates of GDP are calculated using the formula (2.12)

8. U.S. data are also generally seasonally adjusted 9. Text Figure 2.3 shows quarterly annualized U.S. GDP growth rates

Data Application The first time that the national income and product accounts reported real GNP was in February 1959; prior to that time, inflation was usually so low that nominal GNP was all that it was thought necessary to examine.

Numerical Problem 5 provides practice in calculating real and nominal GDP and price indexes given several goods with different prices and quantities in two years.

B. Price Indexes 1. A price index measures the average level of prices for some specified set of goods and services, relative to the prices in a specified base year 2. GDP deflator = 100 ´ nominal GDP/real GDP

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Data Application There are two price indexes available for consumption expenditures: the price index for personal consumption expenditures (PCE) and the consumer price index (CPI). The PCE price index provides a better measure of inflation for most purposes, which is why it is the main inflation measure used by the Federal Reserve.

3. Note that base year P = 100 4. Consumer Price Index (CPI) a. Monthly index of consumer prices; index averages 100 in reference base period (1982 to 1984) b. Based on basket of goods in expenditure base period, which is updated periodically 5. In Touch with Data and Research: The computer revolution and chain-weighted GDP a. Choice of expenditure base period matters for GDP when prices and quantities of a good, such as computers, are changing rapidly b. BEA compromised by developing chain-weighted GDP c. Now, however, components of real GDP don’t add up to real GDP, but discrepancy is usually small

Data Application Calculating chain-weighted indexes is not too hard and you can use the computer-bicycle example in Table 2.4 in the textbook to illustrate how to do so. Define the Laspeyres quantity index (using year 1 prices) for year 1 as the value of year 1 output at year 1 prices: L1 = $46,000; the Laspeyres quantity index of year 2 output is L2 = $62,000. Define the Paasche quantity index (using year 2 prices) for year 1 as the value of year 1 output at year 2 prices: P1 = $51,000; the Paasche quantity index of year 2 output is P2 = $66,000. (These amounts are all calculated in Table 2.4, they just are not labeled this way.) The chain-weighted index is just the geometric mean of the Laspeyres and Paasche indexes: C1 = (L1 ´ P1)1/2 = (46,000 ´ 51,000)1/2 = $48,400; C2 = (L2 ´ P2)1/2 = (62,000 ´ 66,000)1/2 = $63,970.

Note that the growth rate of real GDP in this case is ($63,970 - $48,400)/$48,400 = 32.06%, which is close to the average growth rate calculated by the Laspeyres (34.8%) and Paasche (29.4%) indexes, which is 32.095%.

6. Inflation a. Calculate inflation rate: p t+1 = (Pt+1 - Pt)/Pt = DPt+1/Pt b. Text Fig. 2.4 shows the U.S. inflation rate since 1960 for the GDP deflator 7. Does CPI inflation overstate increases in the cost of living? a. The Boskin Commission reported that the CPI was biased upward by as much as one to two percentage points per year b. One problem is that adjusting the price measures for changes in the quality of goods is very difficult c. Another problem is that price indexes with fixed sets of goods don’t reflect the substitution by consumers that goes on when one good becomes relatively cheaper than another; this problem is known as substitution bias

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Data Application A symposium on the CPI appeared in the Journal of Economic Perspectives 12 (Winter 1998).

Many different aspects of measurement problems were explored. Although the BLS claims that quality adjustments are made, William Nordhaus points out that other than in the categories of new cars and trucks and women’s apparel, only 0.1% of all priced commodities were deemed to have quality changes in a recent year. d. If inflation is overstated, then real incomes are higher than we thought and we have overindexed payments like Social Security e. Latest research (July 2006) suggests bias is still 1% per year or higher C. Application: The Fed’s preferred inflation measures 1. The Federal Reserve focuses its attention on the personal consumption expenditures (PCE) price index a. The Fed forecasts both the overall PCE price index and the core PCE price index 2. The PCE price index is superior to the CPI because it avoids substitution bias and is revised when better data are available 3. Differences between the PCE price index and the CPI include formulas used in their calculation, coverage of different items, and weights given to different items 4. The Fed uses the core PCE price index to measure the underlying trend in inflation 5. But the Fed forecasts both the core and overall PCE price index because the Fed needs to keep its eye on both underlying trends but also the actual inflation rate faced by households 6.

The inflation rate in the overall PCE price index tends to revert to the core measure after a period when the two measures deviate (text Fig. 2.5)

Data Application There are many problems with price indexes; they are imperfect measures of price changes.

What do the indexes do when new goods are introduced? What happens as more efficient stores replace stores that had higher intermediate costs? How do we account for the fact that people substitute cheaper goods for higher-priced goods? Inadequate treatment of these questions means the measures of prices give an overestimate of the inflation rate. The BLS has fixed a number of these problems in recent years, but some overestimate remains. In a comprehensive review of these measurement issues, David E. Lebow and Jeremy B. Rudd (“Measurement Error in the Consumer Price Index: Where Do We Stand?” Journal of Economic Literature (March 2003), pp. 159–201) conclude that the overestimate of inflation in the CPI became about 0.9% per year.

Robert Gordon suggests that the overstatement may still exceed 1.0 % per year (“The Boskin Commission Report: A Retrospective One Decade Later,” NBER Working Paper No. 12311, June 2006). More recently, Brent Moulton finds that the bias in CPI in 2018 is about 0.85% as the Bureau of Economic Analysis and Bureau of Labor Statistics have worked to reduce the bias (“The Measurement of Output, Prices, and Productivity: What’s Changed Since the Boskin Commission?” Brookings Institution, July 2018, www.brookings.edu/research/the-measurementof-output-prices-and-productivity).

Numerical Problems 7 and 9 give practice in calculating inflation rates.

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Interest Rates (Sec. 2.5) A. Real vs. nominal interest rates 1. Interest rate: a rate of return promised by a borrower to a lender 2. Real interest rate: rate at which the real value of an asset increases over time 3. Nominal interest rate: rate at which the nominal value of an asset increases over time 4. Real interest rate = i - p Text Fig. 2.6 plots nominal and real interest rates for the United States since 1960

(2.13)

B. The expected real interest rate 1. r = i - p e 2. If p = p e, real interest rate = expected real interest rate Numerical Problem 8 provides practice in calculating real interest rates.

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(2.14)

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Additional Issues for Classroom Discussion

1.

Welfare Does Not Equal GDP

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You can get students involved in a useful discussion of how our national-income accounts fail to measure our well-being. GDP covers only market activity. Ask your students to come up with some nonmarket activities that are valuable to society, but which aren’t covered as part of GDP. Then you might discuss some activities that increase GDP but reduce welfare in some way, such as activities that cause pollution.

The San Francisco think tank called “Redefining Progress” collects data on what it labels “genuine progress” and compares it to GDP. The genuine progress indicator (GPI) has been declining since the mid-1960s, even though real GDP has been rising. Unlike GDP, which measures only market activity, the GPI accounts for resource depletion, income distribution, housework and nonmarket transactions, changes in leisure time, unemployment and underemployment, pollution, long-term environmental damage, the life span of consumer durables and infrastructure, defensive expenditures, and sustainable investments.

2.

More Implications of Price Mismeasurement

Ask your students to explore the ramifications of the bias in the CPI and other price measures. If the CPI has been overstated by one percentage point per year over the past decade, how much lower should Social Security payments be? If you see data that say the real wage has barely grown over the past decade, where real wage growth is measured by taking nominal wage growth and subtracting off the rate of inflation, what does that imply about how fast real wages have truly grown? Some of the same biases to the price index that apply to the CPI also apply to the GDP price index (though not the substitution bias). Using the GDP price index, official government data show that multifactor productivity (a measure of average output that accounts for growth in both capital and labor) has changed little over the past 20 years. But if the price index is biased upward, what does that imply about both real GDP growth over the past 20 years and about multifactor productivity over that time period? What other macroeconomic variables might be affected by price mismeasurement?

3.

Should the CPI Measure Changes in Prices or Changes in the Cost of Living?

The Boskin Commission on the bias in the CPI raised a point that economists have known about for some time. The economic concept that we’d like our price measures to capture is changes in the cost of living, but our price indexes are set up to measure the change in average prices. The difference is subtle, yet important. A great medical breakthrough, like the discovery of the polio vaccine, greatly improves the quality of life, reducing the cost of living. Inventions like the vacuum cleaner or the transistor also changed the things we do in daily life, vastly improving the quality of our lives. More recently, advances in computer technology have changed the way we get information and the way businesses operate. But these great inventions seldom have much of an impact on price indexes like the CPI or output measures like GDP. The quality-of-life improvements engendered by new products are very difficult to measure. So the government record-keepers let the income and price accounts reflect such quality changes in only a limited way. But should they? The Boskin Commission recommended that the government statistical agencies try to measure changes in the quality of life, rather than just measuring the prices of existing goods. Yet there can never be solid knowledge of exactly how much better new inventions make our lives. So should the government agencies simply continue to do what they’ve been doing, and just measure prices? Or should they take their “best guess” as to the improvement in our lives that new inventions and discoveries cause?

Would the fact that such a “guess” influences things like the monthly payments to Social Security recipients affect your decision?

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Answers to Textbook Problems

Review Questions 1. The three approaches to national income accounting are the product approach, the income approach, and the expenditure approach. They all give the same answer because they are designed that way; any entry based on one approach has an entry in the other approaches with the same value. Whenever output is produced and sold, its production is counted in the product approach, its sale is counted in the expenditure approach, and the funds received by the seller are counted in the income approach.

2. Goods are measured at market value in GDP accounting so that different types of goods and services can be added together. Using market prices allows us to count up the total dollar value of all the economy’s output. The problem with this approach is that not all goods and services are sold in markets, so we may not be able to count everything. Important examples are homemaking and environmental quality.

3. Intermediate goods and services are used up in producing other goods in the same period (year) in which they were produced, while final goods and services are those that are purchased by consumers or are capital goods that are used to produce future output. The distinction is important, because we want to count only the value of final goods produced in the economy, not the value of goods produced each step along the way.

4. GNP is the market value of final goods and services newly produced by domestic factors of production during the current period, whereas GDP is production taking place within a country. Thus, GNP differs from GDP when foreign factors are used to produce output in a country, or when domestic factors are used to produce output in another country. GDP = GNP - NFP, where NFP = net factor payments from abroad, which equals income paid to domestic factors of production by the rest of the world minus income paid to foreign factors of production by the domestic economy. A country that employs many foreign workers will likely have negative NFP, so GDP will be higher than GNP. 5.

The four components of spending are consumption, investment, government purchases, and net exports.

Imports must be subtracted, because they are produced abroad and we want GDP to count only those goods and services that are produced within the country. For example, suppose a car built in Japan is imported into the United States. The car counts as consumption spending in U.S. GDP, but is subtracted as an import as well, so on net it does not affect U.S. GDP. However, it is counted in Japan’s GDP as an export.

6. Private saving is private disposable income minus consumption. Private disposable income is total output minus taxes paid plus transfers and interest received from the government. Private saving is used to finance investment spending, the government budget deficit, and the current account.

National saving is private saving plus government saving.

7. National wealth is the total wealth of the residents of a country, and consists of its domestic physical assets and net foreign assets. Wealth is important because the long-run economic well-being of a country depends on it. National wealth is related to national saving because national saving is the flow of additions to the stock of national wealth.

8. Real GDP is the useful concept for figuring out a country’s growth performance. Nominal GDP may rise because of increases in prices rather than growth in real output.

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9. The CPI is a price index that is calculated as the value of a fixed set of consumer goods and services at current prices divided by the value of the fixed set at base-year prices. CPI inflation is the growth rate of the CPI. CPI inflation overstates true inflation because it is hard to measure changes in quality, and because the price index doesn’t account for substitution away from goods that become relatively more expensive toward goods that become relatively cheaper.

10. The nominal interest rate is the rate at which the nominal (or dollar) value of an asset increases over time. The real interest rate is the rate at which the real value or purchasing power of an asset increases over time, and is equal to the nominal interest rate minus the inflation rate. The expected real interest rate is the rate at which the real value of an asset is expected to increase over time. It is equal to the nominal interest rate minus the expected inflation rate. The concept that is most important to borrowers and lenders is the expected real interest rate, because it affects their decisions to borrow or lend.

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Numerical Problems 1.

GDP is the value of all final goods and services produced during the year. The final output of coconuts is 1000, which is worth 500 fish, because two coconuts are worth one fish. The final output of fish is 500 fish. So in terms of fish, GDP consists of 500 fish worth of coconuts plus 500 fish, with a total value of 1000 fish.

To find consumption and investment, we must find out what happens to all the coconuts and fish.

Gilligan consumes all his 200 coconuts (worth 100 fish) and 100 fish, so his consumption is worth 200 fish. The Professor stores 100 coconuts with a value of 50 fish. In an ideal accounting system, these stored coconuts would be treated as investment. However, in the national income accounts, because it is so difficult to tell when durable goods are consumed and when they are saved, they are counted as consumption. So the Professor’s consumption consists of 800 coconuts (value 400 fish) and 400 fish, for a total value of 800 fish. Thus, the economy’s total consumption is valued at 1000 fish and investment is zero.

In terms of income, Gilligan’s income is clearly worth 200 fish (100 fish plus 200 coconuts worth 100 fish). The Professor’s income is 800 coconuts (1000 coconuts minus the 200 coconuts paid to Gilligan) plus 400 fish (500 fish minus 100 fish paid to Gilligan). In terms of fish, the Professor’s income has a value of 800 fish.

This question illustrates some of the nuances of national income accounting. Many difficult choices and measurement issues are involved in constructing the accounts. Here, for example, it is clear that what we call consumption really isn’t just the amount of goods consumers use up during the year, but also includes consumption goods that are purchased but saved for the future. Since there is no way to measure when goods are used after they are purchased, the accounts are unable to distinguish consumption from storage of goods.

2.

(a) Furniture made in North Carolina that is bought by consumers counts as consumption, so consumption increases by $6 billion, investment is unchanged, government purchases are unchanged, net exports are unchanged, and GDP increases by $6 billion. (b) Furniture made in Sweden that is bought by consumers counts as consumption and imports, so consumption increases by $6 billion, investment is unchanged, government purchases are unchanged, net exports fall by $6 billion, and GDP is unchanged. (c) Furniture made in North Carolina that is bought by businesses counts as investment, so consumption is unchanged, investment increases by $6 billion, government purchases are unchanged, net exports are unchanged, and GDP increases by $6 billion. (d) Furniture made in Sweden that is bought by businesses counts as investment and imports, so consumption is unchanged, investment increases by $6 billion, government purchases are unchanged, net exports decline by $6 billion, and GDP is unchanged.

3.

(a) ABC produces output valued at $2 million and has total expenses of $1.3 million ($1 million for labor, $0.1 million interest, $0.2 million taxes). So its profits are $0.7 million. XYZ produces output valued at $3.8 million ($3 million for the three computers that were sold, plus $0.8 million for the unsold computer in inventory) and has expenses of $3.2 million ($2 million for components, $0.8 million for labor, and $0.4 million for taxes). So its profits are $0.6 million.

According to the product approach, the GDP contributions of these companies are $3.8 million, the value of the final product of XYZ. ABC’s production is of an intermediate good, used completely by XYZ, and so is not counted in GDP.

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According to the expenditure approach, the GDP contribution is also $3.8 million, with $3 million (of sold computers) adding to the capital stock (as investment spending), and $0.8 million (the unsold computer) as inventory investment.

The income approach yields the same GDP total contribution. The amounts are: ABC

XYZ

TOTAL

Labor Profit

$1.0 million $0.7 million

$0.8 million $0.6 million

$1.8 million $1.3 million

Taxes

$0.2 million

$0.4 million

$0.6 million

Interest

$0.1 million

$0.0 million

$0.1 million

Total of all incomes = $3.8 million (b) If ABC pays an additional $.5 million for computer chips from abroad, the results change slightly. The correct answer is easiest to see using the expenditure approach. As in part a, there is $3.8 million spent on final goods, but now there are also net exports of -$0.5 million. So the total expenditure on domestically produced goods is only $3.3 million. The product approach gets the same answer because the $0.5 million is a contribution to GDP of the country in which the chips were made, and so must be deducted from the GDP of the United States. The value added in the United States is only $3.3 million. Finally, the income approach gives the same answer as in part a, except that the cost of importing the chips reduces ABC’s profits by $0.5 million, so the sum of the incomes is only $3.3 million.

4.

(a) Product approach: $2 = gas station’s value added = $28 product minus $26 value of product produced in the previous year. Expenditure approach: $2 = $28 consumption spending plus inventory investment of -$26. Income approach: $2 paid to the factors of production at the gas station (wages of employees, interest, taxes, profits). (b) Product approach: $60,000 broker’s fee for providing brokerage services. Expenditure approach: $60,000 counts as residential investment made by the homebuyer. The important point here is that the transfer of an existing good, even at a higher value than that at which it was originally sold, does not add to GDP. Income approach: $60,000 income to the broker for wages, profits, and so on. (c) Product approach: $40,000 salary plus $16,000 childcare equals $56,000. Note that there is a sense in which the childcare is an intermediate service and should not be counted, because without it the homemaker would not be able to work. But in practice there is no way to separate such intermediate services from final services, so they are all added to GDP. Expenditure approach: $56,000 ($16,000 consumption spending on child care services plus $40,000 in categories that depend on what the homemaker spends his or her income). Income approach: $56,000 ($40,000 compensation of homemaker plus $16,000 income to the factors producing the child care: employees’ wages, interest, taxes, profits). (d) Product approach: $100 million of a capital good. Since it is produced with local labor and materials, and assuming no payments go to Japanese factors of production, this is all added to U.S. GDP. Expenditure approach: $100 million net exports, since the plant is owned by the Japanese. (It is not part of gross domestic investment because the plant is not a capital good owned by U.S. residents.) Income approach: $100 million paid to U.S. factors of production. (e) Product approach: $0 because nothing is produced. Expenditure approach: $0 because this is a transfer, not a government purchase of goods or services. Income approach: $0, because this is not a payment to a factor of production, just a transfer.

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(f ) Product approach: $5,000 worth of advertising services. Expenditure approach: $5,000 of government purchases. Income approach: $5,000 compensation of employees. (g) Product approach: $120 million composed of $100 million of new cars produced plus $20 million of sales services provided by the consortium ($60 million sales price minus $40 million cost).

Expenditure approach: $100 million by Hertz as investment plus $60 million by the public for consumption of the used cars minus $40 million of investment goods sold by Hertz, for a total of $120 million. Income approach: $100 million to the factors of production of GM plus $20 million in payments to the factors of production and profits for the consortium.

5.

Given data: I = 40, G = 30, GNP = 200, CA = -20 = NX + NFP, T = 60, TR = 25, INT = 15, NFP = 7 - 9 = -2. Since GDP = GNP - NFP, GDP = 200 - (-2) = 202 = Y. Since NX + NFP = CA, NX = CA - NFP = -20 - (-2) = -18. Since Y = C + I + G + NX, C = Y - (I + G + NX) = 202 - (40 + 30 + (-18)) = 150.

Spvt = (Y + NFP - T + TR + INT) - C = (202 + (-2) - 60 + 25 + 15) -150 = 30. Sgovt = (T - TR - INT) - G = (60 - 25 - 15) - 30 = -10. S = Spvt + Sgovt = 30 + (-10) = 20. (a) Consumption = 150 (b) Net exports = -18 (c) GDP = 202 (d) Net factor payments from abroad = -2 (e) Private saving = 30 (f ) Government saving = -10 (g) National saving = 20

6.

Base-Year Quantities at Current-Year Prices

At Base-Year Prices

Apples

3000 ´ $3 = $ 9,000

3000 ´ $2 = $ 6,000

Bananas

6000 ´ $2 = $12,000

6000 ´ $3 = $18,000

Oranges

8000 ´ $5 = $40,000 $61,000

8000 ´ $4 = $32,000 $56,000

Total

Current-Year Quantities at Current-Year Prices

At Base-Year Prices

Apples

4,000 ´ $3 = $ 12,000

4,000 ´ $2 = $

Bananas

14,000 ´ $2 = $ 28,000

14,000 ´ $3 = $ 42,000

Oranges

32,000 ´ $5 = $160,000

32,000 ´ $4 = $128,000

$200,000

$178,000

Total

8,000

(a) Nominal GDP is just the dollar value of production in a year at prices in that year. Nominal GDP is $56 thousand in the base year and $200 thousand in the current year. Nominal GDP grew 257% between the base year and the current year: [($200,000/$56,000) - 1] ´ 100% = 257%.

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Chapter 2 The Measurement and Structure of the National Economy

33

(b) Real GDP is calculated by finding the value of production in each year at base-year prices.

Thus, from the table above, real GDP is $56,000 in the base year and $178,000 in the current year.

In percentage terms, real GDP increases from the base year to the current year by [($178,000/$56,000) - 1] ´ 100% = 218%. (c) The GDP deflator is the ratio of nominal GDP to real GDP. In the base year, nominal GDP equals real GDP, so the GDP deflator is 1. In the current year, the GDP deflator is $200,000/$178,000 = 1.124. Thus, the GDP deflator changes by [(1.124/1) - 1] ´ 100% = 12.4% from the base year to the current year. (d) Nominal GDP rose 257%, prices rose 12.4%, and real GDP rose 218%, so most of the increase in nominal GDP is because of the increase in real output, not prices. Notice that the quantity of oranges quadrupled and the quantity of bananas more than doubled.

7.

Calculating inflation rates: 1929–30: [(50.0/51.3) - 1] ´ 100% = -2.5% 1930–31: [(45.6/50.0) - 1] ´ 100% = -8.8% 1931–32: [(40.9/45.6) - 1] ´ 100% = -10.3% 1932–33: [(38.8/40.9) - 1] ´ 100% = -5.1% These all show deflation (prices are declining over time), whereas recently we have had nothing but inflation (prices rising over time).

8.

The nominal interest rate is [(545/500) - 1] ´ 100% = 9%. The inflation rate is [(214/200) - 1] ´ 100% = 7%. So the real interest rate is 2% (9% nominal rate - 7% inflation rate). Expected inflation was only [(210/200) - 1] ´ 100% = 5%, so the expected real interest rate was 4% (9% nominal rate 5% expected inflation rate).

9.

(a) The annual rate of inflation from January 1, 2014 to January 1, 2016, is 10%. This can be found by calculating the constant rate of inflation that would raise the deflator from 200 to 242 in two years. This gives the equation (1 + p)(1 + p) = (242/200), which has the solution p = 10%.

An easy way to think about this question is this. A constant inflation rate of p raises the deflator from 200 on January 1, 2014 to 200 ´ (1 + p) on January 1, 2015, and to 200 ´ (1 + p) ´ (1 + p) = 242 on January 1, 2016. So we need to solve the expression (1 + p)2 = 242/200. (b) By similar reasoning, the inflation rate over the three-year period is (1 + p)3 = 266.2/200, or p = 10%. (c) We can derive a general expression in the same way: 1 + p = P1/P0 1 + p = P2/P1 ××× ××× ××× 1 + p = Pn/Pn–1 Multiplying all these lines together, we get: (1 + p)n = (P1/P0) ´ (P2/P1) ´ ××× ´ (Pn/Pn – 1) = Pn/P0

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Analytical Problems 1.

The key to this question is that real GDP is not the same thing as well-being. People may be better off even if real GDP is lower; for example, this may occur because the improvement in the health of workers is more valuable to society than the loss of GDP due to the regulation. Ideally, we would like to be able to compare the costs and benefits of such regulations; they should be put in place if the overall costs (the reduced GDP in this case) are valued less than the overall benefits (the workers’ health).

2.

National saving does not rise because of the switch to CheapCall because although consumption spending declines by $2 million, total expenditures (GDP) decline by the same amount, and expenditures equal income. Because income and spending both decline by the same amount, national saving is unchanged.

3.

(a) The problem in a planned economy is that prices do not measure market value. When the price of an item is too low, then goods are really more expensive than their listed price suggests—we should include in their market value the value of time spent by consumers waiting to make purchases. Because the item’s value exceeds its cost, measured GDP is too low.

When the price of an item is too high, goods stocked on the shelves may be valued too highly.

This results in an overvaluation of firms’ inventories, and as a result the measured GDP is too high.

A possible strategy for dealing with this problem is to have GDP analysts estimate what the market price should be (perhaps by looking at prices of the same goods in market economies) and use this “shadow” price in the GDP calculations. (b) The goods and services that people produce at home are not counted in the GDP figures because they are not sold on the market, making their value difficult to measure. One way to do it might be to look at the standard of living relative to a market economy, and estimate what income it would take in a market economy to support that standard of living.

4.

From Eq. (2.3), and using GPDI for gross private domestic investment, Y = C + GPDI + (GCE + GI) + NX. From Eq. (2.6), Spvt = Y + NFP – T + TR + INT – C. Substituting Eq. (2.3) into (2.6) to eliminate Y, we get Spvt = C + GPDI + (GCE + GI) + NX + NFP – T + TR + INT – C = GPDI + (GCE + GI) + NX + NFP – T + TR + INT. Under the new definition, Sg = T – TR – INT – GCE. Then, because S = Spvt + Sg, S = GPDI + (GCE + GI) + NX + NFP – T + TR + INT + T – TR – INT – GCE = GPDI + GI + NX + NFP. We define I = GPDI + GI, and since CA = NX + NFP, we have S = I + CA. .

Chapter 2 The Measurement and Structure of the National Economy

35

Example from 2015:Q1 (amounts in billions of dollars): Gross saving = 3366.8, gross domestic investment = 3589.2, and current account balance = –475.1. So gross domestic investment + current account balance = 3114.1, which is 252.7 smaller than gross saving. Capital account transactions = 0.4 and the statistical discrepancy is –252.3, so if we add the statistical discrepancy to gross saving, we get 3114.5. If we add capital account transactions to the sum of investment and current account balance, we also get 3114.5.

Working with Macroeconomic Data 1.

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Abel/Bernanke/Croushore • Macroeconomics, Tenth Edition

Consumption generally increased as a percentage of GDP from 1965 to 2018. I/GDP generally increased from 1960 to 2018 but is more volatile than C/GDP. G/GDP generally decreased from 1960 to 2018. X/GDP and M/GDP generally increased from 1960 to 2018.

2.

S/GDP rose sharply in the recession in 2008-2009, peaked at 24% in 2012, and fell a bit after that before rising in 2018. I/GDP fell significantly from 2008 to 2010 and rose steadily from 2010 to 2014. National investment can exceed national saving if we borrow from foreign countries.

3.

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Chapter 2 The Measurement and Structure of the National Economy

37

The CPI measure is based only on consumer prices, while the GDP deflator measures the prices of all goods included in GDP. The inflation measures are roughly similar most of the time.

4.

The nominal interest rate sometimes rises with inflation, but other times it moves in the opposite direction. The real interest rate is not constant; it is sometimes positive and sometimes negative.

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5.

As of July 2018, the average difference in the growth rates of GDP and GDI in the past five years was 0.2%.

6.

The quarterly data using the percent change from the previous quarter is similar but a muted version of the annualized quarterly growth rate, while the percent change from a year ago is much smoother.

Annualized quarterly growth rates are the most volatile, while quarterly data using the percent change from a year ago are the least volatile. .

Chapter 3 Productivity, Output, and Employment n

Learning Objectives

I.

Goals of Part 2: The Macroeconomics of Full Employment A. Analyze factors that affect the longer-term performance of the economy B. Develop a theoretical model of the macroeconomy 1. Three markets a. Labor market (this chapter) b. Goods market (Ch. 4) c. Asset market (Ch. 7)

II. Goals of Chapter 3 A. B. C. D. E. F.

Discuss production function properties and changes (Section 3.1) Discuss factors that affect the demand for labor (Section 3.2) Discuss the factors that affect the supply of labor (Section 3.3) Identify factors that affect labor market equilibrium (Section 3.4) Explain how the unemployment rate is measured and describe changes in employment status (Section 3.5) Explain the significance of Okun’s law (Section 3.6)

III. Notes to Ninth Edition Users A. A new application discusses the gig economy B. A new application covers recent trends in labor supply, including the decline in labor-force participation rates of men and women following the Great Recession C. We add a description of the extensive margin and intensive margin of labor supply

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n

Teaching Notes

I.

How Much Does the Economy Produce? The Production Function (Sec. 3.1) A. Factors of production 1. Capital (K) 2. Labor (N) 3. Others (raw materials, land, energy) 4. Productivity of factors depends on technology and management B. The production function 1. Y = AF(K, N) (3.1) 2. Parameter A is “total factor productivity” (the effectiveness with which capital and labor are used) C. Application: The production function of the U.S. economy and U.S. productivity growth 1. Cobb-Douglas production function works well for U.S. economy: Y = A K 0.3 N 0.7

(3.2)

2. Data for U.S. economy—text Table 3.1 Numerical Problem 1 gives students practice working with a production function.

3. Productivity growth calculated using production function a. Productivity moves sharply from year to year

Data Application An example of the sharp movements in productivity that are possible can be seen by comparing data on productivity for 2003 to data for 2004. Employment grew about the same amount in both years, but in 2003 productivity grew 1.6%, while in 2004 it grew 2.4%. Economists generally believe that it is measurement error, rather than true changes in productivity, that is responsible for these swings during a given phase of the business cycle. As the business cycle changes phases, for example from recession to expansion, there may be large, true swings in productivity.

For example, in 2009, productivity fell 0.2%, and in 2010 it rose 2.8%.

Roy H. Webb addresses the pitfalls in using productivity statistics in his article “National Productivity Statistics,” Federal Reserve Bank of Richmond Economic Quarterly, Winter 1998, pp. 45–64. b. Productivity grew rapidly in the second half of the 1990s, but grew much more slowly in the 2000s

Policy Application Perhaps the greatest source of uncertainty facing policymakers in the 1990s and early 2000s was trying to figure out the underlying trend in productivity. For a discussion of this issue, see the article “How Fast Can the New Economy Grow?” by Glenn Rudebusch, Federal Reserve Bank of San Francisco Economic Letter, February 25, 2000.

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Chapter 3 Productivity, Output, and Employment

D. The shape of the production function 1. Two main properties of production functions a. Slopes upward: more of any input produces more output b. Slope becomes flatter as input rises: diminishing marginal product as input increases 2. Graph production function (Y vs. one input; hold other input and A fixed) a. Marginal product of capital, MPK = DY/DK (Figure 3.1; Key Diagram 1; like text Figure 3.2)

Figure 3.1 (1) Equal to slope of production function graph (Y vs. K) (2) MPK always positive (3) Diminishing marginal productivity of capital—MPK—declines as K rises b. Marginal product of labor, MPN = DY/DN (Figure 3.2; like text Figure 3.3)

Figure 3.2 (1) Equal to slope of production function graph (Y vs. N) (2) MPN always positive (3) Diminishing marginal productivity of labor Numerical Problem 2 gives students practice calculating the MPK and MPN.

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Abel/Bernanke/Croushore • Macroeconomics, Tenth Edition

E. Supply shocks 1. Supply shock = productivity shock = a change in an economy’s production function 2. Supply shocks affect the amount of output that can be produced for a given amount of inputs 3. Shocks may be positive (increasing output) or negative (decreasing output) 4. Examples: weather, inventions and innovations, government regulations, oil prices 5. Supply shocks shift graph of production function (Figure 3.3; like text Figure 3.4)

Figure 3.3 a. Negative (adverse) shock: Usually slope of production function decreases at each level of input (e.g., if shock causes parameter A to decline) b. Positive shock: Usually slope of production function increases at each level of output (e.g., if parameter A increases) Analytical Problem 1 asks students to draw production functions and show how they change when there are supply shocks.

Theoretical Application At this point, the instructor may wish to introduce the idea of real business cycle analysis (discussed in greater detail in Chapter 10). The basic point to get across is that many business cycle fluctuations may be caused by outside events (supply shocks) over which policy has no control.

II. The Demand for Labor (Sec. 3.2) A. How much labor do firms want to use?

1. Assumptions a. Hold capital stock fixed—short-run analysis b. Workers are all alike c. Labor market is competitive d. Firms maximize profits

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Chapter 3 Productivity, Output, and Employment

43

2. Analysis at the margin: costs and benefits of hiring one extra worker (Figure 3.4; like text Figure 3.5)

Figure 3.4 a. If real wage (w) > marginal product of labor (MPN), the firm is paying the marginal worker more than the worker produces, so the firm should reduce the number of workers to increase profits b. If w < MPN, the marginal worker produces more than he or she is being paid, so the firm should increase the number of workers to increase profits c. Firms’ profits are highest when w = MPN B. The marginal product of labor and labor demand: an example 1. Example: The Clip Joint—setting the nominal wage equal to the marginal revenue product of labor MRPN = P ´ MPN

(3.3)

2. W = MRPN is the same condition as w = MPN, since W = P ´ w and MRPN = P ´ MPN 3. A change in the wage a. Begin at equilibrium where W = MRPN b. A rise in the wage rate means W > MRPN, unless N is reduced so the MRPN rises c. A decline in the wage rate means W < MRPN, unless N rises so the MRPN falls Numerical Problem 3 sets up an example in which students calculate MPN and see what happens when the wage rate or price of the product changes.

C. The marginal product of labor and the labor demand curve 1. Labor demand curve shows relationship between the real wage rate and the quantity of labor demanded 2. It is the same as the MPN curve, since w = MPN at equilibrium

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3. So the labor demand curve is downward sloping; the higher the real wage, the less labor firms want to hire D. Factors that shift the labor demand curve 1. Note: A change in the wage causes a movement along the labor demand curve, not a shift of the curve 2. Supply shocks: Beneficial supply shock raises MPN, so shifts labor demand curve to the right; opposite for adverse supply shock 3. Size of capital stock: Higher capital stock raises MPN, so shifts labor demand curve to the right; opposite for lower capital stock E. Aggregate labor demand (Figure 3.5)

Figure 3.5 1. Aggregate labor demand is the sum of all firms’ labor demand 2. Same factors (supply shocks, size of capital stock) that shift firms’ labor demand cause shifts in aggregate labor demand III. The Supply of Labor (Sec. 3.3) A. Supply of labor is determined by individuals 1. Aggregate supply of labor is sum of individuals’ labor supply 2. Labor supply of individuals depends on labor-leisure choice B. The income-leisure trade-off 1. Utility depends on consumption and leisure 2. Need to compare costs and benefits of working another day a. Costs: Loss of leisure time b. Benefits: More consumption, since income is higher 3. If benefits of working another day exceed costs, work another day 4. Keep working additional days until benefits equal costs C. Real wages and labor supply 1. An increase in the real wage has offsetting income and substitution effects

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Chapter 3 Productivity, Output, and Employment

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a. Substitution effect of a higher real wage: Higher real wage encourages work, since the reward for working is higher b. Income effect of a higher real wage: Higher real wage increases income for the same amount of work time, and with higher income, the person can afford more leisure, so will supply less labor 2. A pure substitution effect: a one-day rise in the real wage a. A temporary real wage increase has just a pure substitution effect, since the effect on wealth is negligible 3. A pure income effect: winning the lottery a. Winning the lottery doesn’t have a substitution effect, because it doesn’t affect the reward for working b. But winning the lottery makes a person wealthier, so a person will both consume more goods and take more leisure; this is a pure income effect 4. The substitution effect and the income effect together: a long-term increase in the real wage a. The reward to working is greater: a substitution effect toward more work b. But with a higher wage, a person doesn’t need to work as much: an income effect toward less work c. The longer the high wage is expected to last, the stronger the income effect; thus labor supply will increase by less or decrease by more than for a temporary reduction in the real wage 5. Empirical evidence on real wages and labor supply a. Overall result: Labor supply increases with a temporary rise in the real wage b. Labor supply falls with a permanent increase in the real wage

Theoretical Application The results of changes in labor supply due to changes in the wage rate play a major role in the real business cycle (RBC) model of the economy that we will examine in Chapter 10.

Analytical Problem 7 examines how workers might change their labor supply if there are changes in Social Security taxes.

D. Application: How big is the gig economy?

1. Gig economy: offline service activities, such as child care or house cleaning; offline sales, such as selling items at flea markets or thrift stores; and online services or sales, such as driving using a ride-sharing app or selling items online 2. How many gig workers are there? a. BLS data show fewer independent contractors in 2017 than in 2005 b. But Federal Reserve found 31 percent of all workers did some gig work in 2017, much of it as secondary income or a hobby c. So gig economy appears to be significant and growing E. The labor supply curve (Figure 3.6; like text Figure 3.7) 1. Increase in the current real wage should raise quantity of labor supplied .

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Abel/Bernanke/Croushore • Macroeconomics, Tenth Edition

2.

Labor supply curve relates quantity of labor supplied to real wage

Figure 3.6

Theoretical Application The field of labor economics studies the determinants of labor supply. One of the major issues in the 1970s and early 1980s had to do with the increased participation rates of women in the labor force. Research on both the causes and consequences of this change occupied many economists and yielded many interesting research results, such as explaining why there is a negative relationship between family income and labor force participation across families, but over time there is a positive relationship. Now, in the 2010s, we are working on research to explain the significant decline in labor force participation that has occurred in recent years, especially since the recession of 2007–2009.

3. Labor supply curve slopes upward because higher wage encourages people to work more F.

Factors that shift the labor supply curve 1. Wealth: Higher wealth reduces labor supply (shifts labor supply curve to the left; text Fig. 3.8) 2. Expected future real wage: Higher expected future real wage is like an increase in wealth, so reduces labor supply (shifts labor supply curve to the left) Analytical problem 4 asks students to think about factors that shift an individual’s labor supply curve.

G. Aggregate labor supply 1. Aggregate labor supply rises when current real wage rises a. Some people work more hours b. Other people enter labor force c. Result: Aggregate labor supply curve slopes upward 2. Labor supply can increase in two ways a. Intensive margin refers to changes in hours worked of existing workers

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Chapter 3 Productivity, Output, and Employment

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b. Extensive margin refers to changes in number of workers hired 3. Factors increasing labor supply a. Decrease in wealth b. Decrease in expected future real wage c. Increase in working-age population (higher birth rate, immigration) d. Increase in labor force participation (increased female labor participation, elimination of mandatory retirement)

Data Application A broad characterization of labor force participation rates (LFPR) is that men’s LFPR had declined fairly steadily from the 1960s to the 1980s, while the LFPR of women was rising. But in the 1990s, women’s LFPR growth slowed, probably due to both economic (a discouraged worker effect) and social considerations (an increased fertility rate). These factors continued in the 2000s, and women’s LFPR actually declined from about 60% in 2000 to about 57% in 2015.

IV. Labor Market Equilibrium (Sec. 3.4) A. Equilibrium: Labor supply equals labor demand (Figure 3.7; Key Diagram 2; like text Figure 3.9)

Figure 3.7 1. Classical model of the labor market—real wage adjusts quickly (later, in Chapter 11, look at other models of labor market in which real wage does not adjust quickly) 2. Determines full-employment level of employment N and market-clearing real wage w 3. Factors that shift labor supply or labor demand affect N and w 4. Problem with classical model: can’t study unemployment Numerical Problems 4, 5, and 6 are exercises in which students are given algebraic labor demand and supply curves and are asked to find the equilibrium. Analytical Problems 3 and 5 are comparative static exercises dealing with labor market equilibrium.

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Data Application There are, of course, many different wages in the economy; our model with just one wage is a simplification. When economists look at real data to see how wages are changing over time, they control for the fact that the mix of jobs changes over time. The employment cost index (ECI) provides a measure of the change in the wage rate that controls for changes in the mix of jobs; economists use changes in the ECI to see how wages change relative to inflation.

Data Application Real wage growth changes substantially over time. In the 1960s, real wages grew 26%, but wage growth slowed considerably after that. The slowest wage growth occurred in the 1980s, as this table shows. (Source: Bureau of Labor Statistics, downloaded from FRED database, Federal Reserve Bank of St. Louis, variable COMPRNFB.) Real Wage Growth by Decade (percent per decade) 1960s 26% 1970s 13% 1980s 7% 1990s 13% 2000s 13% B. Full-employment output 1. Full-employment output = potential output = Y = level of output when labor market is in equilibrium 2. Y = AF(K, N )

(3.4)

3. Y affected by changes in N or production function (example: supply shock, text Fig. 3.10) Analytical Problem 2 asks students to show how different shocks to the economy affect fullemployment output.

Data Application What is full-employment output? For many of our theories about macroeconomics, we need a measure of full-employment output, but it is not clear where to get such a measure. In practice, economists make some assumptions about the structure of the economy, including the production function or the relationship between unemployment and output (see Section 3.6 on Okun’s law), apply these assumptions to the data, and thus estimate what they think is the full-employment level of output.

C. Application: output, employment, and the real wage during oil price shocks 1. Sharp oil price increases in 1973–1974, 1979–1980, 2003–2008 (text Fig. 3.11) 2. Adverse supply shock—lowers labor demand, employment, the real wage, and the fullemployment level of output 3. First two cases: U.S. economy entered recessions 4. Research result: 10% increase in price of oil reduces GDP by 0.4 percentage points

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Chapter 3 Productivity, Output, and Employment

V.

49

Unemployment (Sec. 3.5) A. Measuring unemployment 1. Categories: employed, unemployed, not in the labor force 2. Labor Force = Employed + Unemployed 3. Unemployment Rate = Unemployed/Labor Force 4. Table 3.4 shows current data

Data Application The unemployment rate jumped up sharply in January 1994, not because of any true change in the labor market, but merely because the Bureau of Labor Statistics changed the survey with which it calculates the unemployment statistics. The older survey did not properly distinguish between the classifications of unemployed and not in the labor force. In addition, introducing laptop computers on which to perform the survey eliminated a number of errors in the way people answered questions. The result was a small increase in the measured unemployment rate, but no change in the underlying amount of unemployment.

4. Participation Rate = Labor Force/Adult Population 5. Employment Ratio = Employed/Adult Population Analytical Problem 6 tests students’ ability to use these different measures.

B. Changes in employment status 1. Flows between categories (text Fig. 3.12) 2. Discouraged workers: people who have become so discouraged by lack of success at finding a job that they stop searching

Data Application For an in-depth look at job creation and destruction, see the book by Steven J. Davis, John C. Haltiwanger, and Scott Schuh, Job Creation and Destruction, Cambridge, Mass.: MIT Press, 1996.

Numerical Problems 7 and 8 are quantitative exercises using the unemployment and employment concepts.

C. How long are people unemployed?

1. Most unemployment spells are of short duration a. Unemployment spell = period of time an individual is continuously unemployed b. Duration = length of unemployment spell 2. Most unemployed people on a given date are experiencing unemployment spells of long duration 3. Reconciling 1 and 2—numerical example:

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a. Labor force = 100; on the first day of every month, two workers become unemployed for one month each; on the first day of every year, four workers become unemployed for one year each b. Result: 28 spells of unemployment during year; 24 short (one month), four long (one year); so most spells are short c. At any date, unemployment = six; four have long spells (one year), two have short spells (one month); so most unemployed people on a given date have long spells D. Application: Unemployment Duration and the 2007–2009 Recession 1. The mean duration of unemployment always rises in recessions but in the 2007–2009 the rise was larger than ever before (text Fig. 3.13) 2. Four possible explanations for the increase include measurement issues, the extension of unemployment benefits, very large job losses, and a weak economic recovery E. Why there are always unemployed people 1. Frictional unemployment a. Search activity of firms and workers due to heterogeneity b. Matching process takes time

Policy Application Because the matching process in labor markets takes time, government policy often provides income support for people without jobs in the form of unemployment insurance. But this has disincentive effects—people may prefer to prolong their job searches so they may receive unemployment benefits for a longer time, thus getting income without working. Indeed, some economists believe that the high average rates of unemployment in Europe in the 1980s were in part a consequence of generous unemployment insurance.

2. Structural unemployment a. Chronically unemployed: workers who are unemployed a large part of the time b. Structural unemployment: the long-term and chronic unemployment that exists even when the economy is not in a recession c. One cause: Lack of skills prevents some workers from finding long-term employment d. Another cause: Reallocation of workers out of shrinking industries or depressed regions; matching takes a long time 3. The natural rate of unemployment a. u = natural rate of unemployment; when output and employment are at full-employment levels b. u = frictional + structural unemployment

Data Application There is much controversy about how to measure the natural rate of unemployment, as we will discuss in greater detail in Chapter 12. The problem is that the natural rate is simply not observable directly, so we must use the data we have to try to estimate what the natural rate is based on some model of the labor market. Doing so is quite difficult, and there is much debate among empirical macroeconomists as to the size of the natural rate at any date. c. Cyclical unemployment: difference between actual unemployment rate and natural rate of unemployment (u - u ) .

Chapter 3 Productivity, Output, and Employment

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4. In touch with data and research: labor market data a. BLS employment report (1) Household survey: unemployment, employment (2) Establishment survey: jobs 5. In touch with data and research: alternative measures of the unemployment rate a. U-1: unemployed 15 weeks or more b. U-2: counts job losers or persons who completed temporary jobs, so it does not

count people who have quit their jobs c. U-3: the official rate, as defined in textbook d. U-4: like U-3 but adds discouraged workers (those not looking for work because

they do not think they can find a job) e. U-5: like U-4 but adds marginally attached workers (those who say they are not looking for work but indicate that they want and are available for a job and have looked for work sometime in the past 12 months) f. U-6: like U-5 but adds persons who are employed part time for economic reasons (those who want and are available for full-time work but have had to settle for a part-time schedule) g. Graph (text Fig. 3.14) shows that all measures move similarly over time; however, U-6 measure in 2015 is quite elevated relative to its past level, while U-3 has returned to a normal level by 2015

Data Application The household and establishment surveys often give conflicting results. In September 2012, the household survey showed a rise in employment of 873,000 people, while the establishment survey showed an increase of 114,000 jobs. Part of the difference is that the establishment survey does not count the self-employed, and seems to miss much hiring in small firms.

6. Application: Recent trends in labor supply a. Labor force participation rates have declined since 2010 as baby boomers retire in greater numbers b. Participation rates of prime-age workers (25-54) have also been declining (text Fig. 3.15), even for women c. Some of the decline is attributable to discouraged workers in the aftermath of the Great Recession d. Other causes include increased disability and the opioid crisis e. Women’s participation rates have been held back by a lack of family benefits VI. Relating Output and Unemployment: Okun’s Law (Sec. 3.6) A. Relationship between output (relative to full-employment output) and cyclical unemployment

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Data Application What is more closely related to output: Employment growth (from the establishment survey) or the unemployment rate? Business economists usually focus on employment growth (or the average number of hours worked) rather than the unemployment rate, in part because changes in the labor force participation rate lead to fluctuations in the unemployment rate that are not correlated with output.

B. ( Y - Y)/ Y = 2 (u - u )

(3.5)

C. Why is the Okun’s Law coefficient 2, and not 1?

1. Other things happen when cyclical unemployment rises: Labor force falls, hours of work per worker decline, average productivity of labor declines 2. Result is 2% reduction in output associated with 1 percentage point increase in unemployment rate Numerical Problems 9 and 10 are exercises dealing with Okun’s Law. D. Alternative formulation if average growth rate of full-employment output is 3%: 1. DY/Y = 3 - 2 Du 2. Text Fig. 3.16 shows U.S. data

(3.6)

Data Application In 2009, the unemployment rate increased far more than expected (or, output did not decline as much as expected) under Okun’s law. The reason was remarkably strong growth in productivity in the midst of a bad recession. For an analysis, see Mary Daly and Bart Hobijn, “Okun’s Law and the Unemployment Surprise of 2009,” Federal Reserve Bank of San Francisco Economic Letter, 2010-07, March 8, 2010; available at: www.frbsf.org/publications/economics/letter/el2010-07.pdf.

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Additional Issues for Classroom Discussion

1.

Is the Unemployment Rate a Good Measure of Economic Distress?

53

Macroeconomists often treat the unemployment rate as the key indicator of the business cycle. But terms like “discouraged worker” and “underemployed” suggest that the unemployment rate by itself doesn’t reveal the whole picture. A useful topic for classroom discussion is to have students suggest ways in which the unemployment rate does not reveal fully the economic distress of people in the economy.

2.

What Else Is Important for Production?

To ensure that your students have not forgotten what they learned in their principles course, you may want to ask them to discuss some of the factors besides capital and labor that are factors of production.

Typically, they will bring up things like land, entrepreneurial ability, and natural resources. When we write the equation for the production function Y = A F(K, N), all these other things are lumped together in total factor productivity (A).

3.

As Your Wage Rises, Do You Supply More Labor? Or Less?

The textbook discusses the offsetting income and substitution effects on labor supply of an increase in the wage rate in the Appendix to Chapter 4. Since this chapter uses the basic ideas that an increase in wealth reduces labor supply, while an increase in the reward to working increases labor supply, you can combine these effects and enter a discussion of the overall effect. You could start by asking students if they would work more if they received a higher wage. Would someone who is wealthy make the same decision? Then you might point out that some firms offer employees the chance to “purchase” additional vacation time, based on their wage. Some people buy a lot of extra vacation time when their wage is low, but do not buy as much when their wage rises because the value of their time has increased.

4.

Why Do Oil Price Shocks Hurt the Economy So Much?

The textbook points out that many recessions are associated with increases in oil prices. The reasons that increases in oil prices cause such great economic distress are interesting to discuss with your students. See if your students can relate such shocks to their impact on the production function and whether they recognize the very different sectoral implications of the shocks.

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n

Answers to Textbook Problems

Review Questions 1. A production function shows how much output can be produced with a given amount of capital and labor. The production function can shift due to supply shocks, which affect overall productivity.

Examples include changes in energy supplies, technological breakthroughs, and management practices.

Besides knowing the production function, you must also know the quantities of capital and labor the economy has.

2. The upward slope of the production function means that any additional inputs of capital or labor produce more output. The fact that the slope declines as we move from left to right illustrates the idea of diminishing marginal productivity. For a fixed amount of capital, additional workers each add less additional output as the number of workers increases. For a fixed number of workers, additional capital adds less additional output as the amount of capital increases.

3. The marginal product of capital (MPK) is the output produced per unit of additional capital. The MPK can be shown graphically using the production function. For a fixed level of labor, plot the output provided by different levels of capital; this is the production function. The MPK is just the slope of the production function.

4. The marginal revenue product of labor represents the benefit to a firm of hiring an additional worker, while the nominal wage is the cost. Comparing the benefit to the cost, the firm will hire additional workers as long as the marginal revenue product of labor exceeds the nominal wage, since doing so increases profits. Profits will be at their highest when the marginal revenue product of labor just equals the nominal wage.

The same condition can be expressed in real terms by dividing through by the price of the good. The marginal revenue product of labor equals the marginal product of labor times the price of the good.

The nominal wage equals the real wage times the price of the good. Dividing each of these through by the price of the good yields an equivalent profit-maximizing condition: the marginal product of labor equals the real wage.

5. The MPN curve shows the marginal product of labor at each level of employment. It is related to the production function because the marginal product of labor is equal to the slope of the production function (where output is plotted against employment). The MPN curve is related to labor demand, because firms hire workers up to the point at which the real wage equals the marginal product of labor. So the labor demand curve is identical to the MPN curve, except that the vertical axis is the real wage instead of the marginal product of labor.

6. A temporary increase in the real wage increases the amount of labor supplied because the substitution effect is larger than the income effect. The substitution effect arises because a higher real wage raises the benefit of additional work for a worker. The income effect is small because the increase in the real wage is temporary, so it doesn’t change the worker’s income very much, thus the worker won’t reduce time spent working very much.

A permanent increase in the real wage, however, has a much larger income effect, since a worker’s lifetime income is changed significantly. The income effect may be so large that it exceeds the substitution effect, causing the worker to reduce time spent working.

7. The aggregate labor supply curve relates labor supply and the real wage. The principal factors shifting the aggregate labor supply curve are wealth, the expected future real wage, the country’s working-age population, or changes in the social or legal environment that lead to changes in labor force

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participation. Increases in wealth or the expected future real wage shift the aggregate labor supply curve to the left. Increases in the working-age population or in labor-force participation shift the aggregate labor supply curve to the right.

8. Full-employment output is the level of output that firms supply when wages and prices in the economy have fully adjusted; in the classical model of the labor market, this occurs when the labor market is in equilibrium. When labor supply increases, full-employment output increases, as there is now more labor available to produce output. When a beneficial supply shock occurs, then the same quantities of labor and capital produce more output, so full-employment output rises. Furthermore, a beneficial supply shock increases the demand for labor at each real wage and leads to an increase in the equilibrium level of employment, which also increases output.

9. The classical model of the labor market assumes that any worker who wants to work at the equilibrium real wage can find a job, so it is not very useful for studying unemployment.

10. The labor force consists of all employed and unemployed workers. The unemployment rate is the fraction of the labor force that is unemployed. The participation rate is the fraction of the adult population that is in the labor force. The employment ratio is the fraction of the adult population that is employed.

11. An unemployment spell is a period of time that a person is continuously unemployed. Duration is the length of time of an unemployment spell. Two seemingly contradictory facts are that most unemployment spells have a short duration and that most people who are unemployed at a particular time are experiencing spells with long durations. These can be reconciled by realizing that there may be a lot of people with short spells and a few people with long spells. On any given date, a survey finds a fairly long average duration for the unemployed, because of the people with long spells. For example, suppose that each week one person becomes unemployed for one week, so there are fiftytwo such short unemployment spells during the year. And suppose that there are four people who are unemployed all year, so there are four long unemployment spells during the year. In any given week five people are unemployed: one unemployed person has a spell of one week, while four have spells of a year. So most spells have a short duration (fifty-two short spells compared to four long spells), but most people who are unemployed at a given time are experiencing spells with long duration (one short spell compared to four long spells).

12. Frictional unemployment arises as workers and firms search to find matches. A certain amount of frictional unemployment is necessary, because it is not always possible to find the right match right away. For example, an unemployed banker may not want to take a job flipping hamburgers if he or she cannot find another banking job right away, because the match would be very poor. By remaining unemployed and continuing to search for a more suitable job, the banker is likely to make a better match. That will be better both for the banker (since the salary is likely to be higher) and for society as a whole (since the better match means greater productivity in the economy).

13. Structural unemployment occurs when people suffer long spells of unemployment or are chronically unemployed (with many spells of unemployment). Structural unemployment arises when the number of potential workers with low skill levels exceeds the number of jobs requiring low skill levels, or when the economy undergoes structural change, when workers who lose their jobs in shrinking industries may have difficulty finding new jobs.

14. The natural rate of unemployment is the rate of unemployment that prevails when output and employment are at their full-employment levels. The natural rate of unemployment is equal to the amount of frictional unemployment plus structural unemployment. Cyclical unemployment is the

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difference between the actual rate of unemployment and the natural rate of unemployment. When cyclical unemployment is negative, output and employment exceed their full-employment levels.

15. Okun’s Law is a rule of thumb that tells how much output falls when the unemployment rate rises. It is written either in terms of the levels of output and unemployment, as in Eq. (3.5), ( Y - Y)/ Y = 2 (u - u ), or in terms of changes in output and unemployment, as in Eq. (3.6), DY/Y = 3 - 2 Du. Since the Okun’s law coefficient is 2, a 2 percentage point increase in the unemployment rate causes output to decline by 4%.

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Numerical Problems 1. (a) To find the growth of total factor productivity, you must first calculate the value of A in the production function. This is given by A = Y/(K.3N.7). The growth rate of A can then be calculated as [(Ayear 2 - Ayear 1)/Ayear 1] ´ 100%. The result is: A 13.903 16.463 17.136 19.140 22.245 24.503

1960 1970 1980 1990 2000 2010

% Increase in A — 18.4% 4.1% 11.7% 16.2% 10.2%

(b) Calculate the marginal product of labor by seeing what happens to output when you add 1.0 to N; call this Y2, and the original level of output Y1. [A more precise method is to take the derivative of output with respect to N; dY/dN = 0.7A(K/N).3. The result is the same (rounded).]

1960 1970 1980 1990 2000 2007

Y1 Y2 3109 3142 4722 4764 6450 6495 8955 9008 12,560 12,624 14,784 14,858

MPN 33 42 45 53 64 74

2. (a) The MPK is 0.2, because for each additional unit of capital, output increases by 0.2 units. The slope of the production function line is 0.2. There is no diminishing marginal productivity of capital in this case, because the MPK is the same regardless of the level of K. This can be seen in Figure 3.8 because the production function is a straight line.

Figure 3.8 (b) When N is 100, output is Y = 0.2(100 + 100.5) = 22. When N is 110, Y is 22.0976. So the MPN for raising N from 100 to 110 is (22.0976 - 22)/10 = 0.00976. When N is 120, Y is 22.1909. So the MPN for raising N from 110 to 120 is (22.1909 - 22.0976)/10 = 0.00933. This shows diminishing marginal productivity of labor because the MPN is falling as N increases. In Figure 3.9 this is shown as a decline in the slope of the production function as N increases.

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Figure 3.9 3. (a) N 1 2 3 4 5 6

Y 8 15 21 26 30 33

MRPN (P = 5) 40 35 30 25 20 15

MPN 8 7 6 5 4 3

MRPN (P = 10) 80 70 60 50 40 30

(b) P = $5.

(1) W = $38. Hire one worker, since MRPN ($40) is greater than W ($38) at N = 1. Do not hire two workers, since MRPN ($35) is less than W ($38) at N = 2.

(2) W = $27. Hire three workers, since MRPN ($30) is greater than W ($27) at N = 3. Do not hire four workers, since MRPN ($25) is less than W ($27) at N = 4.

(3) W = $22. Hire four workers, since MRPN ($25) is greater than W ($22) at N = 4. Do not hire five workers, since MRPN ($20) is less than W ($22) at N = 5. (c) Figure 3.10 plots the relationship between labor demand and the nominal wage. This graph is different from a labor demand curve because a labor demand curve shows the relationship between labor demand and the real wage. Figure 3.11 shows the labor demand curve.

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Chapter 3 Productivity, Output, and Employment

Figure 3.10

59

Figure 3.11

(d) P = $10. The table in part (a) shows the MRPN for each N. At W = $38, the firm should hire five workers. MRPN ($40) is greater than W ($38) at N = 5. The firm shouldn’t hire six workers, since MRPN ($30) is less than W ($38) at N = 6. With five workers, output is 30 widgets, compared to 8 widgets in part (a) when the firm hired only one worker. So the increase in the price of the product increases the firm’s labor demand and output. (e) If output doubles, MPN doubles, so MRPN doubles. The MRPN is the same as it was in part (d) when the price doubled. So labor demand is the same as it was in part (d). But the output produced by five workers now doubles to 60 widgets. (f) Since MRPN = P ´ MPN, then a doubling of either P or MPN leads to a doubling of MRPN. Since labor demand is chosen by setting MRPN equal to W, the choice is the same, whether P doubles or MPN doubles.

4. MPN = A(100 - N) (a) A = 1. MPN = 100 - N. (1) W = $10. w = W/P = $10/$2 = 5. Setting w = MPN, 5 = 100 - N, so N = 95.

(2) W = $20. w = W/P = $20/$2 = 10. Setting w = MPN, 10 = 100 - N, so N = 90.

These two points are plotted as line NDa in Figure 3.12. If labor supply = 95, then the equilibrium real wage is 5.

Figure 3.12 (b) A = 2. MPN = 2(100 - N).

(1) W = $10. w = W/P = $10/$2 = 5. Setting w = MPN, 5 = 2(100 - N), so 2N = 195, so N = 97.5.

(2) W = $20. w = W/P = $20/$2 = 10. Setting w = MPN, 10 = 2(100 - N), so 2N = 190, so N = 95.

These two points are plotted as line NDb in Figure 3.12. If labor supply = 95, then the equilibrium real wage is 10.

5. (a) If the lump-sum tax is increased, there’s an income effect on labor supply, not a substitution effect (since the real wage isn’t changed). An increase in the lump-sum tax reduces a worker’s wealth, so labor supply increases.

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(b) If T = 35, then NS = 22 + 12w + (2 ´ 35) = 92 + 12 w. Labor demand is given by w = MPN = 309 - 2N, or 2N = 309 - w, so N = 154.5 - w/2. Setting labor supply equal to labor demand gives 154.5 - w/2 = 92 + 12w, so 62.5 = 12.5w, thus w = 62.5/12.5 = 5.

With w = 5, N = 92 + (12 ´ 5) = 152. (c) Since the equilibrium real wage is below the minimum wage, the minimum wage is binding.

With w = 7, N = 154.5 - 7/2 = 151.0. Note that NS = 92 + (12 ´ 7) = 176, so NS > N and there is unemployment.

6. Since w = 4.5 K 0.5 N -0.5, N -0.5 = 4.5 K 0.5/w, so N = 20.25 K/w 2. When K = 25, N = 506.25/w 2. (a) If t = 0.0, then NS = 100w 2. Setting labor demand equal to labor supply gives 506.25/w 2 = 100w 2, so w 4 = 5.0625, or w = 1.5. Then NS = 100 (1.5)2 = 225. [Check: N = 506.25/1.52 = 225.] Y = 45N0.5 = 45(225)0.5 = 675. The total after-tax wage income of workers is (1 - t) w NS = 1.5 ´ 225 = 337.5. (b) If t = 0.6, then NS = 100 [(1 - 0.6) w] 2 = 16w 2. The marginal product of labor is MPN = 22.5/N 0.5, so N = 100 [(1 - 0.6) ´ 22.5/N 0.5] 2, so N 2 = 8100, so N = 90. Then Y = 45N 0.5 = 45(90) 0.5 = 426.91. Then w = 22.5/900.5 = 2.37. The total after-tax wage income of workers is (1 - t) w NS = 0.4 ´ 2.37 ´ 90 = 85.38. Note that there’s a big decline in output and income, although the wage is higher. (c) A minimum wage of 2 is binding if the tax rate is zero. Then N = 506.25/22 = 126.6, NS = 100 ´ 22 = 400. Unemployment is 273.4. Income of workers is wN = 2 ´ 126.6 = 253.2, which is lower than without a minimum wage, because employment has declined so much.

7. (a) At any date, 25 people are unemployed: 5 have lost their jobs at the start of the month and 20 have lost their jobs either on January 1 or July 1. The unemployment rate is 25/500 = 5%. (b) Each month, 5 people have one-month spells. Every six months, 20 people have six-month spells.

The total number of spells during the year is (5 ´ 12) + (20 ´ 2) = 100. Sixty of the spells (60% of all spells) last one month, while 40 of the spells (40% of all spells) last six months. (c) The average duration of a spell is (0.60 ´ 1 month) + (0.40 ´ 6 months) = 3 months. (d) On any given date, there are 25 people unemployed. Twenty of them (80%) have long spells of unemployment, while 5 of them (20%) have short spells.

8. Number who become unemployed: From not in the labor force: 2% of 93.0 million = 1.860 million From employed: 1% of 148.8 million = 1.488 million Total = 3.348 million Number who become employed: From unemployed: 23% of 8.7 million = 2.001 million From not in the labor force: 5% of 93.0 million = 4.650 million Total = 6.651 million Number who become not in the labor force: From employed: 3% of 148.8 million = 4.464 million From unemployed: 23% of 8.7 million = 2.001 million Total = 6.465 million

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9. Since ( Y - Y) /Y = 2(u - u ), this can be rewritten as Y - Y = 2(u - u ) Y or Y = [1 - 2(u - u )] Y , or Y u = Y/[1 - 2(u - )]. (a) Using the formula above, this table shows the value of Y , given values for u and Y. Year

u

Y

1 2 3 4

0.08 0.06 0.07 0.05

950 1030 1033.5 1127.5

Y 989.6 1030.0 1054.6 1105.4

b. The first calculation of D Y/Y comes from calculating the percent change in Y from part a.

The second calculation of Δ Y/Y comes from using Eq. (3.6): DY/Y = D Y/Y - 2 Du, so D Y/Y = DY/Y + 2 Du. D Y/Y Year Y 1 989.6 — 2 1030.0 0.041 3 1054.6 0.024 4 1105.4 0.048

DY/ Y

Du

D Y/Y

— 0.084 0.003 0.091

— -0.02 +0.01 -0.02

— 0.044 0.023 0.051

The two methods give fairly close answers.

10. (a) Total hours worked per week = 1900 workers ´ 40 hours per worker = 76,000 hours per week.

Total output per week = 76,000 total hours per week ´ 10 units of output per hour = 760,000 units of output. The unemployment rate is 100 unemployed/2000 labor supply = 0.05, or 5%. (b) Employment falls 4% from 1900 to: (1 - 0.04) ´ 1900 = 1824. The labor force falls 0.2% from 2000 to: (1 - 0.002) ´ 2000 = 1996. With a labor force of 1996 and employment of 1824, unemployment is 1996 - 1824 = 172. The unemployment rate is 172/1996 = 0.086, or 8.6%.

Hours worked per employed worker falls 2.5% from 40 to: (1 - 0.025) ´ 40 = 39. Total hours per week = 39 hours per worker ´ 1824 workers = 71,136. So total hours per week falls by (76,000 71,136)/76,000 = 0.064 = 6.4%. Total output per week falls 1.4% for every 1% drop in hours, so output falls by 6.4% ´ 1.4 = 8.96%. Since output was 760,000, it now falls to 760,000 ´ (1 0.0896) = 691,904. The Okun’s Law coefficient is the percent change in output divided by the increase in the unemployment rate = 0.0896/(0.086 - 0.05) = 2.49.

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Analytical Problems 1.

(a) See Figures 3.13 and 3.14.

Figure 3.13

Figure 3.14

(b) In the initial situation, capital K1 and labor N1 produce output Y1; when productivity rises they produce output 1.1 Y1. Suppose that a small increase in capital to K2 with labor left at N1 produces output Y2 in the initial situation. Then it produces 1.1 Y2 when productivity rises by 10%. The marginal product of capital (MPK) in the initial situation is (Y2 - Y1)/(K2 - K1); when productivity rises the new MPK is (1.1 Y2 - 1.1 Y1)/(K2 - K1) = 1.1 (Y2 - Y1)/(K2 - K1). So the new MPK is 10% higher than the old MPK. This argument is completely symmetric, so it holds for MPN as well. If you substitute N for K everywhere and follow the same steps, you will show that the new MPN is 10% higher than the old MPN. (c) Yes, it is possible for a beneficial productivity shock to leave the MPK and MPN unchanged.

This could happen only if the shock was additive—that is, if it shifted the whole production function upward, but did not affect its slope at any point. In Figures 3.15 and 3.16 this is shown as a shift up in the production function, leaving the slope unchanged.

Figure 3.15 .

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Figure 3.16 2.

(a) An increase in the number of immigrants increases the labor force, increasing employment and increasing full-employment output. (b) If energy supplies become depleted, this is likely to reduce productivity, because energy is a factor of production. So the reduction in energy supplies reduces full-employment output. (c) Better education raises future productivity and output, but has no effect on current fullemployment output. (d) This reduction in the capital stock reduces full-employment output (although it may very well increase welfare).

3.

(a) As shown in Figure 3.17, when the real wage (w¢) is above its market-clearing level, labor supply (NS¢) exceeds labor demand (ND¢). The difference is the amount of unemployment (U).

Figure 3.17 (b) Output is lower because of the real wage rigidity. With the real wage higher than the wage that clears the market at full employment, labor demand must be lower than it is at full employment, so employment and output are lower as well.

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4.

(a) The increased value of Helena’s home increases her wealth. The rise in wealth leads to an income effect that leads Helena to reduce her labor supply. (b) The permanent rise in Helena’s real wage gives rise to offsetting income and substitution effects.

The income effect of the higher wage reduces Helena’s labor supply, but the substitution effect increases it. So the result is theoretically ambiguous.

Empirically, women tend to increase labor supply in response to a permanent increase in the real wage, and men tend to reduce labor supply in response to a permanent increase in the real wage. (c) The temporary income tax surcharge is equivalent to a temporary reduction in the real wage, which reduces current labor supply, assuming that the income effect is smaller than the substitution effect.

5.

The tax reduces the marginal product of labor by 6%, since that portion of output goes to the government rather than to the firm. Thus labor demand is reduced. With labor supply unchanged, the downward shift in labor demand reduces the real wage and employment, as shown in Figure 3.18.

Figure 3.18 6.

Yes, it is possible for the unemployment rate and the employment ratio to rise during the same month. For example, suppose the population falls, the labor force is constant, the number of unemployed rises, and the number of employed falls (but by less than the decline in population).

Then the unemployment rate rises, since there are more unemployed but the same labor force, but the employment ratio rises, since population declines more than employment does.

Yes, it is possible for the participation rate to fall at the same time that the employment ratio is rising.

For example, suppose that population is constant, the labor force declines, employment rises, and unemployment falls. The participation rate falls, since there are fewer people in the labor force from the same population. The employment ratio is rising, since employment rises while population is constant.

7.

(a) Since Sally earns $150,000 per year, she is above the cap, so the Social Security tax doesn’t affect her after-tax wage (so there’s no substitution effect)—the higher tax only affects her income—and thus has only an income effect. Since both proposals reduce Sally’s income by the same amount, she’ll increase her labor supply by the same amount under both proposals. (b) Under proposal A, Fred’s labor supply doesn’t change because his tax rate stays the same and he remains below the cap. So there’s neither an income effect nor a substitution effect. Under proposal

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B, the Social Security tax rate Fred faces would rise to 15% from 12.4%, so Fred’s after-tax wage rate declines and there’s both an income effect and a substitution effect. The income effect leads Fred to work more, since the higher tax leads to a reduction in Fred’s income. The substitution effect leads Fred to reduce his supply of labor, since the after-tax wage is lower, so there’s less reward to working. Whether Fred will supply more labor or less labor under proposal B thus depends on whether the substitution effect is stronger or weaker than the income effect.

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Working with Macroeconomic Data 1.

Total factor productivity is generally rising over time. The growth rate of total factor productivity is usually positive, but sometimes negative around the times of recessions. TFP growth generally declines during oil-price shocks.

2.

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Both the overall trend in the ratio of employment to the working-age population and the ratio of the labor force to the working-age population generally increased from 1960 to 2000. Both the overall trend in the ratio of employment to the working-age population and the ratio of the labor force to the working-age population generally decreased from 2000 to 2014. The ratio of employment to the working-age population is more volatile than the ratio of the labor force to the working-age population. The labor-force participation rate of men generally decreased and the labor-force participation rate of women generally increased from 1960 to 2000. Participation rates fell sharply in and following the Great Recession.

3.

Real full-employment GDP is smoother because it continues to grow during recessions, whereas real GDP usually declines in recessions. Real GDP was more volatile before 1980 than after 1980.

Real full-employment GDP growth generally trended down from 1950 to 2010.

4.

.

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Over the past 12 months, energy prices increased about 17 percent. Over the past 12 months, the relative price of energy increased about 11 percent. The differences in the two series tell you about the movement of energy prices relative to overall prices. Over the past 12 months (as of August 2018), energy prices had risen more rapidly than other prices by 11 percent.

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Learning Objectives

I.

Goals of Chapter 4 A. Describe the factors that affect consumption and saving decisions (Sec. 4.1) B. Discuss the factors that affect the investment of firms (Sec. 4.2) C. Explain the factors affecting goods market equilibrium (Sec. 4.3)

II. Notes to Ninth Edition Users A. We contrast “saving” with “savings” where saving is the flow of funds that is not consumed out of income and savings is the stock of funds that represents the accumulated amount of net saving over time B. We note that in 2017, the Tax Cut and Jobs Act reduced the statutory corporate tax rate from 35 percent to 21 percent C. We modified the empirical measure of Tobin’s q because of newly available data

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Teaching Notes

I.

Consumption and Saving (Sec. 4.1) A. The importance of consumption and saving 1. Desired consumption: consumption amount desired by households 2. Desired national saving: level of national saving when consumption is at its desired level Sd = Y - Cd - G

(4.1)

3. Note that saving refers to the flow of funds that is not consumed out of income and savings is the stock of funds that represents the accumulated amount of net saving over time

Data Application Recall from Chapter 2 that measured consumption in the national income accounts includes spending on durable consumption goods, like autos and major appliances. But consumption theory requires that consumption be defined to include only the services from durable consumer goods. So empirical researchers must adjust the national income data to arrive at a measure of consumption that matches the theory. For example, they might assume that durable goods provide services proportional to the stock of durables.

B. The consumption and saving decision of an individual 1. A person can consume less than current income (saving is positive) 2. A person can consume more than current income (saving is negative) 3. Trade-off between current consumption and future consumption a. The price of 1 unit of current consumption is 1 + r units of future consumption, where r is the real interest rate b. Consumption-smoothing motive: the desire to have a relatively even pattern of consumption over time C. Effect of changes in current income 1. Increase in current income: both consumption and saving increase (vice versa for decrease in current income) 2. Marginal propensity to consume (MPC) = fraction of additional current income consumed in current period; between 0 and 1 3. Aggregate level: When current income (Y) rises, C d rises, but not by as much as Y, so Sd rises

Theoretical Application The classic discussions of consumption are the permanent-income hypothesis of Milton Friedman (A Theory of the Consumption Function, Princeton: Princeton University Press, 1957) and the life-cycle hypothesis of Franco Modigliani and Richard Brumberg (“Utility Analysis and the Consumption Function: An Interpretation of Cross-Section Data,” in Ken Kurihara, ed., Post-Keynesian Economics, New Brunswick, N.J.: Rutgers University Press, 1954). The permanent income hypothesis focuses on what consumers do with stochastic income receipts; the life-cycle hypothesis is concerned with predictable changes in income over the life cycle.

.

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D. Effect of changes in expected future income 1. Higher expected future income leads to more consumption today, so saving falls 2. Application: consumer sentiment and forecasts of consumer spending a. Do consumer sentiment indexes help economists forecast consumer spending? b. Data do not seem to give much warning before recessions c. Data on consumer spending are correlated with data on consumer confidence d. But formal statistical analysis shows that data on consumer confidence do not improve forecasts of consumer spending based on real-time data E. Effect of changes in wealth 1. Increase in wealth raises current consumption, so lowers current saving F.

Effect of changes in real interest rate 1. Increased real interest rate has two opposing effects a. Substitution effect: Positive effect on saving, since rate of return is higher; greater reward for saving elicits more saving b. Income effect (1) For a saver: Negative effect on saving, since it takes less saving to obtain a given amount in the future (target saving) (2) For a borrower: Positive effect on saving, since the higher real interest rate means a loss of wealth c. Empirical studies have mixed results; probably a slight increase in aggregate saving

Theoretical Application You can use the concept of income and substitution effects to show your class how saving responds to an effective change in the expected real interest rate that occurs because of IRAs (individual retirement accounts). Since IRAs allow people to avoid taxes on a portion of their income, they produce two kinks in the budget constraint. Whether IRAs will boost saving or consumption depends on a person’s preferences, namely how strong the income and substitution effects are. There is a substitution effect because the slope of the budget line gets steeper (the return to saving rises), so people will want more future consumption and less current consumption. There is an income effect because the budget line is shifted out, which increases both future and current consumption. The overall effect on current consumption, and hence saving, is ambiguous, depending on how strong are the income and substitution effects. The exception is that if a person would have saved more than the IRA limit both with and without IRAs, then there is only an income effect and saving will decline. If, in the presence of IRAs, a person would save exactly the amount of the IRA limit, then whether saving rises or falls depends on whether, in the absence of IRAs, they would have saved more or less.

Empirical evidence suggests that every $100 of IRA saving reduces current consumption by $32, so at least for some people, the substitution effect is strong enough to increase saving.

2. Taxes and the real return to saving a. Expected real after-tax interest rate: ra–t = (1 - t)i - p e b. Simple examples: i = 5%, p = 2%; if t = 30%, ra–t = 1.5%; if t = 20%, ra–t = 2% e

.

(4.2)

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Data Application Eytan Sheshinski, in “Treatment of Capital Income in Recent Tax Reforms and the Cost of Capital in Industrialized Countries,” in Larry Summers, ed., Tax Policy and the Economy 4, Cambridge, Mass.: MIT Press, 1990, pp. 25–42, finds that real after-tax interest rates were negative for the United States and many other countries in the 1970s. Even with fairly low inflation, because nominal returns, rather than real returns, are taxed, the real after-tax interest rate (for taxpayers in the top bracket) is fairly low relative to the pretax real interest rate. For example, in the United States in 1985, the real pretax interest rate was 6.3%; the real after-tax interest rate was 0.9% (p = 3.6%, t = 55%). In 1987, the real pretax rate was 4.9%; the real aftertax interest rate was 2.1% (p = 3.7%, t = 33%).

3. In touch with data and research: interest rates a. Discusses different interest rates, default risk, term structure (yield curve), and tax status b. Since interest rates often move together, we frequently refer to “the” interest rate Numerical Problem 1 explores how changes in income, future income, wealth, and interest rates affect consumption.

G. Fiscal policy 1. Affects desired consumption through changes in current and expected future income 2. Directly affects desired national saving, Sd = Y - Cd - G 3. Government purchases (temporary increase) a. Higher G financed by higher current taxes reduces after-tax income, lowering desired consumption b. Even true if financed by higher future taxes, if people realize how future incomes are affected c. Since Cd declines less than G rises, national saving (Sd = Y - Cd - G) declines d. Thus, government purchases reduce both desired consumption and desired national saving

Data Application Empirical analysis confirms this theory. See the paper by Shaghil Ahmed, in “Temporary and Permanent Government Spending in an Open Economy: Some Evidence for the United Kingdom,” Journal of Monetary Economics, March 1986, pp. 197–224. He finds, using a long time series of British data, that temporary government purchases indeed crowd out consumption spending, even though the expenditures are useful in increasing the marginal productivity of private capital and providing a substitute for consumption goods.

4. Taxes a. Lump-sum tax cut today, financed by higher future taxes b. Decline in future income may offset increase in current income; desired consumption could rise or fall c. Ricardian equivalence proposition (1) If future income loss exactly offsets current income gain, no change in consumption (2) Tax change affects only the timing of taxes, not their ultimate amount (present value) (3) In practice, people may not see that future taxes will rise if taxes are cut today; then a .

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tax cut leads to increased desired consumption and reduced desired national saving

Theoretical Application Ricardian equivalence may not hold for a number of reasons. The text notes that if people do not see that future taxes are equal (in present value) to a current tax cut, then Ricardian equivalence may not hold. Appendix 4.A covers an additional reason for the failure of Ricardian equivalence, liquidity constraints. It may also be possible for people to avoid future taxes, even if they foresee them, by moving or dying; however, in the latter case, if those people planned to leave bequests to future generations, they would increase their bequests by the increased tax liability (Robert Barro, “Are Government Bonds Net Wealth?” Journal of Political Economy, Nov./Dec. 1974, pp. 1095–1117). Other reasons for the failure of Ricardian equivalence include: (1) If the current tax cut is given to a different people than those who will have to pay the future taxes, and those people have differing marginal propensities to consume. (2) If taxes are distortionary, rather than lump sum. (3) If future tax rates or future income are not known with certainty. For a useful overview and further details, see Andrew B. Abel, “Ricardian Equivalence Theorem,” in John Eatwell et al., eds., The New Palgrave: A Dictionary of Economics, London: Macmillan Press, 1987. Empirically, the evidence on Ricardian equivalence is mixed; for a review, see B. Douglas Bernheim, “Ricardian Equivalence: An Evaluation of Theory and Evidence,” in Stanley Fischer, ed., NBER Macroeconomics Annual, Cambridge, Mass.: MIT Press, 1987, pp. 263–304.

H. Application: How consumers respond to tax rebates 1. The government provided tax rebates in the recessions of 2001 and 2007–2009, hoping to stimulate the economy 2. Research by Shapiro and Slemrod suggests that consumers did not increase spending much in 2001, when the government provided a similar tax rebate 3. New research by Agarwal, Liu, and Souleles finds that even though consumers originally saved much of the tax rebate, later they increased spending and increased their credit-card debt 4. The new research comes from credit-card payments, purchases, and debt over time 5. People getting the tax rebates initially made additional payments on their credit cards, paying down their balances; but after nine months they had increased their purchases and had more credit-card debt than before the tax rebate 6. Younger people, who were more likely to face binding borrowing constraints, increased their purchases on credit cards the most of any group in response to the tax rebate 7. People with high credit limits also tended to pay off more of their balances and spent less.

They were less likely to face binding borrowing constraints and behaved more in the manner suggested by Ricardian equivalence 8. New evidence on the tax rebates in 2008 and 2009 was provided in a research paper by Parker et al., who found that consumers spent 50%–90% of the tax rebates, which is inconsistent with Ricardian equivalence II. Investment (Sec. 4.2) A. Why is investment important?

1. Investment fluctuates sharply over the business cycle, so we need to understand investment to understand the business cycle 2. Investment plays a crucial role in economic growth B. The desired capital stock 1. Desired capital stock is the amount of capital that allows firms to earn the largest expected profit .

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2. Desired capital stock depends on costs and benefits of additional capital 3. Since investment becomes capital stock with a lag, the benefit of investment is the future marginal product of capital (MPKf ) 4. The user cost of capital a. Example of Kyle’s Bakery: cost of capital, depreciation rate, and expected real interest rate b. User cost of capital = real cost of using a unit of capital for a specified period of time = real interest cost + depreciation c. uc = rpK + dpK = (r + d)pK (4.3) 5. Determining the desired capital stock (Figure 4.1; like text Figure 4.3)

Figure 4.1 a. Desired capital stock is the level of capital stock at which MPKf = uc b. MPK f falls as K rises due to diminishing marginal productivity c. uc doesn’t vary with K, so is a horizontal line d. If MPK f > uc, profits rise as K is added (marginal benefits > marginal costs) e. If MPK f < uc, profits rise as K is reduced (marginal benefits < marginal costs) f. Profits are maximized where MPK f = uc

Theoretical Application The first general use of the user cost of capital concept was by Dale Jorgenson, “Capital Theory and Investment Behavior,” American Economic Review Papers and Proceedings, May 1963, pp. 247–259.

C. Changes in the desired capital stock 1. Factors that shift the MPKf curve or change the user cost of capital cause the desired capital stock to change 2. These factors are changes in the real interest rate, depreciation rate, price of capital, or technological changes that affect the MPKf (text Figure 4.4 shows effect of change in uc) 3. Taxes and the desired capital stock a. With taxes, the return to capital is only (1 - t)MPKf b. A firm chooses its desired capital stock so that the return equals the user cost, so (1 - t)MPKf = uc, which means:

.

Chapter 4 Consumption, Saving, and Investment

MPKf = uc/(1 - t) = (r + d)pK/(1 - t)

75

(4.4)

c. Tax-adjusted user cost of capital is uc/(1 - t) d. An increase in t raises the tax-adjusted user cost and reduces the desired capital stock Numerical Problems 2 and 4 give students practice in working with the marginal product of capital and the user cost of capital. e. In reality, there are complications to the tax-adjusted user cost (1) We assumed that firm revenues were taxed (a) In reality, profits, not revenues, are taxed (b) So depreciation allowances reduce the tax paid by firms, because they reduce profits (2) Investment tax credits reduce taxes when firms make new investments (3) Summary measure: the effective tax rate—the tax rate on firm revenue that would have the same effect on the desired capital stock as do the actual provisions of the tax code (4) Table 4.2 shows effective tax rates for many different countries (5) Note that in 2017, the Tax Cut and Jobs Act reduced the statutory corporate tax rate from 35 percent to 21 percent

Data Application Another simplification that we use in this chapter is the assumption that taxes depend on a firm’s real revenue. In reality, taxes on nominal revenue combine with inflation to create a large distortion to investment. The first broad discussion of this issue is by Martin Feldstein, “Inflation, Tax Rules, and Investment: Some Econometric Evidence,” Econometrica, July 1982, pp. 825–862. f. Application: measuring the effects of taxes on investment (1) Do changes in the tax rate have a significant effect on investment?

(2) A 1994 study by Cummins, Hubbard, and Hassett found that after major tax reforms, investment responded strongly; elasticity about -0.66 (of investment to user cost of capital)

Theoretical Application For further discussions of the effects of tax policy on investment, see Robert E. Hall and Dale W. Jorgenson, “Tax Policy and Investment Behavior,” American Economic Review, June 1967, pp. 391–414.

D. From the desired capital stock to investment 1. The capital stock changes from two opposing channels a. New capital increases the capital stock; this is gross investment b. The capital stock depreciates, which reduces the capital stock c. Net investment = gross investment (I) minus depreciation: Kt+1 - Kt = It - dKt .

(4.5)

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where net investment equals the change in the capital stock d. Text Figure 4.6 shows gross and net investment for the United States 2. Rewriting (4.5) gives It = Kt+1 - Kt + dKt a. If firms can change their capital stocks in one period, then the desired capital stock (K*) = Kt+1 b. So It = K* - Kt + dKt (4.6) c. Thus investment has two parts (1) Desired net increase in the capital stock over the year (K* - Kt) (2) Investment needed to replace depreciated capital (dKt) 3. Lags and investment a. Some capital can be constructed easily, but other capital may take years to put in place

Theoretical Application Acknowledging that it may take time to get capital in place may be crucial to modeling the business cycle. See Finn E. Kydland and Edward C. Prescott, “Time to Build and Aggregate Fluctuations,” Econometrica, November 1982, pp. 1345–1370. b. So investment needed to reach the desired capital stock may be spread out over several years E. In touch with data and research: investment and the stock market 1. Firms change investment in the same direction as the stock market: Tobin’s q theory of investment 2. If market value > replacement cost, then firm should invest more 3. Tobin’s q = capital’s market value divided by its replacement cost a. If q < 1, don’t invest b. If q > 1, invest more 4. Stock price times number of shares equals firm’s market value, which equals value of firm’s capital a. Formula: q = V/(pKK), where V is stock market value of firm, K is firm’s capital, pK is price of new capital b. So pKK is the replacement cost of firm’s capital stock c. Stock market boom raises V, causing q to rise, increasing investment 5. Data show general tendency of investment to rise when stock market rises; but relationship is not strong because many other things change at same time (text Fig. 4.7) 6. This theory is similar to text discussion a. Higher MPKf increases future earnings of firm, so V rises b. A falling real interest rate also raises V as people buy stocks instead of bonds c. A decrease in the cost of capital, pK, raises q F.

Investment in inventories and housing 1. Marginal product of capital and user cost also apply, as with equipment and structures Numerical Problem 3 applies the user-cost concept to the purchase or rental of a home.

III. Goods Market Equilibrium (Sec. 4.3) A. The real interest rate adjusts to bring the goods market into equilibrium .

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1. Y = Cd + Id + G (4.7) goods market equilibrium condition 2. Differs from income-expenditure identity, as goods market equilibrium condition need not hold; undesired goods may be produced, so goods market won’t be in equilibrium 3. Alternative representation: since Sd = Y - Cd - G, Sd = Id

(4.8)

B. The saving-investment diagram 1. Plot Sd vs. Id (Figure 4.2; Key Diagram 3; like text Figure 4.8)

Figure 4.2 2. Equilibrium where Sd = Id 3. How to reach equilibrium? Adjustment of r 4. Shifts of the saving curve a. Saving curve shifts right due to a rise in current output, a fall in expected future output, a fall in wealth, a fall in government purchases, a rise in taxes (unless Ricardian equivalence holds, in which case tax changes have no effect) b. Example: Temporary increase in government purchases shifts S left c. Result of lower savings: higher r, causing crowding out of I Numerical Problem 5 and 6 and Analytical Problem 5 examine what happens when government spending changes.

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Theoretical Application What happens to the economy if government taxes change? Under Ricardian equivalence, a tax cut today that is financed by higher future taxes has no effect on national saving, because private saving rises by the amount of the tax cut, just offsetting the decline in government saving. Since there is no shift in national saving, there’s no change in the equilibrium real interest rate. Suppose, however, that people do not foresee the future tax change, or for some other reason national saving declines. Then the shift to the left of the desired saving curve leads to a new equilibrium at a higher real interest rate and lower level of investment. The true burden of the government debt comes about because the lower investment rate means a lower capital stock, so that the economy is less productive in the future. Thus, future generations bear the burden of today’s government debt.

5. Shifts of the investment curve a. Investment curve shifts right due to a fall in the effective tax rate or a rise in expected future marginal productivity of capital b. Result of increased investment: higher r, higher S and I C. Application: Macroeconomic consequences of the boom and bust in stock prices 1. Sharp changes in stock prices affect consumption spending (a wealth effect) and capital investment (via Tobin’s q), seen in text Figure 4.11 2. Consumption and the 1987 crash a. When the stock market crashed in 1987, wealth declined by about $1 trillion b. Consumption fell somewhat less than might be expected, and it was not enough to cause a recession c. There was a temporary decline in confidence about the future, but it quickly reversed d. The small response may have been because there had been a large run-up in stock prices between December 1986 and August 1987, so the crash mostly erased this run-up 3. Consumption and the rise in stock market wealth in the 1990s a. Stock prices more than tripled in real terms b. But consumption was not strongly affected by the run-up in stock prices 4. Consumption and the decline in stock prices in the early 2000s a. In the early 2000s, wealth in stocks declined by about $5 trillion b. But consumption spending increased as a share of GDP in that period 5. Investment and the declines in the stock market in the 2000s a. Investment and Tobin’s q were correlated in 2000 and 2008, when the stock market fell sharply b. Investment tended to lag the decline in the stock market, reflecting lags in the process of making investment decisions 6. The financial crisis of 2008 a. Stock prices plunged in fall 2008 and early 2009, and home prices fell sharply as well, leading to a large decline in household net wealth b. Despite the decline in wealth, the ratio of consumption to GDP did not decline much 7. The stock market boom since 2009 a. Stock prices rose more than 200% from 2009 to early 2018

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Policy Application Should tax policy be used to promote savings or investment? Many policymakers and economists have argued that obtaining the correct amount of future economic growth requires us to have a higher capital stock, so that we need more investment than we have. They suggest tax policies like IRAs to encourage saving and tax breaks for businesses to encourage investment.

As we have seen in this chapter, such policies could indeed affect people’s decisions to save (by affecting the after-tax real rate of interest) and to invest (by reducing the after-tax cost of capital). What isn’t so clear is whether or not investment really is too low. After all, to save today requires reducing consumption today; people may prefer not to save any more than they are already saving. Also, if the government goes too far in encouraging investment, we may end up with an inefficiently large capital stock; for example, in the late 1980s there was a large overbuilding of commercial real estate (office buildings) in big cities, due partly to tax incentives (and partly due to myopia about the future marginal product of office buildings). In summary, it is not perfectly clear that government policies that encourage saving and investment are appropriate; we first need to show clearly that some externality creates a need for such government intervention.

Analytical Problems 1, 2, 3, and 4 all look at shocks to the economy and changes in variables needed to restore equilibrium.

For a useful summary of research on consumption and investment, see Andrew B. Abel, “Consumption and Investment,” in B. Friedman and F. Hahn, eds., Handbook of Monetary Economics, vol. 2, Netherlands: Elsevier Science Publishers, 1990, pp. 725–778.

IV. Appendix 4.A: A Formal Model of Consumption and Saving A. How much can the consumer afford? The budget constraint 1. Current income y; future income y f; initial wealth a 2. Choice variables: a f = wealth at beginning of future period; c = current consumption; c f = future consumption 3. a f = (y + a - c)(1 + r), so c f = (y + a - c)(1 + r) + y f (4.A.1) the budget constraint B. The budget line 1. Graph budget line in (c, c f ) space (Figure 4.A.1)

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Figure 4.A.1 2. Slope of line = -(1 + r) Analytical Problem 7 looks at what happens to the budget line when the interest rate on borrowing differs from the interest rate on lending.

C. Present values 1. Present value is the value of payments to be made in the future in terms of today’s dollars or goods 2. Example: At an interest rate of 10%, $12,000 today invested for one year is worth $13,200 ($12,000 ´ 1.10); so the present value of $13,200 in one year is $12,000 3. General formula: Present value = future value/(1 + i), where amounts are in dollar terms and i is the nominal interest rate 4. Alternatively, if amounts are in real terms, use the real interest rate r instead of the nominal interest rate i Once you’ve established the intuition about the present value formula for one period, you can extend it to additional periods to show that the present value of an amount X to be received in n years is X/(1 + i)n.

D. Present value and the budget constraint 1. Present value of lifetime resources: PVLR = y + y f/(1 + r) + a

(4.A.2)

2. Present value of lifetime consumption: PVLC = c + c f/(1 + r) 3. The budget constraint means PVLC = PVLR 4. c + c f/(1 + r) = y + y f/(1 + r) + a 5. Horizontal intercept of budget line is c = PVLR, c f = 0 E. What does the consumer want? Consumer preferences

.

(4.A.3)

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1. Utility = a person’s satisfaction or well-being 2. Graph a person’s preference for current versus future consumption using indifference curves 3. An indifference curve shows combinations of c and cf that give the same utility (Figure 4.A.2)

Figure 4.A.2 4. A person is equally happy at any point on an indifference curve 5. Three important properties of indifference curves a. Slope downward from left to right: Less consumption in one period requires more consumption in the other period to keep utility unchanged b. Indifference curves that are farther up and to the right represent higher levels of utility, because more consumption is preferred to less c. Indifference curves are bowed toward the origin, because people have a consumptionsmoothing motive, they prefer consuming equal amounts in each period rather than consuming a lot one period and little the other period If students want more help on indifference curves, you can refer them to a principles of economics or intermediate microeconomics text, such as Michael Parkin, Economics, 5th edition, Reading, Mass.: Addison Wesley Longman, 2000.

F.

The optimal level of consumption 1. Optimal consumption point is where the budget line is tangent to an indifference curve (Figure 4.A.3)

Figure 4.A.3

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2. That’s the highest indifference curve that it’s possible to reach 3. All other points on the budget line are on lower indifference curves G. The Effects of Changes in Income and Wealth on Consumption and Saving 1. The effect on consumption of a change in income (current or future) or wealth depends only on how the change affects the PVLR a. An increase in current income (Figure 4.A.4)

Figure 4.A.4 (1) Increases PVLR, so shifts budget line out parallel to old budget line (2) If there is a consumption-smoothing motive, both current and future consumption will increase (3) Then both consumption and saving rise because of the rise in current income b. An increase in future income (1) Same outward shift in budget line as an increase in current income (2) Again, with consumption smoothing, both current and future consumption increase (3) Now saving declines, since current income is unchanged and current consumption increases c. An increase in wealth (1) Same parallel shift in budget line, so both current and future consumption rise (2) Again, saving declines, since c rises and y is unchanged Numerical Problem 8 deals with the income effect on consumption and saving. d. The permanent income theory (1) Different types of changes in income (a) Temporary increase in income: y rises and y f is unchanged (b) Permanent increase in income: Both y and y f rise (2) Permanent income increase causes bigger increase in PVLR than a temporary income increase (a) So current consumption will rise more with a permanent income increase (b) So saving from a permanent increase in income is less than from a temporary increase in income

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(3) This distinction between permanent and temporary income changes was made by Milton Friedman in the 1950s and is known as the permanent income theory (a) Permanent changes in income lead to much larger changes in consumption (b) Thus permanent income changes are mostly consumed, while temporary income changes are mostly saved H. Consumption and Saving Over Many Periods: The Life-Cycle Model 1. Life-cycle model was developed by Franco Modigliani and associates in the 1950s a. Looks at patterns of income, consumption, and saving over an individual’s lifetime b. Typical consumer’s income and saving pattern shown in Figure 4.A.5

Figure 4.A.5 c. Real income steadily rises over time until near retirement; at retirement, income drops sharply d. Lifetime pattern of consumption is much smoother than the income pattern (1) In reality, consumption varies somewhat by age (2) For example, when raising children, household consumption is higher than average (3) The model can easily be modified to handle this and other variations e. Saving has the following lifetime pattern (1) Saving is low or negative early in working life (2) Maximum saving occurs when income is highest (ages 50 to 60)

.

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(3) Dissaving occurs in retirement 2. Bequests and saving a. What effect does a bequest motive (a desire to leave an inheritance) have on saving? b. Simply consume less and save more than without a bequest motive 3. Ricardian equivalence a. We can use the two-period model to examine Ricardian equivalence b. The two-period model shows that consumption is changed only if the PVLR changes c. Suppose the government reduces taxes by 100 in the current period, the interest rate is 10%, and taxes will be increased by 110 in the future period d. Then the PVLR is unchanged, and thus there is no change in consumption 4. Excess sensitivity and borrowing constraints a. Generally, theories about consumption, including the permanent income theory, have been supported by looking at real-world data b. But some researchers have found that the data show that the impact of an income or wealth change is different than that implied by a change in the PVLR c. There seems to be excess sensitivity of consumption to changes in current income (1) This could be due to shortsighted behavior (2) Or it could be due to borrowing constraints d. Borrowing constraints mean people cannot borrow as much as they want Lenders may worry that a consumer won’t pay back the loan, so they won’t lend e. If a person would not borrow anyway, the borrowing constraint is said to be nonbinding f. But if a person wants to borrow and can’t, the borrowing constraint is binding g. A consumer with a binding borrowing constraint spends all income and wealth on consumption (1) So an increase in income or wealth will be entirely spent on consumption as well (2) This causes consumption to be excessively sensitive to current income changes h. How prevalent are borrowing constraints? Perhaps 20% to 50% of the U.S. population faces binding borrowing constraints Numerical Problem 9 deals with borrowing constraints.

I.

The Real Interest Rate and the Consumption-Saving Decision 1. The real interest rate and the budget line (Figure 4.A.6)

Figure 4.A.6 .

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a. When the real interest rate rises, one point on the old budget line is also on the new budget line: the no-borrowing, no-lending point b. Slope of new budget line is steeper 2. The substitution effect a. A higher real interest rate makes future consumption cheaper relative to current consumption b. Increasing future consumption and reducing current consumption increases saving c. Suppose a person is at the no-borrowing, no-lending point when the real interest rate rises (Figure 4.A.7)

Figure 4.A.7 (1) An increase in the real interest rate unambiguously leads the person to increase future consumption and decrease current consumption (2) The increase in saving, equal to the decrease in current consumption, represents the substitution effect 3. The income effect a. If a person is planning to consume at the no-borrowing, no-lending point, then a rise in the real interest rate leads just to a substitution effect b. But if a person is planning to consume at a different point than the no-borrowing, no-lending point, there is also an income effect c. The intuition of the income effect (1) If the person originally planned to be a lender, the rise in the real interest rate gives the person more income in the future period; the income effect works in the opposite direction of the substitution effect, since more future income increases current consumption (2) If the person originally planned to be a borrower, the rise in the real interest rate gives the person less income in the future period; the income effect works in the same direction as the substitution effect, since less future income reduces current consumption further

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4. The income and substitution effects together a. Split the change in the budget line into two parts (Figure 4.A.8)

Figure 4.A.8 (1) A budget line with the same slope as the new budget line, but going through the original consumption point (BLint) (2) The substitution effect is shown by the change from budget line BL1 to budget line BLint, with the consumption point changing from point D to point P (3) The income effect is shown by the change from budget line BLint to budget line BL2, with consumption point changing from point P to point Q b. The substitution effect decreases current consumption, but the income effect increases current consumption; so saving may increase or decrease c. Both effects increase future consumption d. For a borrower, both effects decrease current consumption, so saving definitely increases but the effect on future consumption is ambiguous Analytical Problem 6 asks the student to show the income and substitution effects for a borrower. e. The effect on aggregate saving of a rise in the real interest rate is ambiguous theoretically (1) Empirical research suggests that saving increases (2) But the effect is small

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Additional Issues for Classroom Discussion

1.

Do You Believe in Ricardian Equivalence?

87

Economists have debated the idea of Ricardian equivalence for some time now (Robert Barro’s classic article, “Are Government Bonds Net Wealth?” appeared in 1974). An interesting debate for students is for them to take sides as to whether or not Ricardian equivalence holds. You can discuss many possible reasons why it might not hold and other reasons why it may be a useful benchmark for comparison to other theories.

2.

The Interaction of Taxation and Inflation

Macroeconomists like to debate whether the central bank should drive inflation down to zero or merely maintain it at a low level. The evidence on the interaction of inflation with the tax system may convince some people that inflation should be zero. As the example in text table 4.1 shows, if you get a nominal interest rate (i) of 5%, expected inflation (p e) is 2%, and you are in the 30% tax (t) bracket, your expected after-tax real interest rate is (1 - t)i - p e = 1.5%. If you invested $10,000, you get a nominal return of $500, of which you get to keep $150 in real terms, inflation eats away $200, and the government gets $150. So the government gets the same amount as you do—so your real tax rate is 50%. In the 1970s and early 1980s when inflation reached double digits, the real tax rate on investment income was well over 100%, so that nearly any investment had a negative return, but the government made a large return.

Present this idea to your students and see how many change their minds about the desirability of reducing inflation to zero (or at least reforming the tax system).

3.

Should the Government Reduce Taxes on Capital?

Our analysis of investment and the desired capital stock shows that taxes are important. A policy issue that has been discussed by economists in recent years is a proposal to eliminate capital taxation. You might ask your students to debate the pros and cons of doing so. What would be the benefits? What would happen to real interest rates and to investment and the capital stock? Are there any costs to such a policy? Who do you think earns most of the capital income in the United States? What would the consequences be for the distribution of income among people of different income groups?

4.

Is Saving Too Low in the United States?

The analytical framework developed in the textbook can be used to analyze the consequences of the fall in the U.S. saving rate. From 1988 to 2008, saving as a proportion of GDP declined substantially. Can your students provide some economic rationale for why this has occurred? One rationale that doesn’t work is the change in demographics, which should have boosted saving in the 1980s as baby boomers reached their prime working years; instead, the saving rate declined. What other reasons can your students come up with that explains the decline?

Next, you may wish to discuss the consequences of the decline. Based on the textbook model, the decline in saving raises the real interest rate and reduces the equilibrium amount of investment. But is this something the government should try to counteract? Does the answer to this question depend on the reasons listed above for the decline in the saving rate?

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5.

Should Social Security Funds Be Invested in the Stock Market?

The Social Security trust fund is projected to decline to zero around the year 2034, thanks to demographic changes, especially the aging of the population and lower birth rates. A number of solutions are possible, including reducing Social Security benefits or increasing taxes. Another possibility is to allow the trust fund to invest in the stock market, so the returns to the fund would be higher than they are now. Currently, the trust fund buys just federal government bonds, which have a significantly lower return over time than do investments in the stock market.

The question to discuss with your class is: Should Social Security funds be invested in the stock market?

Your students will likely point out the key issue, which is risk versus return. There are also important details that affect the decision that are worth thinking about, such as: (1) Should individuals control their own portfolios? (2) What happens if the stock market crashes? (3) What happens in the transition to people who have put money into the current plan (which is pay-as-you-go)? (4) What if people make bad investment decisions, considering that Social Security is supposed to provide a safety net?

6.

How Are You Trading Off the Present for the Future?

The material in the appendix may seem theoretical and abstract, but it is easy to show students that they’re really acting in the way the chapter describes. Ask them what tradeoffs they are making between the present and the future. The most obvious tradeoff is the fact that they are in college, acquiring human capital, rather than working for pay. Even more, many of them have borrowed money to pay for college, so they are accumulating debt today to increase income and consumption in the future. What is the rate at which they trade off the present for the future? It is the interest rate—the additional amount they’ll owe because of their borrowing today.

7.

What Borrowing Constraints Do You Face?

Some of your students may have already faced severe borrowing constraints in their lives. Some may note that they could not obtain credit very easily. Fortunately, many will have been able to borrow enough money to go to college, thanks to government programs that allow equal opportunity in education. In terms of borrowing for consumption spending, your students are likely to have faced dramatically different circumstances.

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Answers to Textbook Problems

Review Questions 1. Saving is current income minus consumption. For given income, any increase in consumption means an equal decrease in saving, so consumption and saving are inversely related. The basic motivation for saving is to provide for future consumption.

2. When a consumer gets an increase in current income, both current consumption and future consumption increase. Since current consumption rises, but by less than the increase in current income, saving increases. When the consumer gets an increase in expected future income, again both current and future consumption increase. Since current income does not increase, but current consumption does, saving decreases. When the consumer gets an increase in wealth, both current and future consumption again rise. Again, there has been no increase in current income, so saving decreases. At the aggregate level, these changes in consumption and saving made by individuals are decisions that change the aggregate level of desired consumption and saving.

3. The effect on desired saving of an increase in the expected real interest rate is potentially ambiguous.

An increase in the real interest rate has two effects on desired saving: (1) the substitution effect increases saving, because the amount of future consumption that can be obtained in exchange for giving up a unit of current consumption rises; and (2) the income effect may increase or reduce saving. The income effect reduces saving for a lender, because a person who saves is better off as a result of having a higher real interest rate, so he or she increases current consumption. However, for a borrower, the income effect increases saving, because the borrower is worse off having to face a higher real interest rate, and so reduces current consumption. So the income effects work in different directions depending on whether a person is a lender or a borrower. For a borrower, then, both the income and substitution effects work in the same direction, and saving definitely increases. For a lender, however, the income and substitution effects work in opposite directions, so the result on desired saving is ambiguous.

4. The expected real after-tax interest rate is the nominal after-tax interest rate, (1 - t)i, minus the expected rate of inflation, p e, and represents the real return earned by a saver when a portion, t, of interest income must be paid as taxes. If the tax rate on interest income declines (that is, t declines), then 1 - t becomes larger, so the expected real after-tax interest rate increases.

5. When government purchases increase temporarily, consumers see that higher taxes will be required in the future to pay off the deficit. They reduce both current consumption and future consumption, but current consumption declines by less than the amount of the government purchases. Since national saving is output minus desired consumption minus government purchases, and government purchases have increased more than current desired consumption has decreased, national saving declines at a given real interest rate.

In the case of a lump-sum tax increase, consumers have higher taxes today, but lower taxes in the future. If consumers take this into account, current desired consumption is unchanged, and since output and government purchases didn’t change, desired national saving is unchanged as well. This is the case of Ricardian equivalence, and is controversial because consumers may not understand that higher taxes today imply lower future taxes. As a result, they may reduce desired consumption today, increasing desired national saving.

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6. The two components of the user cost of capital are the interest cost and the depreciation cost.

The depreciation cost is the value lost as the capital wears out during the period. The interest cost represents the opportunity cost of not using the funds that purchased the capital in some other way; an example would be if the money was invested in bonds rather than buying capital goods.

7. The desired capital stock is the amount of capital that allows the firm to earn the largest possible profit. The higher the expected future marginal product of capital, the higher the desired capital stock, since any given amount of capital will be more productive in the future. The higher the user cost of capital, the lower the desired capital stock, since a higher user cost yields lower profits on each unit of capital. The higher the effective tax rate, the lower the desired capital stock, again because the firm gets lower profits on each unit of capital.

8. Gross investment represents the total purchase or construction of new capital goods that takes place during a period. Net investment is gross investment minus the depreciation on existing capital. Thus net investment is the overall increase in the capital stock. Yes, it is possible for gross investment to be positive when net investment is negative. This occurs whenever gross investment is less than the amount of depreciation (and, in fact, happened in the United States during World War II).

9. Equilibrium in the goods market occurs when the aggregate supply of goods (Y) equals the aggregate demand for goods (Cd + Id + G). Since desired national saving (Sd ) is Y - C d - G, an equivalent condition is Sd = Id. Equilibrium is achieved by the adjustment of the real interest rate to make the desired level of saving equal to the desired level of investment, as shown in text Figure 4.6.

10. The saving curve slopes upward because saving is assumed to increase with an increase in the expected real interest rate. The investment curve slopes downward because investment is lower the higher is the expected real interest rate. The saving curve would be shifted to the right by an increase in current output, a decrease in expected future output, a decrease in wealth, a decrease in government purchases, and possibly by a rise in taxes. The investment curve would shift to the right by a decline in the effective tax rate or a rise in expected future marginal product of capital.

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Numerical Problems 1.

First, a general formulation of the problem is useful. With income of Y1 in the first year and Y2 in the second year, the consumer saves Y1 - C in the first year and Y2 - C in the second year, where C is the consumption amount, which is the same in both years. Saving in the first year earns interest at rate r, where r is the real interest rate. And the consumer needs to accumulate just enough after two years to pay for college tuition, in the amount T. So the key equation is (Y1 - C)(1 + r) + (Y2 - C) = T. (a) Y1 = Y2 = $50,000, r = 10%, T = $16,800. The key equation gives ($50,000 - C)1.1 + ($50,000 - C) = $16,800. This can be simplified to $50,000 - C = $16,800/2.1 = $8000, which can be solved to get C = $42,000. Then S = Y - C = $50,000 - $42,000 = $8000. (b) Y1 = $54,200. The key equation is now ($54,200 - C)1.1 + ($50,000 - C) = $16,800. This can be simplified to ($54,200 ´ 1.1) + $50,000 - $16,800 = 2.1 C, or $92,820 = 2.1 C, so C = $44,200.

Then S = Y1 - C = $54,200 - $44,200 = $10,000. This illustrates that a rise in current income increases saving. (c) Y2 = $54,200. The key equation is now ($50,000 - C)1.1 + ($54,200 - C) = $16,800. This can be simplified to ($50,000 ´ 1.1) + $54,200 - $16,800 = 2.1 C, or $92,400 = 2.1 C, so C = $44,000.

Then S = Y1 - C = $50,000 - $44,000 = $6000. This illustrates that a rise in future income decreases saving. (d) With the increase in wealth of W, the total amount invested for the second period is W + Y1 - C, so the key equation becomes ($1050 + $50,000 - C)1.1 + ($50,000 - C) = $16,800. This can be simplified to ($51,050 ´ 1.1) + $50,000 - $16,800 = 2.1 C, or $89,355 = 2.1 C, so C = $42,550.

Then S = Y1 - C = $50,000 - $42,550 = $7450. This illustrates that a rise in wealth decreases saving. (e) T = $18,900. The key equation is now ($50,000 - C)1.1 + ($50,000 - C) = $18,900. This can be simplified to $50,000 - C = $18,900/2.1 = $9000, which can be solved to get C = $41,000. Then S = Y - C = $50,000 - $41,000 = $9000. The rise in targeted wealth needed in the future raises current saving. (f ) r = 0.24. The key equation is now ($50,000 - C)1.24 + ($50,000 - C) = $16,800. This can be simplified to $50,000 - C = $16,800/2.24 = $7500, which can be solved to get C = $42,500. Then S = Y - C = $50,000 - $42,500 = $7500. The rise in the real interest rate, with a given wealth target, reduces current saving.

2.

(a) This chart shows the MPKf as the increase in output from adding another fabricator: # Fabricators 0 1 2 3 4 5 6

MPKf — 100 50 30 15 10 5

Output 0 100 150 180 195 205 210

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(b) uc = (r + d)pK = (0.12 + 0.20)$100 = $32. HHHHC should buy two fabricators, since at two fabricators, MPK f = 50 > 32 = uc. But at three fabricators, MPK f = 30 < 32 = uc. You want to add fabricators only if the future marginal product of capital exceeds the user cost of capital. The MPK f of the third fabricator is less than its user cost, so it should not be added. (c) When r = 0.08, uc = (0.08 + 0.20)$100 = $28. Now they should buy three fabricators, since MPK f = 30 > 28 = uc for the third fabricator and MPK f = 15 < 28 = uc for the fourth fabricator. (d) With taxes, they should add additional fabricators as long as (1 - t)MPK f > uc. Since t = 0.4, 1 - t = 0.6. They should buy just one fabricator, since (1 - t)MPK f = 0.6 ´ 100 = 60 > 32 = uc.

They shouldn’t buy two, since then (1 - τ)MPK f = 0.6 ´ 50 = 30 < 32 = uc. (e) When output doubles, the MPKf doubles as well. At r = 0.12, they should buy three fabricators, since then MPK f = 60 > 32 = uc; they shouldn’t buy four, since then MPK f = 30 < 32 = uc.

At r = 0.08, they should buy four fabricators, since then MPK f = 30 > 28 = uc; they shouldn’t buy five, since then MPK f = 20 < 28 = uc.

3.

(a) The expected real after-tax interest rate is r = i(1 - t) - pe = 0.10 (1 - 0.30) - 0.05 = 0.07 - 0.05 = 0.02. (b) The cost of maintaining the house is depreciation. So the annual user cost of capital is uc = (r + d)pK = (0.02 + 0.06)$300,000 = $24,000. (c) You should be indifferent between buying and renting if the rent is $24,000 per year.

4.

Since the price of capital declines from 60 to 51, the depreciation rate is 9/60 = .15. (a) uc = (r + d)pK = (.10 + .15)60 = 15 units of output per year. (b) The desired capital stock is such that MPK f = uc, so 165 - 2K = 15, or 2K = 150, so K = 75. (c) The tax-adjusted user cost of capital is uc/(1 - t), so with t = .4, the condition for the desired capital stock is 165 - 2K = 15/0.6, or 2K = 140; the solution is K = 70. Thus taxation decreases the firm’s desired capital stock. (d) The investment tax credit lowers the price of capital from 60 to (1 - 0.2)60 = 48. So the taxadjusted user cost of capital is only (.25 ´ 48)/0.6 = 20. Then the equation for setting the desired capital stock is 165 - 2K = 20, or 2K = 145; the solution is K = 72.5. Thus, the investment tax credit increases the firm’s desired capital stock.

5.

(a) Desired consumption declines as the real interest rate rises because the higher return to saving encourages higher saving; desired investment declines as the real interest rate rises because the user cost of capital is higher, reducing the desired capital stock, and thus investment. (b) Use the following table, where Sd = Y - Cd - G = 9000 - Cd - 2000 = 7000 - Cd. r 2 3 4 5 6

Cd 6100 6000 5900 5800 5700

Id 1500 1400 1300 1200 1100

Sd 900 1000 1100 1200 1300

C d + Id + G 9600 9400 9200 9000 8800

(c) Equation (4.7) says that Y = Cd + Id + G at equilibrium. Looking at the last column of the table,

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with Y = 9000, this is true only at r = 5%. At this point, Sd = Id = 1200. Equation (4.8) says that Sd = Id at equilibrium. From the table, this occurs at r = 5%. (d) When government purchases fall by 400 to 1600, each Sd entry in the table is higher by 400, and each Cd + Id + G entry is lower by 400. Then Y = Cd + Id + G occurs at r = 3%, as does Sd = Id = 1400.

6.

r

Cd

Id

Sd

C d + Id + G

2 3 4 5 6

6100 6000 5900 5800 5700

1500 1400 1300 1200 1100

1300 1400 1500 1600 1700

9200 9000 8800 8600 8400

(a) Sd = Y - Cd - G = Y - (3600 - 2000r + 0.1Y) - 1200 = -4800 + 2000r + 0.9Y (b) (1) Using Eq. (4.7): Y = Cd + Id + G Y = (3600 - 2000r + 0.1Y) + (1200 - 4000r) + 1200 = 6000 - 6000r + 0.1Y So 0.9Y = 6000 - 6000r At full employment, Y = 6000. Solving 0.9 ´ 6000 = 6000 - 6000r, we get r = 0.10.

(2) Using Eq. (4.8): Sd = Id -4800 + 2000r + 0.9Y = 1200 - 4000r 0.9Y = 6000 - 6000r When Y = 6000, r = 0.10.

So we can use either Eq. (4.7) or (4.8) to get to the same result. (c) When G = 1440, desired saving becomes Sd = Y - Cd - G = Y - (3600 - 2000r + 0.1Y) - 1440 = -5040 + 2000r + 0.9Y. Sd is now 240 less for any given r and Y; this shows up as a shift in the Sd line from S1 to S2 in Figure 4.3.

Figure 4.3

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Setting Sd = Id, we get: -5040 + 2000r + 0.9Y = 1200 - 4000r 6000r + 0.9Y = 6240 At Y = 6000, this is 6000r = 6240 - (0.9 ´ 6000) = 840, so r = 0.14. The market-clearing real interest rate increases from 10% to 14%.

7.

(a) r = 0.10 uc/(1 - τ) = (r + d)pK/(1 - t) = [(.1 + 0.2) ´ 1]/(1 - 0.15) = 0.35.

MPK f = uc/(1 - t), so 20 - 0.02K = 0.35; solving this gives K = 982.5.

Since K - K-1 = I - dK, I = K - K-1 + dK = 982.5 - 900 + (.2 ´ 900) = 262.5. (b) i. Solving for this in general: uc/(1 - t) = (r + d)pK/(1 - τ) = [(r + .2) ´ 1]/(1 - 0.15) = .235 + 1.176r.

MPKf = uc/(1 - t), so 20 - 0.02K = 0.235 + 1.176r; solving this gives K = 988.25 - 58.8r.

I = K - K-1 + dK = 988.25 - 58.8r - 900 + (0.2 ´ 900) = 268.25 - 58.8r. ii. Y = C + I + G 1000 = [100 + (.5 ´ 1000) - 200r] + (268.25 - 58.8r) + 200 1000 = 1068.25 - 258.8r, so 258.8r = 68.25 r = 0.264 C = 100 + (0.5 ´ 1000) - (200 × 0.264) = 547.2 I = 268.25 - (58.8 × 0.264) = 252.7 = S uc/(1 - t) = 0.235 + (1.176 ´ 0.264) = 0.545 K = 988.25 - (58.8 × 0.264) = 972.7

8.

(a) PVLR = y + [y f/(1 + r)] + a = 90 + (110/1.10) + 20 = 210. f (b) c + [c / (1 + r)] = PVLR. c + (c f / 1.10) = 210.

When c = 0, c f = 231; this is the vertical intercept of the budget line, shown in Figure 4.4.

When c f = 0, c = 210; this is the horizontal intercept of the budget line.

Figure 4.4 .

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(c) c = c f: c + (c/1.10) = 210.

1.10c + c = 210 ´ 1.10.

2.1c = 231. c = 110. s=y-c = 90 - 110 = -20. (d) y increases by 11, so new PVLR = 221.

2.1c = 221 ´ 1.1 = 243.1. c = 115.76. s = y - c = 101 - 115.76 = - 14.76.

So part of the temporary increase in income is consumed and part is saved. (e) y f increases by 11, so PVLR rises by 11/1.10 = 10. New PVLR = 220.

2.1c = 220 ´ 1.1 = 242. c = 115.24. s = y - c = 90 - 115.24 = -25.24.

So a rise in future income leads to an increase in current consumption but a decrease in saving. (f) A rise in initial wealth has the same effect on the PVLR and thus on consumption as an increase in current income of the same amount, so c = 115.76 as in part (d). s = y - c = 90 - 115.76 = -25.76.

So an increase in wealth increases current consumption and decreases saving.

9.

(a) PVLR = a + yl + yw + yr = 1500.

(1) No borrowing constraint: cl + cw + cr = 1500. cl = cw = cr = c = 1500/3 = 500. sl = 200 - 500 = -300; sw = 800 - 500 = 300; sr = 200 - 500 = -300.

(2) A borrowing constraint is nonbinding, since a + y l = 500 = cl, and cw = 500 < 800 = yw.

So consumption and saving are the same in each period as in part (1) above. (b) PVLR = 1200.

(1) No borrowing constraint: c = 1200/3 = 400. sl = 200 - 400 = -200; sw = 800 - 400 = 400; sr = 200 - 400 = -200.

(2) The borrowing constraint is now binding, since cl = 400 > a + yl = 200. So cl is constrained to be 200. That leaves PVLR of 1000 for cw + cr, so they both equal 500. cw = 500 < 800 = yw, so the borrowing constraint is not binding in working age. sl = 200 - 200 = 0; sw = 800 - 500 = 300; sr = 200 - 500 = -300.

Consumption can’t be lower in all periods due to a binding borrowing constraint, because the present value of lifetime consumption must be the same with and without borrowing constraints.

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Analytical Problems 1.

(a) As Figure 4.5 shows, the shift to the right in the saving curve from S1 to S2 causes saving and investment to increase and the real interest rate to decrease.

Figure 4.5 (b) This is really just a transfer from the general population to veterans. The effect on saving depends on whether the marginal propensity to consume (MPC) of veterans differs from that of the general population. If there is no difference in MPCs, there will be no shift of the saving curve; neither investment nor the real interest rate is affected. If the MPC of veterans is higher than the MPC of the general population, then desired national saving declines and the saving curve shifts to the left; the real interest rate rises and investment declines. If the MPC of veterans is lower than that of the general population, the saving curve shifts to the right; the real interest rate declines and investment rises. (c) The investment tax credit encourages investment, shifting the investment curve from I1 to I2 in Figure 4.6. Saving and investment increase, as does the real interest rate.

Figure 4.6

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(d) The increase in expected future income decreases current desired saving, as people increase desired consumption immediately. The rise of the future marginal productivity of capital shifts the investment curve to the right. The result, as shown in Figure 4.7, is that the real interest rate rises, with ambiguous effects on saving and investment.

Figure 4.7 2.

(a) With a lower capital stock, the marginal product of labor is reduced, so the labor demand curve shifts to the left from ND1 to ND2 in Figure 4.8. Then the new equilibrium point is one with lower employment and a lower real wage. With lower employment and a lower capital stock, fullemployment output will be lower.

Figure 4.8 (b) Because the capital stock is lower, the marginal product of capital will be higher, so desired investment will increase. (c) The increase in desired investment shows up as a shift to the right in the Id curve, from I1 to I2 in Figure 4.9. Then the new equilibrium (assuming no change in desired saving) is at a higher level of investment and a higher real interest rate.

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Figure 4.9 3.

(a) The temporary increase in the price of oil reduces the marginal product of labor, causing the labor demand curve to shift to the left from ND1 to ND2 in Figure 4.10. At equilibrium, there is a reduced real wage and lower employment.

Figure 4.10 The productivity shock results in a reduction of output. Because the shock is temporary, the only effect on desired saving or investment is due to the reduction in current output, causing desired national saving to fall. This shifts the saving curve to the left, raising the real interest rate and reducing the level of desired investment, as well as desired national saving, as shown in Figure 4.11.

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Figure 4.11 (b) The permanent increase in the price of oil reduces the marginal product of labor, causing the labor demand curve to shift to the left, again as in Figure 4.10. (Also, the decline in future income means the labor-supply curve will shift to the right; but we’ll assume that this shift is less than the shift to the left of the labor-demand curve.) At equilibrium, there is a reduced real wage and lower employment.

The productivity shock results in a reduction of current output. Because the shock is permanent, it reduces future output as well, and reduces the future marginal product of capital. The desired investment curve shifts to the left, from I1 to I2 in Figure 4.12, because the future marginal product of capital is lower. The effect on desired saving is ambiguous—the reduction in current income reduces desired saving, but the reduction in expected future income increases desired saving. Let’s assume that the former effect outweighs the latter, so that the desired saving curve shifts to the left from S1 to S2. Then national saving and investment both decline. Again, the effect on the real interest rate is ambiguous. (Alternatively, if the effects on desired saving of the reductions in current income and future income offset each other exactly, the desired saving curve does not shift. In this case, the leftward shift of the investment curve along an unchanged saving curve reduces the real interest rate, saving, and investment.)

Figure 4.12 4.

A temporary increase in government spending reduces national saving. Whether the spending is financed by current taxes or by borrowing (and raising future taxes), consumption falls, but not by the full amount of the spending. Since S = Y - Cd - G, national saving declines. This is shown in Figure 4.13 as a shift to the left in the saving curve. The real interest rate must increase to get S = I, so I declines as well. It makes no difference whether the temporary increase in spending is funded by .

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taxes or by borrowing.

Figure 4.13 In the case of infrastructure spending, MPK f rises, so investment increases. Saving shifts from S1 to S2 and investment shifts from I1 to I2 in Figure 4.14. With upward shifts in both saving and investment, the new equilibrium is one with a higher real interest rate. However, saving and investment at the new equilibrium may be higher or lower. The effect on consumption is unclear as well. The higher real interest rate reduces consumption, but future income is higher, which increases consumption. If investment actually rises, then the increase in government spending causes private investment to be “crowded in” rather than “crowded out.” In this case consumption is crowded out.

Figure 4.14 5.

When there is a temporary increase in government spending, consumers foresee future taxes. As a result, consumption declines, both currently and in the future. Thus current consumption does not fall by as much as the increase in G, so national saving (Sd = Y - Cd - G) declines at the initial real interest rate, and the saving curve shifts to the left from S1 to S2, as shown in Figure 4.15. Thus the real interest rate increases and consumption and investment both fall.

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Figure 4.15 When there is a permanent increase in government spending, consumers foresee future taxes as well, with both current and future consumption declining. But if there is an equal increase in current and future government spending, and consumers try to smooth consumption, they will reduce their current and future consumption by about the same amount, and that amount will be about the same amount as the increase in government spending. So the saving curve in the saving-investment diagram does not shift, and there is no change in the real interest rate.

Since the saving curve shifts upward more in the case of a temporary increase in government spending, the real interest rate is higher, so investment declines by more. However, consumption falls by more in the case of a permanent increase in government spending.

6.

See Figure 4.16. The consumer is originally on budget line BL1, with consumption at point D. An increase in the real interest rate shifts the budget line to BL2, with consumption at point Q. The change can be broken down into two steps. First, the substitution effect shifts the budget line from BL1 to BLint, and the consumption point changes from point D to point P. The substitution effect results in higher future consumption and lower current consumption. The income effect shifts the budget line from BLint to BL2, with the consumption point changing from point P to point Q. The income effect results in lower current and future consumption. Thus, the income and substitution effects work in the same direction, reducing current consumption and increasing saving.

Figure 4.16

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7.

The difference in interest rates between borrowing and lending means there is a kink in the budget constraint at the no-lending, no-borrowing point, as shown in Figure 4.17. Borrowing is zero when c = y + a. If current consumption is less than y + a, the person is a saver (lender), and the budget line has slope - (1 + rl). If current consumption is greater than y + a, the person is a borrower, and faces a steeper budget constraint with slope - (1 + rb), because the interest rate is higher.

Figure 4.17 An increase in either interest rate would steepen only the portion of the budget constraint for which that interest rate is relevant. An increase in the real interest rate on lending is shown as a shift in the budget line segment from BL1 to BL2 in Figure 4.18. An increase in the real interest rate on borrowing is shown as a shift in the budget line segment from BL3 to BL4. If the indifference curve hits the budget line at the no-borrowing, no-lending point, as shown, then there will be no change in current or future consumption due to a change in either interest rate.

Figure 4.18

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An increase in the consumer’s initial wealth would lead to a parallel rightward shift of both segments of the budget line, as shown in Figure 4.19.

Figure 4.19

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Working with Macroeconomic Data Questions 1.

Generally, higher values of consumer sentiment are associated with higher growth rates of consumer spending, but the relationship is not very tight.

Generally, higher values of consumer sentiment are associated with higher growth rates of consumer spending on durable goods, but the relationship is not very tight.

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2.

Real stock prices generally declined in the 1970s, but increased in other decades, especially in the 1990s. As a result, the household saving rate should have been higher in the 1970s than it was in periods with increases in real stock prices.

With low wealth in the 1970s, people should save more, and indeed we observe a high saving rate.

Note also that as the real value of the stock market rises over time, we observe a declining saving rate. Thus, the theoretical prediction roughly holds true in the data. In the financial crisis of 20082009, the real value of the stock market declined by about 50%, and the saving rate doubled, again

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consistent with the theory.

3.

The level of the real after-tax interest rate in the 1970s and 2000s was usually negative. The level of the real after-tax interest rate in the 1980s and 1990s was usually positive, except around the 1990-1991 recession.

4.

a. b.

Residential investment as a percent of GDP usually declines in recessions. In that respect, residential investment is similar to other types of investment.

The ratio of residential investment to GDP was generally higher during the baby boom and lower in the baby bust, except for the housing boom in the early 2000s.

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5.

The high-grade corporate bond rate (AAA) and the mortgage rate (MORTG) tend to be the highest. They are long-term interest rates with some default risk. The ten-year T-bond rate (GS10) and the three-month T-bill rate (TB3MS) tend to be the lowest. They are issued by the U.S. government and have low default risk. The bank prime loan rate (MPRIME) tends to be in the middle of the other rates in normal times. All the interest rates tend to move together, with the long-term rates moving very closely with each other, and the short-term interest rates also moving very closely with each other.

6.

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Investment in equipment has an upward trend, investment in structures has a flat trend, and investment in intellectual property products has an upward trend. Computers and technology have become relatively more important over time than buildings.

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Learning Objectives

I.

Goals of Chapter 5 A. Explain how the balance of payments is calculated (Sec. 5.1) B. Discuss goods market equilibrium in an open economy (Sec. 5.2) C. Describe the factors that affect saving and investment and determine the current account balance in a small open economy (Sec. 5.3) D. Describe the factors that affect saving and investment and determine the current account balance in a large open economy (Sec. 5.4) E. Analyze the relationship between the government budget deficit and the current account deficit (Sec. 5.5)

II. Notes to Ninth Edition Users A. In the Application “The Impact of Globalization on the U.S. Economy,” we add a discussion of research on the impact of Chinese imports on U.S. labor markets B. In the Application “Recent Trends in the U.S. Current Account Deficit,” we discuss bilateral trade balances compared with overall trade balances, as well as the impact of tariffs

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Teaching Notes

I.

Balance of Payments Accounting (Sec. 5.1) A. Balance of payments accounts 1. The record of a country’s international transactions 2. Text Table 5.1 shows recent U.S. data 3. In touch with data and research: the balance of payments accounts Data released quarterly in Survey of Current Business B. The current account 1. Net exports of goods and services (NX) 2. Net income from abroad (NFP) a. Net income from abroad is part of the current account, and is about equal to net factor payments 3. Net unilateral transfers a. Payments made from one country to another b. Negative net unilateral transfers for the United States, since the United States is a net donor to other countries 4. Sum of net exports of goods and services, net income from abroad, and net unilateral transfers is the current account balance CA = NX + NFP + NUT a. Positive current account balance implies current account surplus b. Negative current account balance implies current account deficit Students may be helped if you draw the basic balance of payments chart without numbers, but with + and - signs, so they can see more clearly where the different entries go: Negative (–) Current Account Net exports Exports of goods Exports of services Imports of goods Imports of services

Positive (+)

__________ __________ __________ __________

Net income from abroad Income receipts from abroad Income payments to foreigners

__________

Net unilateral transfers Transfers from foreigners Transfers to foreigners

__________

Financial Account Increase in foreign-owned assets Increase in U.S.-owned assets abroad

.

__________

__________

__________ __________

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Data Application Though the U.S. government generally is a net donor to other countries, providing significant amounts of aid for development, in 1991 the U.S. government received billions of dollars from foreign countries—so much that the United States as a whole netted over $31 billion in transfers from foreigners. What happened? Foreign countries like Kuwait, Saudi Arabia, Japan, and Germany paid the United States for their share of the expenses from the Gulf war with Iraq in 1991.

C. The financial account 1. The financial account records trades in existing assets, either real (e.g., houses) or financial (e.g., stocks and bonds) a. When home country sells assets to foreign country, there is a capital inflow for the home country and an increase in the financial account b. When assets are purchased from a foreign country, there is a capital outflow from the home country and a decrease in the financial account c. Financial account balance equals value of financial inflows minus value of financial outflows, plus net increase in foreign-owned derivatives 3. The balance of payments a. Transactions in official reserve assets are conducted by central banks of countries b. Official reserve assets are assets (foreign government securities, bank deposits, and SDRs of the IMF, gold) used in making international payments c. Central banks buy (or sell) official reserve assets with (or to obtain) their own currencies

Policy Application In the United States, trades of official reserve assets are carried out through a trading desk in the Federal Reserve Bank of New York. The “foreign desk,” as it is called, makes trades for both the United States and foreign governments that may not have trading capability in the United States. Decisions by the United States to trade in official reserve assets are made jointly by the Federal Reserve and the Treasury Department of the U.S. government. For a description of how the activities of the foreign desk and international finance fit into monetary policy decisions, see the Federal Reserve Bank of New York’s website at www.ny.frb.org/ aboutthefed/fedpoint/fed44.html. d. Balance of payments equals net increase in a country’s official reserve assets e. For the United States, the net increase in official reserve assets is the rise in U.S. government reserve assets minus foreign central bank holdings of U.S. dollar assets f. Having a balance of payments surplus means a country is increasing its official reserve assets; a balance of payments deficit is a reduction in official reserve assets Analytical Problem 1 gives students practice in making entries into a balance of payments table.

D. The relationship between the current account and the financial account 1. Current account balance (CA) + financial account balance (FA) = 0 (5.1) 2. CA + FA = 0 by accounting; every transaction involves offsetting effects 3. Examples given of offsetting transactions (text Table 5.2)

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Analytical Problem 2 gives students practice with offsetting transactions in the balance of payments accounts, while Numerical Problem 1 has them calculating various important balances.

4. In practice, measurement problems, recorded as a statistical discrepancy, prevent CA + FA = 0 from holding exactly

Data Application Sometimes the statistical discrepancy can be quite large, as counting cross-border transactions is difficult. For example, in 2014 the current account balance was –$390 billion, but the statistical discrepancy was $150 billion.

E. Net foreign assets and the balance of payments accounts 1. Net foreign assets are a country’s foreign assets minus its foreign liabilities a. Net foreign assets may change in value (e.g., change in stock prices) b. Net foreign assets may change through acquisition of new assets or liabilities 2. The net increase in foreign assets equals a country’s current account surplus 3. A current account surplus implies a financial account deficit, and thus a net increase in holdings of foreign assets (a financial outflow) 4. A current account deficit implies a financial account surplus, and thus a net decline in holdings of foreign assets (a financial inflow) 5. Foreign direct investment: a foreign firm buys or builds capital goods a. Causes an increase in financial account balance b. Portfolio investment: foreigners acquire U.S. securities; also increases financial account balance 6. Summary: Equivalent measures of a country’s international trade and lending Current account surplus = financial account deficit = net acquisition of foreign assets = net foreign lending = (if NFP and net unilateral transfers are zero) net exports Numerical Problem 6 looks at the balance of payments when there are internationally traded assets.

F.

Application: The United States as international debtor 1. The rise in foreign liabilities by the United States since the early 1980s has been very large (text Figure 5.1) 2. The United States has become the world’s largest international debtor 3. But the net foreign debt of the United States relative to U.S. GDP is relatively small (40%) compared with other countries (some of whom have net foreign debt of over 100% of GDP) 4. Despite the large net foreign debt, the United States has direct foreign investment (companies, land) in other countries about equal in size to other countries’ foreign direct investment in the United States 5. What really matters is not size of net foreign debt, but country’s wealth (physical and human capital) a. If net foreign debt rises but wealth rises, there is no problem b. But U.S. wealth is not rising as much as net foreign debt, which is worrisome

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II. Goods Market Equilibrium in an Open Economy (Sec. 5.2) A. From Ch. 2, S = I + CA = I + (NX + NFP)

(5.2)

1. So national saving has two uses: a. Increase the capital stock by domestic investment b. Increase the stock of net foreign assets by lending to foreigners 2. To get goods market equilibrium, national saving and investment must equal their desired levels: a. Sd = Id + CA = Id + (NX + NFP) (5.3) b. Goods market equilibrium in an open economy c. Assuming net factor payments are zero, Sd = Id + NX 3. Alternative method: a. Y = C d + Id + G + NX b. NX = Y – (C d + Id + G) Net exports equal output (Y) minus absorption (C d + Id + G)

(5.4) (5.5) (5.6)

III. Saving and Investment in a Small Open Economy (Sec. 5.3) A. Small open economy: an economy too small to affect the world real interest rate 1. World real interest rate (rw): the real interest rate in the international capital market 2. Key assumption: Residents of the small open economy can borrow or lend at the expected world real interest rate (Figure 5.1; Key diagram 4; like text Figures 5.2 and 5.3)

Figure 5.1 3. Result: rw may be such that Sd > Id, Sd = Id, or Sd < Id a. If rw = r1, then Sd > Id, so the excess of desired saving over desired investment is lent internationally (net foreign lending is positive) and NX > 0 b. If rw = r2, then Sd = Id, so there is no net foreign lending and NX = 0

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c. If rw = r3, then Sd < Id, so the excess of desired investment over desired saving is financed by borrowing internationally (net foreign lending is negative) and NX < 0 4. Alternative interpretation: in terms of output and absorption 5. Net exports equals net foreign lending equals the current account balance (assuming net factor payments and net unilateral transfers are zero) Numerical Problems 2 and 3 look at saving and investment in small open economies.

B. The effects of economic shocks in a small open economy 1. Anything that increases desired national saving (Y rises, future output falls, or G falls) relative to desired investment (MPKf falls, t rises) at a given world interest rate increases net foreign lending, and vice versa 2. A temporary adverse supply shock Temporary drop in income leads to a drop in saving, so net foreign lending declines; shown in text Figure 5.4

Data Application Does the international capital market work well? Maurice Obstfeld, in his article, “Capital Mobility in the World Economy: Theory and Measurement,” in K. Brunner and A. Meltzer, eds., CarnegieRochester Conference Series on Public Policy, vol. 24, Spring 1986, finds that the international capital market works well. Very small economies show little relationship between saving and investment, suggesting that they are able to borrow and lend internationally without much effect on the real interest rate. Larger economies tend to have a closer relationship between saving and investment, suggesting that they fit our textbook definition of a large open economy. For example, when income rises, saving rises, causing the real interest rate to decline and investment to rise.

Policy Application There may be circumstances in which it is best for sovereign governments to default on their loans, and yet lenders in other countries may be willing to lend to them again. This could happen if some totally unexpected event affects the government’s ability to repay the loan, as suggested by Behzad Diba and Herschel Grossman, “Sovereign Debt as a Contingent Claim: Excusable Default, Repudiation, and Reputation,” American Economic Review, December 1988, pp. 1088–1097.

IV. Saving and Investment in Large Open Economies (Sec. 5.4) A. Large open economy: an economy large enough to affect the world real interest rate 1. Suppose there are just two economies in the world a. The home or domestic economy (saving S, investment I) b. The foreign economy, representing the rest of the world (saving SFor, investment IFor) 2. The world real interest rate moves to equilibrate desired international lending by one country with desired international borrowing by the other (Figure 5.2; Key diagram 5; text Figure 5.5)

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Figure 5.2 3. Equivalent statement: The equilibrium world real interest rate is determined such that a current account surplus in one country is equal in magnitude to the current account deficit in the other Note: A key assumption is that the international capital market is integrated, so that there is a free flow of funds across countries. This is not always true; for example, for many years Japan had backward and restrictive financial markets, though they have developed more in recent years.

4. Changes in the equilibrium world real interest rate: Any factor that increases desired international lending of a country relative to desired international borrowing causes the world real interest rate to fall Numerical Problem 4 and Analytical Problems 3, 5, and 6 are all exercises dealing with large open economies.

B. Application: The impact of globalization on the U.S. economy 1. World’s economies are increasingly interdependent—more international trade and investment a. Should the U.S. reign in globalization?

2. Historical data on trends in trade from 1929 to 2017 a. Text Figure 5.6 b. Note large gains in both exports and imports over past 50 years (as % of GDP) 3. Costs of globalization: U.S. jobs lost in particular sectors 4. Benefits of globalization: U.S. jobs gained in particular sectors 5. Generally, benefits exceed costs but government could also aid people in transition 6. Research finds that China’s imports led to adverse impacts on U.S. workers a. So government should understand and prepare for such significant costs C. Application: Recent trends in the U.S. current account deficit 1. U.S. current account deficit is large (text Fig. 5.7) 2. Why? Increased saving by developing countries a. Many developing nations want to invest in safe places like the United States, rather than borrowing and getting into financial crises b. They changed from being international borrowers to being international lenders

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3. A country may have an overall current account deficit but bilateral trade surpluses with some countries and deficits with others d. The bilateral trade balance is a misleading indicator 4. A country can impose tariffs on others but their retaliation will lead to making both countries worse because of the loss of comparative advantage V.

Fiscal Policy and the Current Account (Sec. 5.5) Are government budget deficits necessarily accompanied by current account deficits? That is, are there “twin deficits”?

A. The critical factor: the response of national saving 1. An increase in the government budget deficit raises the current account deficit only if the increase in the budget deficit reduces desired national saving 2. In a small open economy, if an increase in the government budget deficit reduces desired national saving, the saving curve shifts left, thus reducing the current account balance (text Fig. 5.8) Analytical Problem 4 asks students to work out the case of a large open economy with an increase in the government budget deficit.

B. The government budget deficit and national saving 1. A deficit caused by increased government purchases a. No question here: The deficit definitely reduces national saving b. Result: The current account balance declines 2. A deficit resulting from a tax cut a. Sd falls only if C d rises b. So Sd won’t change if Ricardian equivalence holds, since then a tax cut won’t affect consumption c. But if people do not foresee the future taxes implied by a tax cut today, they will consume more, desired saving will decline, and so will the current account balance C. Application: the twin deficits 1. Relationship between the U.S. government budget deficit and U.S. current account deficit 2. Text Figure 5.9 shows data 3. The deficits appear to be twins in the 1980s and early 1990s, moving closely together 4. But at other times (during World Wars I and II) government budget deficits grew, yet the current account balance increased 5. The evidence is also mixed for foreign countries Analytical problem 4 looks at the relationship between government budget deficits and the current account balance for a large open economy.

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Additional Issues for Classroom Discussion

1.

How Open Is Our Economy?

117

Many people do not realize the extent of our interdependence with other countries. Though net exports are small as a proportion of GDP, imports and exports are substantial, as each is over 10% of GDP today, compared with less than 5% in 1960.

Ask your students to list some of the ways in which our country interacts with others. What goods and services do we buy from other countries? What goods and services do other countries buy from us?

You might also show them some data describing the size of imports and exports as a percent of GDP. Here is a FRED graph from September 2018 showing this.

2.

Should We Run Balance of Payments Surpluses?

Because people seem worried that the United States has run continual balance of payments deficits, you might discuss with your students whether it would be desirable for the country to have balance of payments surpluses instead. You might begin by asking them what they think the pros and cons of such a plan might be. Would it be good for a country to reduce its investment to own more of the world’s capital?

Would it be good to reduce government spending to do so? You could also discuss the plan of the mercantilists to run balance of payments surpluses to acquire gold.

3.

Should We Worry About Foreign Ownership of U.S. Assets?

In 1994, Mexico faced severe economic problems when foreign investors began pulling their money out of the country. Could the United States face a similar crisis? For example, in recent years, foreigners (especially Japanese and Chinese investors) have purchased a large quantity of U.S. government bonds. As we will see in Chapter 7, foreigners hold many U.S. dollars. What would happen if foreign investors

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soured on the United States and sold many of their government bonds and brought many of their dollars back into the United States?

To help focus your classroom discussion on this issue, you might ask your students to think about what would happen to interest rates if there were a suddenly increased supply of government bonds that foreign investors tried to sell. Also, ask them to think about what would happen to interest rates if foreign demand for the bonds were not as high. You might point out that although this scenario is a possibility, unlike in Mexico, foreign ownership of U.S. assets is not nearly as large a proportion of U.S. GDP.

4.

Should Countries Cooperate?

As we have seen in this chapter, government policies in one country may have effects in others. Fiscal and monetary policies affect interest rates both at home and abroad. Yet for the most part, countries decide on their fiscal and monetary policies independently of other countries. The question is, should this fact lead countries to cooperate with each other? Should they notify each other of plans to tighten monetary policy, and do so in a coordinated fashion? Would this lead larger countries to have more power over smaller countries because their policy effects are more powerful? Or should each country do its own thing, without regard to the impact on others? (Note that these issues will be discussed in Chapter 13, in material on the European monetary union, optimal currency areas, and fixed exchange rates.)

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Answers to Textbook Problems

Review Questions 1. Positive items in the current account are exports of goods and services and income receipts from abroad. Negative items in the current account are imports of goods and services, income payments to foreigners, and net unilateral transfers. Adding all of the items gives the current account balance. The current account balance equals net exports plus net income from abroad plus net unilateral transfers.

2. The current account includes only the trade of currently produced goods and services. Trades of existing assets are counted in the financial account.

3. The sale of books from the United States to Brazil increases the U.S. current account balance.

Offsetting transactions include anything that is a negative item in the current account or the financial account. Some examples of offsetting transactions are: (1) A U.S. citizen buys $200 worth of stock in a Brazilian company, so that the offsetting item is an increase in U.S.-owned assets abroad, which is a negative item in the financial account. (2) A U.S. firm imports $200 worth of nuts from Brazil, so the offsetting item is an import of goods, which reduces the current account balance.

4. In any period, the net amount of new foreign assets that a country acquires equals its current account surplus, which in turn must equal its financial account deficit. A country with greater net foreign assets than another is not necessarily better off. What really counts is total national wealth, which consists of both net foreign assets and net domestic assets. For example, the United States has lower net foreign assets than other countries, but has one of the world’s highest levels of total national wealth per citizen.

5. In a small open economy, saving does not have to be equal to investment. Saving can be used to finance domestic investment or it can be lent abroad. So saving equals investment plus net exports.

Similarly, output need not equal absorption. Absorption is a country’s total spending on consumption, investment, and government purchases. Absorption may be different from output because some output may be exported. The difference between output and absorption is net exports.

6. A small open economy is likely to run a large current account deficit and to borrow abroad if desired investment increases substantially or if desired national saving declines substantially. Desired investment could increase if there is an increase in the expected future marginal product of capital or a decline in the user cost of capital, both of which would shift the desired investment curve to the right, reducing the current account balance, and possibly leading to a large current account deficit.

Desired national saving might decrease if current output declines, if expected future output rises, if wealth increases, if government expenditures rise temporarily, or if taxes decline and Ricardian equivalence does not hold. For example, a temporary supply shock would cause a decline in current output but not future output, thus reducing desired national saving. A reduction in desired national saving would reduce the current account balance and possibly lead to a large current account deficit.

7. In a world with two large open economies, the world real interest rate is determined such that desired international lending by one country equals desired international borrowing by the other country.

When the world real interest rate is at its equilibrium value, the current accounts of the two countries sum to zero.

8. An increase in desired national saving in a large open economy reduces the world real interest rate.

The shift to the right in the saving curve increases the country’s current account at the current world real interest rate, so the international asset market is out of equilibrium. To restore equilibrium, the world real interest rate must fall.

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An increase in desired investment has the opposite effect. The increase in investment reduces the domestic country’s current account and leads to an increase in the world real interest rate to restore equilibrium.

The reason that changes in desired saving and investment affect the world real interest rate in large open economies but not small open economies is that saving and investment in small open economies are so small relative to saving and investment in the world that changes in them simply have no impact. On the other hand, a large open economy may account for a substantial fraction of the world’s saving and investment, so a change there has a significant impact.

9. An increase in the government budget deficit raises the current account deficit of a small open economy if and only if the increase in the budget deficit reduces national saving. Since the current account is the difference between national saving and investment, the current account balance changes by the amount that national saving changes. The government budget deficit and the current account balance are connected because if an increase in the government budget deficit reduces national saving it leads to an increased current account deficit. So the government budget deficit and the current account deficit move in the same direction.

10. The United States has had twin deficits in the 1980s and first half of the 1990s; but in World Wars I and II, in the late 1990s, and from 2008 to 2011, the deficits moved in opposite directions.

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Numerical Problems 1.

Credit (+)

Debits (-)

Goods

100

125

Services

90

80

Income from/to foreigners Total

110 300

150 355

Current Account

Current account balance (CA) = 300 – 355 = –55.

Net exports (NX) = (100 + 90) – (125 + 80) = –15.

Credit (+)

Financial Account Increase in home country assets abroad

Debits (-) 160

Increase in foreign assets in home country

200

Total

200

160

Notice that the increase in home reserve assets is just a subcategory of the increase in home country assets, so it is not included separately. Similarly, the increase in foreign reserve assets is just a subcategory of the increase in foreign assets in the home country. The information about the changes in home and foreign reserve assets is included for calculation of the balance of payments only; it does not affect the financial account.

Financial account balance (FA) = 200 - 160 = 40.

Statistical discrepancy (SD): CA + FA + SD = 0 -55 + 40 + SD = 0 SD = 15 Balance of payments = increase in home official reserve assets minus increase in foreign official reserve assets = 30 - 35 = -5.

2.

The following table calculates key variables for this question for different values of the real interest rate. The column for S is calculated by the equation S = Y - (Cd + G). The column headed S - I is foreign lending. Absorption (A) is Cd + Id + G. Net exports (NX) are output (Y) minus absorption (A).

Every column except r consists of dollar amounts in billions. r

Cd

Id

S

S-I

A

NX

5% 4%

12 13

3 4

7 6

4 2

21 23

4 2

3%

14

5

5

0

25

0

2%

15

6

4

–2

27

–2

Net exports and foreign lending are identical.

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3.

All variables but interest rates are in billions of dollars. (a) S = 10 + (100 ´ 0.03) = 13 I = 15 - (100 ´ 0.03) = 12 NX = CA = S - I = 13 - 12 = 1 C = Y - ( I + G + NX ) = 50 - (12 + 10 + 1)

= 27 A=C+I+G = 27 + 12 + 10 = 49 (b) S = 13, as before.

I = 17 - (100 ´ 0.03) = 14 NX = CA = S - I = 13 - 14 = -1 C = Y - ( I + G + NX ) = 50 - (14 + 10 - 1) = 27 A=C +I +G = 27 + 14 + 10 = 51 4.

(a) To find the equilibrium interest rate (rw), we must first calculate the current account for each country as a function of rw. Then we can find the value of rw that clears the goods market, that is, where CA + CAFor = 0.

Home: Cd = 320 + 0.4(1000 - 200) - 200rw = 320 + 320 - 200 rw = 640 - 200 rw CA = NX = Sd – Id = Y – (Cd + Id + G) = 1000 – (640 – 200 rw + 150 – 200rw + 275) = –65 + 400 rw Foreign: d CFor = 480 + 0.4(1500 - 300) - 300 r w

= 480 + 480 - 300r w = 960 - 300r w

CAFor = NXFor = SdFor - IdFor = YFor - (CdFor + IdFor + GFor) = 1500 - (960 - 300rw + 225 - 300rw + 300) = 15 + 600 rw At equilibrium, CA + CAFor = 0, so: –65 + 400 rw + 15 + 600 rw = 0

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–50 + 1000 rw = 0 rw = 0.05 C = 640 - 200 rw = 630 CFor = 960 - 300 rw = 945 S = Y - C - G = 1000 - 630 - 275 = 95 SFor = YFor - CFor - GFor = 1500 - 945 - 300 = 255 I = 150 - 200 rw = 140 IFor = 225 - 300 rw = 210 CA = S - I = 95 - 140 = -45 CAFor = SFor - IFor = 255 - 210 = 45 (b) Cd = 320 + 0.4(1000 - 250) - 200 rw = 320 + 300 - 200 rw = 620 - 200 rw CA = NX = Sd - Id = Y - (Cd + Id + G) = 1000 - (620 - 200 rw + 150 - 200 rw + 325) = -95 + 400 rw At equilibrium, CA + CAFor = 0, so: -95 + 400 rw + 15 + 600 rw = 0 -80 + 1000 rw = 0 rw = 0.08 C = 620 - 200 rw = 604 CFor = 960 - 300 rw = 936 S = Y - C - G = 1000 - 604 - 325 = 71 SFor = YFor - CFor - GFor = 1500 - 936 - 300 = 264 I = 150 - 200 rw = 134 IFor = 225 - 300 rw = 201 CA = S - I = 71 - 134 = -63 CAFor = SFor - IFor = 264 - 201 = 63 So a balanced-budget increase in government spending increases the home country’s current account deficit.

5.

(a) SH = YH - CH - GH = 1000 - [100 + (0.5 ´ 1000) - 500r] - 155 = 245 + 500r SF = YF - CF - GF = 1200 - [225 + (0.7 ´ 1200) - 600r] - 190 = -55 + 600r (b) NXH = SH - IH = 245 + 500r - (300 - 500r)

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= -55 + 1000r NXF = SF – IF = -55 + 600r - (250 - 200r) = -305 + 800r In equilibrium, NXH + NXF = 0, so -55 + 1000r + (-305 + 800r) = 0 1800r = 360 r = 0.20 (c) CH = 100 + (0.5 ´ 1000) - (500 ´ 0.20) = 500 SH = 245 + (500 ´ 0.20) = 345 IH = 300 - (500 ´ 0.20) = 200 CAH = NXH = -55 + (1000 ´ 0.20) = 145 (assume NFP = 0) absorptionH = CH + IH + GH = 500 + 200 + 155 = 855 CF = 225 + (0.7 ´ 1200) - (600 ´ 0.20) = 945 SF = -55 + (600 ´ 0.20) = 65 IF = 250 - (200 ´ 0.20) = 210 CAF = NXF = –305 + (800 ´ 0.20) = -145 (assume NFP = 0) absorptionF = CF + IF + GF = 945 + 210 + 190 = 1345 6.

GDP = Y = $1,000,000 = total production of coconuts GNP = $1,025,000 = production of coconuts + net factor income from abroad NFP = $25,000 I = $0 S = Y + NFP - C - G = $1,000,000 + $25,000 - $1,025,000 - $0 = $0 CA = S - I = $0 NX = CA - NFP = $0 - $25,000 = -$25,000 FA = -CA = $0 The $500,000 in foreign bonds provides income of $500,000 ´ 0.05 = $25,000 per year. Since people consume exactly $1,025,000, they must be using the $25,000 of foreign interest receipts to buy imported consumption goods. So net exports are –$25,000 and the current account balance is zero.

Since the current account balance is zero, the financial account balance is also zero.

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Analytical Problems 1.

(a) Export of merchandise: + entry in current account. (b) No entry: just changes the type of foreigner holding U.S. assets. (c) Decrease in U.S. official reserve assets: + entry in financial account. (d) Income receipt from abroad: + entry in current account. (e) Import of assets: - entry in financial account. (f) Import of services: - entry in current account. (g) Increase in foreign ownership of U.S. assets: + entry in financial account.

2.

There are many possible answers; an example for each is given here. (a) U.S. citizens buy cars from the foreign country: - entry in current account. (b) No transaction needed. (c) The Federal Reserve sells dollars to, and buys euros from, the European Central Bank: - entry in financial account. (d) Brazilian citizens receive interest on U.S. Treasury bonds they own: - entry in current account. (e) The IRS sells a bankrupt singer’s home to an Egyptian citizen: + entry in financial account. (f) Kuwait pays for the services of Red Adair’s U.S. team of oil fire fighters: + entry in current account. (g) A U.S. bank buys U.K. government bonds: - entry in financial account.

3.

In Figure 5.3, before the capital controls are imposed, the home country has a current account deficit of the amount CA, while the foreign country has a matching current account surplus. The effect of the capital controls is to make saving equal investment in each country. In the home country, the real interest rate rises, investment declines, saving increases, and the current account balance increases to zero. The world real interest rate (the interest rate in the foreign country) declines.

Figure 5.3

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In Figure 5.4, suppose initially that both countries have a zero current account. A rise in the government budget deficit has no effect on desired investment, so it affects the current account only if it affects desired national saving. If desired national saving is affected, the saving curve shifts to the left from S1 to S2. This raises the world real interest rate, reduces investment in both countries, and increases the foreign country’s current account balance.

Figure 5.4 5.

(a) The home country’s saving curve shifts to the right, from S1 to S2 in Figure 5.5. The real world interest rate falls, so that the current account surplus in the home country equals the current account deficit in the foreign country. From Figure 5.5, S rises, I rises, CA rises, rw falls.

Figure 5.5

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Chapter 5 Saving and Investment in the Open Economy

1 to 2 in Figure 5.6. The real (b) The foreign country’s saving curve shifts to the right, from SFor SFor world interest rate must fall, so the current account surplus in the foreign country equals the current account deficit in the home country. As shown in the figure, S falls, I rises, CA falls, rw falls.

Figure 5.6 1 to 2 in Figure 5.7. The real (c) The foreign country’s saving curve shifts to the left, from SFor SFor world interest rate must rise, so the current account deficit in the foreign country equals the current account surplus in the home country. As shown in the figure, S rises, I falls, CA rises, rw rises.

Figure 5.7 (d) If Ricardian equivalence holds, there is no effect. If Ricardian equivalence does not hold, then the result is the same as in part (b), as the foreign country’s saving curve shifts to the right.

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A temporary adverse supply shock hitting the foreign economy causes the foreign saving curve to 1 to 2 in Figure 5.7. This raises the equilibrium world real interest rate, shift to the left, from SFor SFor increasing home country saving and decreasing home country investment. Since saving rises and investment falls, the home country’s current account balance increases.

Now consider a worldwide temporary adverse productivity shock, which causes both the saving curve in the home country and the saving curve in the foreign country to shift to the left. As a result of these shifts, the world real interest rate increases (by more than if the productivity shock were confined to the foreign country). The increase in the world real interest rate reduces investment in both countries (by more than if the productivity shock were confined to the foreign country). Depending on the sizes of the shocks in both countries and the slopes of the saving and investment curves, the current account balance in the home country could either increase or decrease (but in any case it would be smaller than if the productivity shock were confined to the foreign country). Figure 5.8 shows the borderline case, in which the current account balances in both countries are unchanged. Finally, worldwide saving falls because worldwide saving equals worldwide investment, and we have shown that investment falls in both countries. Though worldwide saving, that is, the sum of saving in the home country and saving in the foreign country, falls, it is possible that saving increases in one country, depending on the sizes of the productivity shocks in the two countries and the slopes of the saving and investment curves.

Figure 5.8 7.

The shock shifts the saving curve to the right, with no change in the investment curve, since the future marginal product of capital is unaffected. Since income rises and saving rises, consumption rises, but less than income. Thus, although imports rise somewhat, the amount is small, so that the current account increases, it doesn’t fall. The statement is false.

8.

Note that when the government of Eastland makes this change, it isn’t changing total government purchases, so there’s no effect on national saving. Thus the current account balance is unaffected.

How can that be, given that Eastland’s government is now purchasing more goods from Westland?

The answer is that the private sector offsets the government’s actions by increasing its net exports to Westland.

The point of this exercise is to show that a government can’t affect the current account balance by changing its purchasing decisions if its total purchases of goods and services remain unchanged; it

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can only do so if it changes national saving or investment, since the current account equals saving minus investment.

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Working with Macroeconomic Data 1.

The trend in the openness index is a gradual increase over time. The openness index was about 6% in the 1950s, rising to over 30% by 2011 and continuing to increase. The openness index usually declines in recessions. The rise in the index is attributable to reductions in the costs of trade, improved communications and transportations, and reductions in trade barriers, such as tariffs.

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2.

Output and absorption differ by a similar amount to the current-account balance. The difference between saving and investment is close to the difference between output and absorption. Thus, both graphs show similar phenomena.

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3.

Exports and imports of goods and services have all increased, in general, over time. Recessions are often associated with dramatic declines in both imports and exports. The U.S. economy has become more interdependent with other economies.

4.

The highest ratio of international debt securities to GDP is for Europe; the lowest of the three is Japan. Over the past five years, the ratio has been declining in the United States but rising in Japan.

Europe’s international debt ratio was falling from 2011 to 2014 but rose in 2015.

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Learning Objectives

I.

Goals of Chapter 6 A. Discuss the sources of economic growth and the fundamentals of growth accounting (Sec. 6.1) B. Explain the factors affecting long-run living standards in the Solow model (Sec. 6.2) C. Summarize endogenous growth theory (Sec. 6.3) D. Discuss government policies for raising long-run living standards (Sec. 6.4)

II. Notes to Ninth Edition Users A. We replaced the Application “The Post-1973 Slowdown in Productivity Growth” with a new Application “Waves of Productivity Growth over Time” B. In the Application “The Rebound in U.S. Productivity Growth,” we added material on possible explanations for the productivity growth slowdown after 2008 C. In section 6.2, after discussing the Solow model, we added a new discussion of economic models, endogenous variables, and exogenous variables D. We added a new Application “The Changing Distribution of Income in the United States,” to show some facts about how the U.S. income distribution has changed over time

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Teaching Notes

I.

Introduction A. Introduction 1. Countries have grown at very different rates over long spans of time (text Table 6.1) 2. We would like to explain why this happens

II.

The Sources of Economic Growth (Sec. 6.1) A. Production function Y = AF(K, N)

(6.1)

1. Decompose into growth rate form: the growth accounting equation DY/Y = DA/A + aK DK/K + aN DN/N

(6.2)

2. The a terms are the elasticities of output with respect to the inputs (capital and labor) 3. Interpretation a. A rise of 10% in A raises output by 10% b. A rise of 10% in K raises output by aK times 10% c. A rise of 10% in N raises output by aN times 10% 4. Both aK and aN are less than 1 due to diminishing marginal productivity B. Growth accounting 1. Four steps in breaking output growth into its causes (productivity growth, capital input growth, labor input growth) a. Get data on DY/Y, DK/K, and DN/N, adjusting for quality changes b. Estimate aK and aN from historical data c. Calculate the contributions of K and N as aK DK/K and aN DN/N, respectively d. Calculate productivity growth as the residual: DA/A = DY/Y – aK DK/K – aN DN/N Numerical Problems 1 and 2 are growth accounting exercises.

2. Growth accounting and productivity trends a. Denison’s results for 1929–1982 (text Table 6.3) (1) Entire period output growth 2.92%; due to labor 1.34%; due to capital 0.56%; due to productivity 1.02% (2) Pre-1948 capital growth was much slower than post-1948 (3) Post-1973 labor growth slightly slower than pre-1973 (4) Productivity growth is major difference (a) Entire period: 1.02% (b) 1929–1948: 1.01% (c) 1948–1973: 1.53% (d) 1973–1982: –0.27% b. Productivity growth slowdown occurred in all major developed countries

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Theoretical Application Growth accounting provides the basis for the real business cycle (RBC) model of the economy, which we will discuss in greater detail in Chapter 10. The RBC model takes movements in total factor productivity to be the primary source of business cycle fluctuations.

3. Application: Waves of productivity growth over time a. Productivity growth has occurred in waves, back to the 1800s b. Could productivity growth destroy jobs and lead to poverty? c. Should governments provide guaranteed income for displaced workers? d. In the past, such concerns have proved to be groundless; but this time could be different

Data Application Mark Wynne’s article, “The Comparative Growth Performance of the U.S. Economy in the Postwar Period,” Federal Reserve Bank of Dallas Economic Review, First Quarter 1992, pp. 1–16, argues that the postwar period up to the mid-1970s showed extraordinary productivity growth. After the mid-1970s, productivity returned to more normal levels.

4. Application: the rebound in U.S. productivity growth a. Labor productivity growth increased sharply in the second half of the 1990s b. Labor productivity and TFP grew steadily from 1982 to 2008 (text Fig. 6.1) c. Labor productivity growth generally exceeded TFP growth from 1995 to 2008 (text Fig. 6.2) d. The gap between labor productivity growth and TFP growth can be seen in the equation DY DN DA æ DK DN ö = + aK ç Y N A N ÷ø è K

(6.3)

(1) Equation (6.3) suggests that labor productivity growth (the left-side term) exceeds TFP growth (the first right-side term) when capital growth exceeds labor growth e. The increase in labor productivity can be traced to the ICT (information and communications technologies) revolution (1) But other countries also had an ICT revolution, and their labor productivity did not rise as much as in the United States (2) Why did ICT growth contribute to U.S. productivity growth but not in other countries? (a) Government regulations (b) Lack of competitive pressure (c) Available labor force (d) Ability to adapt quickly f. Why is there such a lag between ICT investment and increases in productivity?

(1) Because productivity improvements require not just technological advances, but also investment in intangible capital—research and development, reorganization of firms, and worker training g. Is the 1995 to 2008 episode unique in U.S. history?

(1) Not really: 1873–1890—steam power, trains, telegraph; 1917–1927—electrification in factories; 1948–1973—transistor h. Since 2008, productivity growth slowed, with three alternative possible explanations

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(1) It could reflect measurement difficulties, especially related to intangible investment (2) Major technological innovations may have run out (3) Firms may be unable to keep up with technology i. It may be that people benefit from technology but GDP does not show it III. Long-Run Growth: The Solow Model (Sec. 6.2) A. Two basic questions about growth 1. What is the relationship between the long-run standard of living and the saving rate, population growth rate, and rate of technical progress?

2. How does economic growth change over time? Will it speed up, slow down, or stabilize?

B. Setup of the Solow model 1. Basic assumptions and variables a. Population and workforce grow at same rate n b. Economy is closed and G = 0 c. Ct = Yt - It d. Rewrite everything in per-worker terms: yt = Yt/Nt; ct = Ct/Nt; kt = Kt/Nt e. kt is also called the capital-labor ratio 2. The per-worker production function a. yt = f(kt) b. Assume no productivity growth for now c. Plot of per-worker production function—text Figure 6.3 d. Same shape as aggregate production function

(6.4)

(6.5)

Numerical Problem 3 and Analytical Problem 6 work with the per-worker production function.

3. Steady states a. Steady state: yt, ct, and kt are constant over time b. Gross investment must (1) Replace worn out capital, dKt (2) Expand so the capital stock grows as the economy grows, nKt c. It = (n + d)Kt d. From Eq. (6.4), Ct = Yt - It = Yt - (n + d)Kt

(6.6) (6.7)

e. In per-worker terms, in steady state c = f(k) - (n + d)k f. Plot of c, f(k), and (n + d)k (Figure 6.1; like text Figure 6.4) g. Increasing k will increase c up to a point (1) This is kG in the figure, the Golden Rule capital-labor ratio (2) For k beyond this point, c will decline (3) But we assume henceforth that k is less than kG, so c always rises as k rises

.

(6.8)

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Figure 6.1 4. Reaching the steady state a. Suppose saving is proportional to current income: St = sYt,

(6.9)

where s is the saving rate, which is between 0 and 1 b. Equating saving to investment gives sYt = (n + d)Kt

(6.10)

c. Putting this in per-worker terms gives sf(k) = (n + d)k d. Plot of sf(k) and (n + d)k (Figure 6.2; like text Figure 6.5)

.

(6.11)

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Figure 6.2 e. The only possible steady-state capital-labor ratio is k* f. Output at that point is y* = f(k*); consumption is c* = f(k*) - (n + d)k* g. If k begins at some level other than k*, it will move toward k* (1) For k below k*, saving > the amount of investment needed to keep k constant, so k rises (2) For k above k*, saving < the amount of investment needed to keep k constant, so k falls Numerical Problems 5, 6, and 7 look at equilibrium in the Solow model. h. To summarize, with no productivity growth, the economy reaches a steady state, with constant capital-labor ratio, output per worker, and consumption per worker C. The fundamental determinants of long-run living standards 1. The saving rate a. Higher saving rate means higher capital-labor ratio, higher output per worker, and higher consumption per worker (shown in text Figure 6.6) b. Should a policy goal be to raise the saving rate?

(1) Not necessarily, since the cost is lower consumption in the short run (2) There is a trade-off between present and future consumption 2. Population growth a. Higher population growth means a lower capital-labor ratio, lower output per worker, and lower consumption per worker (shown in text Figure 6.7) b. Should a policy goal be to reduce population growth?

(1) Doing so will raise consumption per worker (2) But it will reduce total output and consumption, affecting a nation’s ability to defend itself or influence world events c. The Solow model also assumes that the proportion of the population of working age is fixed (1) But when population growth changes dramatically this may not be true (2) Changes in cohort sizes may cause problems for social security systems and areas like health care

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3. Productivity growth a. The key factor in economic growth is productivity improvement b. Productivity improvement raises output per worker for a given level of the capital-labor ratio (text Fig. 6.8) c. In equilibrium, productivity improvement increases the capital-labor ratio, output per worker, and consumption per worker (text Fig. 6.9) (1) Productivity improvement directly improves the amount that can be produced at any capital-labor ratio (2) The increase in output per worker increases the supply of saving, causing the long-run capital-labor ratio to rise d. Can consumption per worker grow indefinitely?

(1) The saving rate can’t rise forever (it peaks at 100%) and the population growth rate can’t fall forever (2) But productivity and innovation can always occur, so living standards can rise continuously e. Summary: The rate of productivity improvement is the dominant factor determining how quickly living standards rise Analytical Problems 1, 2, 3, and 4 look at how changes in the fundamentals affect an economy’s economic growth.

D. Economic models, endogenous variables, and exogenous variables 1. An equilibrium condition is an equation that solves a model, often a point where one curve intersects another curve 2. Exogenous versus endogenous variables a. Exogenous variable: taken as given (e.g., n, s, and d in Solow model) b. Endogenous variable: determined by the equilibrium in a model (e.g., k, y, and c in Solow model) c. How does a change in an exogenous variable affect the endogenous variables? d. Meaningless to ask how a change in an endogenous variable affects other variables e. Key to economic modeling: identifying which variables are exogenous and endogenous, as well as finding equilibrium conditions E. Application: The growth of China 1. China is an economic juggernaut a. Population 1.4 billion people b. Real GDP per capita is low but growing (Table 6.4) c. Starting with low level of GDP, but growing rapidly (Fig. 6.10) 2. Fast output growth attributable to a. Huge increase in capital investment b. Fast productivity growth (in part from changing to a market economy) c. Increased trade 3. Will China be able to keep growing rapidly? a. Rapid growth because of use of underemployed resources, using advanced technology developed elsewhere, and making the transition from a centrally-planned economy to a market economy b. Such gains may not last 4. So, it may take China a long time to catch up with the rest of the developed world

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IV. Endogenous Growth Theory—Explaining the Sources of Productivity Growth (Sec. 6.3) A. Aggregate production function Y = AK 1.

(6.12)

Constant MPK a. Human capital (1) Knowledge, skills, and training of individuals (2) Human capital tends to increase in same proportion as physical capital b. c.

Research and development programs Increases in capital and output generate increased technical knowledge, which offsets decline in MPK from having more capital B. Implications of endogenous growth 1. Suppose saving is a constant fraction of output: S = sAK 2. Since investment = net investment + depreciation, I = DK + dK 3. Setting investment equal to saving implies: DK + dK = sAK

(6.13)

DK/K = sA - d

(6.14)

4. Rearrange (6.13): 5. Since output is proportional to capital, DY/Y = DK/K, so DY/Y = sA - d

(6.15)

6. Thus the saving rate affects the long-run growth rate (not true in Solow model)

Theoretical Application The Wall Street Journal discussed the theory of endogenous growth and the contributions of Stanford economist Paul Romer, in the article “Wealth of Notions,” January 21, 1997.

C. Summary 1. Endogenous growth theory attempts to explain, rather than assume, the economy’s growth rate 2. The growth rate depends on many things, such as the saving rate, that can be affected by government policies

Policy Application For a good review of how government policy can contribute to economic growth, see Satyajit Chatterjee, “Making More Out of Less: The Recipe for Long-Term Economic Growth,” Federal Reserve Bank of Philadelphia Business Review, May/June 1994.

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Data Application Is the Solow model or the model of endogenous growth a better representation of how economic growth is determined? To find out, Ben S. Bernanke and Refet S. Gürkaynak of Princeton University examined data from many different countries from 1960 to 1998 (“Is Growth Exogenous? Taking Mankiw, Romer, and Weil Seriously,” NBER Macroeconomics Annual 2001, in Ben S. Bernanke and Kenneth Rogoff, eds., Cambridge, MA: MIT Press, 2002). They tested whether the Solow model or several alternative models of endogenous growth were more consistent with the data.

Bernanke and Gürkaynak tested a key implication of the Solow model: that the steady-state growth rate of a country does not depend on variables such as the rate of human capital accumulation and the saving rate. They found that, in fact, countries’ growth rates are closely correlated with both the saving rate and the rate of human capital accumulation, which suggests either that the Solow model does not work well or that the economies are not in steady state.

However, the Solow model implies that even if an economy is not in a steady state, the growth rate of total factor productivity (TFP) is exogenous: it does not depend on the saving rate or on any other behavioral variable, such as the level of education in a country or the growth rate of the labor force. After constructing measures of long-run TFP growth for about 50 countries, Bernanke and Gürkaynak examined the relationship between it and other variables. They found that there is, in fact, a strong relationship between TFP growth and the saving rate, some relationship between TFP growth and the growth rate of the labor force, and a weaker relationship between TFP growth and the level of education. Thus, the data do not support the Solow model.

Models of endogenous growth imply that human capital formation and physical capital accumulation should be related to the long-run growth rate of output. Bernanke and Gürkaynak found that there is indeed such a relationship in the data across many countries. However, the models they test are not perfect, as they cannot explain why savings rates and rates of human capital accumulation differ so much across countries.

Overall, the research of Bernanke and Gürkaynak suggests that models of endogenous growth hold more promise than the Solow model in explaining economic growth.

V.

Government Policies to Raise Long-Run Living Standards (Sec. 6.4) A. Policies to affect the saving rate 1. If the private market is efficient, the government should not try to change the saving rate a. The private market’s saving rate represents its trade-off of present for future consumption b. But if tax laws or myopia cause an inefficiently low level of saving, government policy to raise the saving rate may be justified 2. How can saving be increased? a. One way is to raise the real interest rate to encourage saving; but the response of saving to changes in the real interest rate seems to be small b. Another way is to increase government saving (1) The government could reduce the deficit or run a surplus (2) But under Ricardian equivalence, tax increases to reduce the deficit will not affect national saving B. Policies to raise the rate of productivity growth 1. Improving infrastructure a. Infrastructure: highways, bridges, utilities, dams, and airports b. Empirical studies suggest a link between infrastructure and productivity

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c. U.S. infrastructure spending has declined in the last two decades d. Would increased infrastructure spending increase productivity?

(1) There might be reverse causation: Richer countries with higher productivity spend more on infrastructure, rather than vice versa (2) Infrastructure investments by government may be inefficient, since politics, not economic efficiency, is often the main determinant 2. Building human capital a. There’s a strong connection between productivity and human capital b. Government can encourage human capital formation through educational policies, worker training and relocation programs, and health programs c. Another form of human capital is entrepreneurial skill Government could help by removing barriers like red tape 3. Encouraging research and development a. Support scientific research b. Fund government research facilities c. Provide grants to researchers d. Contract for particular projects e. Give tax incentives f. Provide support for science education

Policy Application Many issues relating to government policy and its effects on growth are discussed in a special issue of the Journal of Monetary Economics, December 1993. The articles were presented at a World Bank Conference on the research project, “How Do National Policies Affect Long-Run Growth?”

C. Application: The changing distribution of income in the United States 1. What does the U.S. income distribution look like and how has it changed over time?

2. Lorenz curve (text Fig. 6.11) illustrates difference between 1967 and 2016 a. Horizontal axis shows cumulative share of population b. Vertical axis shows cumulative share of income c. So, higher line on right side of graph in 2016 means people with higher incomes have a great share of total income than before, so a less equal income distribution 3. Gini coefficient calculates area under 45-degree line and above Lorenz curve a. Equal incomes: Gini coefficient equals zero b. Higher Gini coefficient means more unequal distribution of income c. Gini coefficient has generally trended up from 1967 to 2016, meaning less equal distribution of income (text Fig. 6.12) 4. Observations about more unequal income distribution (Kearney) a. Increased compensation going to those with high skills is major cause of increased inequality b. Rise in inequality leading to increased educational gaps between rich and poor, causing more future inequality c. Increased inequality will be self-perpetuating if people with lower incomes give up trying to earn more .

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Additional Issues for Classroom Discussion

1.

Financial Institutions and Growth

143

We often take for granted our well-developed financial system. However, many countries have financial institutions that are much more primitive than ours. You may wish to discuss with your class the relationship between financial institutions and growth.

You could begin by asking how small, medium, and large companies in the United States obtain financing for investment. Your students will note that smaller companies more likely rely on banks or internally generated funds, while larger companies can borrow directly in the stock and bond markets. Then you can discuss how individuals borrow to buy houses and other durable goods. Again, there are a variety of financial sources. Next, ask them to think about whether such financial institutions are likely to be available in either war torn countries or newly industrializing countries. Finally, you might point out that even advanced countries like Japan have suffered in recent years from failing to have strong financial institutions in place.

2.

Is Growth Good?

Students like to discuss the benefits versus the costs of growth. While it is easy for the government to calculate output (GDP), it’s much harder to account for the quality of life. And everyone is aware of the trade-offs between growth and quality of life, as seen in such side effects of growth as pollution, traffic, and suburban sprawl.

Ask your students whether they think our economy’s current growth rate is about right, or should it be slower to prevent some of the problems growth causes? Should we allow strip mines to rip giant holes in the earth, just to provide coal and minerals at lower prices? Should we allow the production of radioactive waste, just to have cheaper electricity? Should we allow species to become extinct, just to allow new housing developments? Should we destroy the rainforests, just to reduce the cost of doing business in South America?

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Answers to Textbook Problems

Review Questions 1.

The three sources of economic growth are capital growth, labor growth, and productivity growth. The growth accounting approach is derived from the production function.

2.

A decline in productivity growth is the primary reason for the slowdown in output growth in the United States since 1973. Productivity growth may have declined because of deterioration in the legal and human environment, reduced rates of technological innovation, and the effects of high oil prices.

To some extent, the apparent decline in productivity may be due to measurement difficulties.

3.

The rise in productivity growth in the 1990s occurred because of the revolution in information and communications technologies (ICT). Not only were there improvements in ICT, but also government regulations did not rein in the growth of productivity in the United States, as they did in other countries, such as those in Europe. In addition, intangible investment (research and development, reorganization of firms, and worker training) allowed the ICT improvements to boost productivity.

4.

A steady state is a situation in which the economy’s output per worker, consumption per worker, and capital stock per worker are constant.

5.

If there is no productivity growth, then output per worker, consumption per worker, and capital per worker will all be constant in the long run. This represents a steady state for the economy.

6.

The statement is false. Increases in the capital-labor ratio increase consumption per worker in the steady state only up to a point. If the capital-labor ratio is too high, then consumption per worker may decline due to diminishing marginal returns to capital, and the need to divert much of output to maintaining the capital-labor ratio.

7.

(a) An increase in the saving rate increases long-run living standards, as higher saving allows for more investment and a larger capital stock. (b) An increase in the population growth rate reduces long-run living standards, as more output must be used to equip the larger number of new workers with capital, leaving less output available to increase consumption or capital per worker. (c) A one-time increase in productivity increases living standards directly, by increasing output, and indirectly, since by raising incomes it also raises saving and the capital stock.

8.

Endogenous growth theory suggests that the main sources of productivity growth are accumulation of human capital (the knowledge, skills, and training of individuals) and technological innovation (research and development, as well as learning by doing). The production function in an endogenous growth model does not exhibit diminishing marginal productivity of capital. This differs from the production function in the Solow model, which has diminishing marginal productivity of capital.

9.

Government policies to promote economic growth include policies to raise the saving rate and policies to increase productivity. One way to increase the saving rate is to increase the real return to saving by providing a tax break, as Individual Retirement Accounts did in the United States.

Unfortunately, the response of saving to increases in the real rate of return is small. Another way to increase the saving rate is to reduce the government budget deficit. However, the theory of Ricardian equivalence suggests that this will not do much to increase national saving. Note that an increase in the saving rate will increase the steady-state capital-labor ratio, but will not increase the long-run rate of economic growth.

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One way that government policy can increase productivity is by spending more on the economy’s infrastructure, which has been neglected over the past two decades in the United States. Another possibility is to support the creation of human capital by spending more on education and training programs, and reducing barriers to entrepreneurial activity. The issue is whether the government should intervene in the market to do these things, or whether the free market by itself provides an efficient outcome.

A one-time increase in productivity will increase the steady-state capital-labor ratio but will not increase the long-run rate of economic growth. To increase the long-run rate of economic growth, the growth rate of productivity must be permanently increased.

Endogenous growth theory modifies these conclusions to some extent. A rise in the saving rate leads to a higher long-run rate of economic growth in endogenous growth models.

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Numerical Problems 1.

Hare: $5000 ´ (1.03)70 = $39,589 Tortoise: $5000 ´ (1.01)70 = $10,034

2.

20 Years Ago

Today

Percent Change

1000 2500 500

1300 3250 575

30% 30% 15%

Y K N

(a) DA/A = DY/Y - aK DK/K - aN DN/N = 30% - (0.3 ´ 30%) - 0.7 ´ 15% = 30% - 9% - 10.5% = 10.5% Capital growth contributed 9% (aK DK/K), labor growth contributed 10.5% (aN DN/N), productivity growth was 10.5%. (b) DA/A = 30% - (0.5 ´ 30%) - (0.5 ´ 15%) = 30% - 15% - 7.5% = 7.5% Capital growth contributed 15% (aK DK/K), labor growth contributed 7.5% (aN DN/N), productivity growth was 7.5%.

3.

(a) Year

K

N

Y

K/N

Y/N

1 2 3

200 250 250

1000 1000 1250

617 660 771

0.20 0.25 0.20

0.617 0.660 0.617

4

300

1200

792

0.25

0.660

This production function can be written in per-worker form since Y/N = K.3N.7/N = K.3/N.3 = (K/N).3. Note that K/N is the same in years 1 and 3, and so is Y/N. Also, K/N is the same in years 2 and 4, and so is Y/N. (b) Year

K

N

Y

K/N

Y/N

1 2

200 250

1000 1000

1231 1316

0.20 0.25

1.231 1.316

3

250

1250

1574

0.20

1.259

4

300

1200

1609

0.25

1.341

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This production function can’t be written in per-worker form since Y/N = K.3N.8/N = K.3/N.2. Note that K/N is the same in years 1 and 3, but Y/N is not the same in these years. The same is true for years 2 and 4.

4.

To answer this problem, an approximate solution can be found by finding the ratio GDP (2016)/GDP (1950), taking the natural logarithm of that ratio and dividing by 66. This is the answer given in the table below.

Real GDP Per Capita 1950 2016

Ratio

Growth Rate (%)

Australia Canada

13,466 12,333

48,845

3.63

43,745

3.55

2.0 1.9

France

8,531

37,124

4.35

2.2

Germany

7,840

44,689

5.70

2.6

Japan Sweden

3,023 11,385

37,465 44,659

12.39 3.92

3.8 2.1

United Kingdom

10,846

37,334

3.44

1.9

United States

15,241

53,015

3.48

1.9

Germany and Japan had the highest growth rates because damage from World War II caused capital per worker to be lower than its steady-state level, and thus output per worker was temporarily low.

5.

(a) sf(k) = (n + d)k 0.3 ´ 3k.5 = (0.05 + 0.1)k 0.9k.5 = 0.15k 0.9/0.15 = k/k.5 6 = k.5 k = 62 = 36 y = 3k.5 = 3 ´ 6 = 18 c = y - (n + d)k = 18 - (0.15 ´ 36) = 12.6 (b) sf(k) = (n + d)k 0.4 ´ 3k.5 = (0.05 + 0.1)k 1.2k.5 = 0.15k 1.2/0.15 = k/k.5 8 = k.5 k = 82 = 64 y = 3k.5 = 3 ´ 8 = 24 c = y - (n + d)k = 24 - (0.15 ´ 64) = 14.4 (c) sf(k) = (n + d)k 0.3 ´ 3k.5 = (0.08 + 0.1)k 0.9k.5 = 0.18k 0.9/0.18 = k/k.5 5 = k.5

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k = 52 = 25 y = 3k.5 = 3 ´ 5 = 15 c = y – (n + d)k = 15 - (0.18 ´ 25) = 10.5 (d) sf(k) = (n + d)k 0.3 ´ 4k.5 = (0.05 + 0.1)k 1.2k.5 = 0.15k 1.2/0.15 = k/k.5 8 = k.5 k = 82 = 64 y = 4k.5 = 4 ´ 8 = 32 c = y – (n + d)k = 32 - (0.15 ´ 64) = 22.4 6.

(a) In steady state, sf(k) = (n + d)k 0.1 ´ 6k.5 = (0.01 + 0.14)k 0.6k.5 = 0.15k 0.6/0.15 = k/k.5 4 = k.5 k = 42 = 16 = capital per worker y = 6k.5 = 6 ´ 4 = 24 = output per worker c = .9 y = .9 ´ 24 = 21.6 = consumption per worker (n + d)k = 0.15 ´ 16 = 2.4 = investment per worker (b) To get y = 2 ´ 24 = 48, since y = 6k.5, then 48 = 6k.5, so k.5 = 8, so k = 64. The capital-labor ratio would need to increase from 16 to 64. To get k = 64, since sf(k) = (n + d)k, s ´ 48 = 0.15 ´ 64, so s = 0.2. Saving per worker would need to double.

7.

First, derive saving per worker as sy = y - c - g = [1 - 0.5(1 - t) - t] 8k.5 = 0.5(1 - t)8k.5 = 4 (1 - t)k.5 (a) When t = 0, sy = 4 (1 - 0)k.5 = 4k.5 = national saving per worker Investment per worker = (n + d)k = 0.1k In steady state, sy = (n + d)k, so 4k.5 = 0.1k, or 40k.5 = k, so 1600k = k2, so k = 1600. Since k = 1600, y = 8 ´ 1600.5 = 320, c = 0.5(1 - 0)320 = 160, and (n + d)k = 0.1 ´ 1600 = 160 = investment per worker. (b) When t = 0.5, sy = 4 (1 - 0.5)k.5 = 2k.5 = national saving per worker Investment per worker = (n + d)k = .1k In steady state, sy = (n + d)k, so 2k.5 = 0.1k, or 20k.5 = k, so 400k = k2, so k = 400. Since k = 400, y = 8 ´ 400.5 = 160, c = 0.5(1 - 0.5)160 = 40, and (n + d)k = 0.1 ´ 400 = 40 = investment per worker, g = ty = 0.5 ´ 160 = 80.

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Analytical Problems 1.

(a) The destruction of some of a country’s capital stock in a war would have no effect on the steady state, because there has been no change in s, f, n, or d. Instead, k is reduced temporarily, but equilibrium forces eventually drive k to the same steady-state value as before. (b) Immigration raises n from n1 to n2 in Figure 6.3. The rise in n lowers steady-state k, leading to a lower steady-state consumption per worker.

Figure 6.3 (c) The rise in energy prices reduces the productivity of capital per worker. This causes sf(k) to shift down from sf 1(k) to sf 2(k) in Figure 6.4. The result is a decline in steady-state k. Steady-state consumption per worker falls for two reasons: (1) Each unit of capital has a lower productivity, and (2) steady-state k is reduced.

Figure 6.4 (d) A temporary rise in s has no effect on the steady-state equilibrium. (e) The increase in the size of the labor force does not affect the growth rate of the labor force, so there is no impact on the steady-state capital-labor ratio or on consumption per worker. However, because a larger fraction of the population is working, consumption per person increases.

.

150

2.

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(a) Solow model The rise in capital depreciation shifts up the (n + d)k line from (n + d1)k to (n + d2)k, as shown in Figure 6.5. The equilibrium steady-state capital-labor ratio declines. With a lower capital-labor ratio, output per worker is lower, so consumption per worker is lower (using the assumption that the capital-labor ratio is not so high that an increase in k will reduce consumption per worker).

There is no effect on the long-run growth rate of the total capital stock, because in the long run the capital stock must grow at the same rate (n) as the labor force grows, so that the capital-labor ratio is constant.

Figure 6.5 (b) Endogenous growth model In an endogenous growth model, the growth rate of output is DY/Y = sA - d, so the rise in the depreciation rate reduces the economy’s growth rate. Similarly, the growth rate of capital equals DK/K = sA - d, which also declines when the depreciation rate rises. Since consumption is a constant fraction of output, its growth rate declines as well. So the increase in the depreciation rate reduces the long-run growth rate of the capital stock, as well as long-run capital, output, and consumption per worker.

3.

(a) With a balanced budget T/N = g. National saving is S = s(Y – T) = sN[(Y/N) - (T/N)] = sN( y – g). Setting saving equal to investment gives S = I, sN(y – g) = (n + d)K, s(y – g) = (n + d)k, s[f(k) – g] = (n + d)k.

This equilibrium point k* is shown in Figure 6.6.

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Figure 6.6 (b) If the government permanently increases purchases per worker, the s[ f(k) – g] curve shifts down from s[ f(k) – g1] to s[ f(k) – g2] in Figure 6.7. In steady-state equilibrium, the capital-labor ratio is lower. Output per worker, capital per worker, and consumption per worker are lower in the steady state. The optimal level of government purchases is not zero—it depends on the benefits of the government purchases as well as on the costs of these purchases.

Figure 6.7 4.

St = sYt – hKt = Nt(syt – hkt). Setting St = It yields Nt(syt – hkt) = (n + d)Kt. Dividing through by Nt and eliminating time subscripts for steady-state variables gives sy – hk = (n + d)k. Rearranging and using the expression y = f(k) gives sf(k) = (n + d + h)k.

The steady-state value of capital per worker, k*, is given by the intersection of the (n + d + h)k line with the sf(k) curve, as shown in Figure 6.8. Output per worker is f(k*). Since Ct = Yt – St, c = y – (sy – hk) = (1 – s)f(k*) + hk*. This expression gives consumption per worker.

.

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Figure 6.8 A change in the steady-state value of h increases the slope of the (n + d + h)k line, as shown in Figure 6.9. This reduces the steady-state value of per-worker capital (k*), per-worker output [since y* = f(k*)], and per-worker consumption [since c* = (1 - s)y* + hk* and both y* and k* decline].

Figure 6.9 5.

The initial level of the capital-labor ratio is irrelevant for the steady state. Two economies that are identical except for their initial capital-labor ratios will have exactly the same steady state.

Since the two economies must have the same growth rate at the steady state, and since the economy with the higher current capital-labor ratio has higher current output per worker, then the country with the lower current capital-labor ratio must grow faster.

The answer holds true regardless of which country is in a steady state. If the country with a higher initial capital-labor ratio is in a steady state at capital-labor ratio k*, then the other country’s capitallabor ratio will rise until it too equals k*. So the country with the lower capital-labor ratio grows faster than the one with the higher capital-labor ratio.

If the country with the lower initial capital-labor ratio is in a steady state at capital-labor ratio k*, then the other country’s capital-labor ratio is too high and it will decline until it equals k*. So the country with the higher capital-labor ratio must grow more slowly than the country with the lower capital-

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labor ratio. If the two countries are allowed to trade with each other, then their convergence to the same capital-labor ratio and output per worker will occur even faster.

6.

The growth accounting equation is DY/Y = DA/A + (aK DK/K) + (aN DN/N).

We are just increasing the amount of capital and labor, and there is no change in productivity, so DA/A = 0. If the production function can be written in per-worker terms, then total output must increase in the same proportion as the percentage increase in capital and labor, so DK/K = DN/N = DY/Y = X. Plugging this into the growth accounting equation, DY/Y = DA/A + (aK DK/K) + (aN DN/N), X = 0 + aKX + aNX, X = (aK + aN)X, aK + aN = 1.

7.

Assume there are a constant number of workers, N, so that Ny = Y and Nk = K. Since y = Akah1–a and h = Bk, then y = Ak a(Bk)1–a = (AB1–a)k. Then Y = Ny = (AB1–a)K = XK, where X equals AB1–a. This puts the production function in notation used in the chapter.

Investment is DK + dK = sY = national saving. Dividing through both sides of that expression by K and using the production function gives DK/K + d = sXK/K = sX, so DK/K = sX - d, which is the longrun growth rate of physical capital. Since output and human capital are proportional to physical capital, they will all grow at that same rate.

.

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Working with Macroeconomic Data 1.

a. After 1973, productivity contributes less to GDP growth than before 1973. Productivity’s contribution declines sharply in the 1970s and early 1980s. b. Large spikes upward in oil prices are associated with large downward spikes in the contribution of productivity to GDP growth, suggesting that oil shocks contribute substantially to declines in GDP. 2.

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The capital-labor ratio looks like it has stabilized in the past 7 years but both output per person and consumption per person continue to rise. According to the Solow model, these can rise if capital per worker rises or if TFP rises. Since the capital-labor ratio has been steady for the past 7 years, this suggests that TFP has continued to rise.

3.

Results here will depend on the countries picked and the time period chosen. There is some evidence that countries that start with low real output per capita grow faster than countries that start with higher output per capita (China, for example), but it is not the case for all countries.

4.

In 2017, the data show the following GDP per capita (in 2010 U.S. dollars): U.S.

53,129

Japan

48,557

China

7,329

U.S. GDP per capita is 625% higher than China’s GDP per capita (as a percent of China’s GDP per capita).

If the growth rates over the past 25 years of 1.5% for the U.S. and 8.8% for China continued in the future, China’s GDP per capita would exceed U.S. GDP per capita in 2046 (based on data through 2017).

.

Chapter 7 The Asset Market, Money, and Prices n

Learning Objectives

I.

Goals of Chapter 7 A. Define money, discuss its functions, and describe how it is measured in the United States (Sec. 7.1) B. Discuss the factors that affect how people choose which assets they own (Sec. 7.2) C. Examine macroeconomic variables that affect the demand for money (Sec. 7.3) D. Discuss the fundamentals of asset market equilibrium (Sec. 7.4) D. Discuss the relationship between money growth and inflation (Sec. 7.5)

II.

Notes to Ninth Edition Users A. We added an application on “Bitcoin and Cryptocurrencies”

.

Chapter 7 The Asset Market, Money, and Prices

n

Teaching Notes

I.

What Is Money? (Sec. 7.1)

157

A. Money: assets that are widely used and accepted as payment B. The functions of money 1. Medium of exchange a. Barter is inefficient—it requires a double coincidence of wants b. Money allows people to trade their labor for money and then use the money to buy goods and services in separate transactions c. Money thus permits people to trade with less cost in time and effort d. Money also allows specialization, since trading is much easier, so people do not have to produce their own food, clothing, and shelter

Theoretical Application There have been a number of attempts to supply detailed microfoundations theory for money. An explicit theory that shows the superiority of money to barter has been developed by Nobuhiro Kiyotaki and Randall Wright (“On Money as a Medium of Exchange,” Journal of Political Economy, August 1989, pp. 927–954). They show how introducing fiat money unambiguously improves society’s welfare. Much recent research builds on this type of money model.

2. Unit of account a. Money is the basic unit for measuring economic value b. This simplifies comparisons of prices, wages, and incomes c. The unit-of-account function is closely linked with the medium-of-exchange function d. But countries with very high inflation may use a different unit of account, so they do not have to constantly change prices 3. Store of value a. Money can be used to hold wealth b. Most people use money only as a store of value for a short period and for small amounts, because it earns less interest than money in the bank

Theoretical Application Money’s usefulness as a store of value declines the higher the inflation rate. In hyperinflations (very high inflations), people try to avoid the use of money; on receiving their wages, they rush to buy things before prices rise. And they tend to use currencies other than their own, a phenomenon known as currency substitution.

4. In touch with data and research: money in a prisoner-of-war camp a. Radford article on the use of cigarettes as money b. Cigarette use as money developed because barter was inefficient c. Even nonsmokers used cigarettes as money d. Characteristics of cigarettes as money: standardized (so value was easy to ascertain), low in value (so “change” could be made), portable, fairly sturdy e. Problem with having commodity money like cigarettes: cannot smoke them and use them as money at the same time

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Policy Application For an introduction to how technological changes affect the role for money in the economy, see the article by James J. McAndrews, “Making Payments on the Internet,” Federal Reserve Bank of Philadelphia Business Review, January/February 1997.

C. Measuring money—the monetary aggregates 1. Distinguishing what is money from what isn’t money is sometimes difficult a. For example, MMMFs allow check writing but give a higher return than bank checking accounts: Are they money? b. There’s no single best measure of the money stock 2. The M1 monetary aggregate a. Consists of currency and traveler’s checks held by the public, and transaction accounts (which allow the owner to write checks) b. All components of M1 are used in making payments, so M1 is the closest money measure to our theoretical description of money 3. The M2 monetary aggregate a. M2 = M1 + less money like assets b. Additional assets in M2 include savings deposits, small (< $100,000) time deposits, noninstitutional MMMF balances, money-market deposit accounts (MMDAs) (1) Savings deposits include passbook savings accounts (2) Time deposits bear interest and have a fixed term (substantial penalty for early withdrawal) (3) MMMFs invest in very short-term securities and allow limited check writing (4) MMDAs are offered by banks as a competitor to MMMFs 4. Table 7.1 shows recent data 5. In touch with data and research: the monetary aggregates a. The Federal Reserve Board of Governors compiles and reports data on M1 and M2 b. Data are released every Thursday afternoon c. Publication of the data keeps the public informed about how the Fed is changing the money supply Analytical Problem 1 looks at portfolio changes and how they affect M1 and M2 D. In touch with data and research: where have all the dollars gone?

1. In 2018, U.S. currency averaged about $4800 per person 2. Some is held by businesses and the underground economy, but 50% or more is held abroad 3. Foreigners hold dollars because of inflation in their local currency and political instability 4. The data show large fluctuations in M1 when major events occur abroad, for example, military conflicts 5. The United States benefits from foreign holdings of our currency, since we essentially get an interest-free loan E. The money supply 1. Money supply = money stock = amount of money available in the economy 2. How does the central bank of a country increase the money supply? a. Use newly printed money to buy financial assets from the public—an open-market purchase

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b. To reduce the money supply, sell financial assets to the public to remove money from circulation—an open-market sale c. Open-market purchases and sales are called open-market operations d. Could also buy newly issued government bonds directly from the government (i.e., the Treasury) (1) This is the same as the government financing its expenditures directly by printing money (2) This happens frequently in some countries (though is forbidden by law in the United States) 3. Throughout the text, use the variable M to represent money supply; this might be M1, M2, or some other aggregate II. Portfolio Allocation and the Demand for Assets (Sec. 7.2) How do people allocate their wealth among various assets? The portfolio allocation decision A. Expected return 1. Rate of return = an asset’s increase in value per unit of time a. Bank account: Rate of return = interest rate b. Corporate stock: Rate of return = dividend yield + percent increase in stock price 2. Investors want assets with the highest expected return (other things equal) 3. Returns aren’t always known in advance (e.g., stock prices fluctuate unexpectedly), so people must estimate their expected return B. Risk 1. Risk is the degree of uncertainty in an asset’s return 2. People do not like risk, so prefer assets with low risk (other things equal) 3. The risk premium is the amount by which the expected return on a risky asset exceeds the return on an otherwise comparable safe asset

Theoretical Application Their separate work in developing financial theory brought the 1990 Nobel Prize in Economics to Harry Markowitz, Merton Miller, and William Sharpe. Their main contributions were to recognize the trade-off between risk and expected return (Markowitz), to develop the Capital Asset Pricing Model as a general equilibrium theory for pricing assets (Sharpe), and to examine the corporate financial decision about whether to raise funds via debt or equity (Miller). For an overview of their research, see Hal Varian, “A Portfolio of Nobel Laureates: Markowitz, Miller, and Sharpe,” Journal of Economic Perspectives, Winter 1993, pp. 159–169.

C. Liquidity 1. Liquidity is the ease and quickness with which an asset can be traded 2. Money is very liquid 3. Assets like automobiles and houses are very illiquid—it may take a long time and large transaction costs to trade them 4. Stocks and bonds are fairly liquid, some more so than others 5. Investors prefer liquid assets (other things equal) D. Time to maturity 1. Time to maturity: the amount of time until a financial security matures and the investor is repaid the principal

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2. Expectations theory of the term structure of interest rates: the idea that investors compare returns on bonds with differing times to maturity; in equilibrium, holding different types of bonds over the same period yields the same expected return 3. Because long-term interest rates usually exceed short-term interest rates, a risk premium exists: the compensation to an investor for bearing the risk of holding a long-term bond E. Types of assets and their characteristics 1. People hold many different assets, including money, bonds, stocks, houses, and consumer durable goods 2. Money has a low return, but low risk and high liquidity 3. Bonds have a higher return than money, but have more risk and less liquidity 4. Stocks pay dividends and can have capital gains and losses, and are much more risky than money 5. Ownership of a small business is very risky and not liquid at all, but may pay a very high return 6. Housing provides housing services and the potential for capital gains, but is quite illiquid 7. Households must consider what mix of assets they wish to own; text Table 7.2 shows the mix in 2006, 2009, and 2017. The table illustrates the large declines in the value of stocks, pension funds, and housing in the financial crisis and shows how the value of stocks and pension funds rebounded by 2017 to a level substantially higher than it was in 2006, while the value of housing surpassed its 2006 level by mid-2016 F.

In touch with data and research: the housing crisis of 2007 to 2011 1. People gained tremendous wealth in their houses in the 2000s 2. As house prices rose, houses became increasingly unaffordable, leading mortgage lenders to create subprime loans for people who would not normally qualify to buy houses 3. Most subprime loans had adjustable interest rates, with a low initial interest rate that would later rise in a process known as mortgage reset 4. As long as housing prices kept rising, both lenders and borrowers thought the subprime loans would work out, as the borrowers could always sell their houses to pay off the loans 5. But housing prices stopped rising as much, leading more subprime borrowers to default, so banks began to tighten their lending standards, reducing the demand for housing and leading housing prices to start falling (text Figure 7.1) 6. Many homeowners lost their homes and financial institutions lost hundreds of billions of dollars because of mortgage loan defaults 7. Because many mortgage loans had been securitized and were parts of mortgage-backed securities, the increased default rate on mortgages led to a financial crisis in Fall 2008, as many investors simultaneously tried to sell risky assets, including mortgage-backed securities and stocks

Data Application Was the housing crisis caused by insiders trying to capitalize on foolish homeowners or a failure by bank regulators? According to Christopher L. Foote, Kristopher S. Gerardi, and Paul S. Willen, in their paper “Why Did So Many People Make So Many Ex Post Bad Decisions? The Causes of the Foreclosure Crisis,” Federal Reserve Bank of Boston Public Policy Discussion Paper 12-2, May 2012, many people made bad decisions in an atmosphere that appeared to be a bubble in housing prices. Given views about future housing prices that turned out to be too optimistic, homeowners, lenders, and investors all made bad decisions.

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G. Asset demands 1. Trade-off among expected return, risk, liquidity, and time to maturity 2. Assets with low risk and high liquidity, such as checking accounts, have low expected returns 3. Investors consider diversification: spreading out investments in different assets to reduce risk 4. The amount a wealth holder wants of an asset is his or her demand for that asset 5. The sum of asset demands equals total wealth III. The Demand for Money (Sec. 7.3) A. The demand for money is the quantity of monetary assets people want to hold in their portfolios 1. Money demand depends on expected return, risk, and liquidity 2. Money is the most liquid asset 3. Money pays a low return 4. People’s money-holding decisions depend on how much they value liquidity against the low return on money B. Key macroeconomic variables that affect money demand 1. Price level a. The higher the price level, the more money you need for transactions b. Prices are 10 times as high today as 65 years ago, so it takes 10 times as much money for equivalent transactions c. Nominal money demand is thus proportional to the price level 2. Real income a. The more transactions you conduct, the more money you need b. Real income is a prime determinant of the number of transactions you conduct c. So money demand rises as real income rises d. But money demand is not proportional to real income, since higher-income individuals use money more efficiently, and since a country’s financial sophistication grows as its income rises (use of credit and more sophisticated assets) e. Result: Money demand rises less than 1-to-1 with a rise in real income 3. Interest rates a. An increase in the interest rate or return on nonmonetary assets decreases the demand for money b. An increase in the interest rate on money increases money demand c. This occurs as people trade off liquidity for return d. Though there are many nonmonetary assets with many different interest rates, because they often move together we assume that for nonmonetary assets there’s just one nominal interest rate, i e. The real interest rate, which affects saving and investment decisions, is r = i - pe f. The nominal interest paid on money is im C. The money demand function 1. Md = P ´ L(Y, i) a. Md is nominal money demand (aggregate) b. P is the price level c. L is the money demand function d. Y is real income or output e. i is the nominal interest rate on nonmonetary assets 2. As discussed above, nominal money demand is proportional to the price level 3. A rise in Y increases money demand; a rise in i reduces money demand

.

(7.1)

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4. We exclude im from Eq. (7.1) since it does not vary much 5. Alternative expression: Md = P ´ L(Y, r + pe)

(7.2)

A rise in r or p e reduces money demand 6. Alternative expression: Md/P = L(Y, r + pe)

(7.3)

7. The left side of Eq. (7.3) is the demand for real balances, or real money demand D. Other factors affecting money demand 1. Wealth: A rise in wealth may increase money demand, but not by much 2. Risk a. Increased riskiness in the economy may increase money demand b. Times of erratic inflation bring increased risk to money, so money demand declines 3. Liquidity of alternative assets: Deregulation, competition, and innovation have given other assets more liquidity, reducing the demand for money 4. Payment technologies: Credit cards, ATMs, and other financial innovations reduce money demand E. Application: Bitcoin and cryptocurrencies 1. Cryptocurrencies, such as Bitcoin, do not exist in physical form but only as records in a computer system 2. Bitcoin uses blockchain technology to record who owns how many bitcoins 3. Cryptocurrencies allow for anonymous transactions; so are sometimes used by tax evaders and criminals 4. Blockchain works by using public records verified by others and replicated by many computers throughout the system; the technology has many possible business applications 5. Shortcomings of cryptocurrencies include high transactions costs and lack of stable value, plus some questions about security F.

Elasticities of money demand 1. How strong are the various effects on money demand?

2. Statistical studies on the money demand function show results in elasticities 3. Elasticity: The percent change in money demand caused by a one percent change in some factor 4. Income elasticity of money demand a. Positive: Higher income increases money demand b. Less than one: Higher income increases money demand less than proportionately c. Goldfeld’s results: income elasticity = 2/3 5. Interest elasticity of money demand Small and negative: Higher interest rate on nonmonetary assets reduces money demand slightly 6. Price elasticity of money demand is unitary, so money demand is proportional to the price level

G. Velocity and the quantity theory of money 1. Velocity (V) measures how much money “turns over” each period 2. V = nominal GDP/nominal money stock = PY/M

.

(7.4)

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Numerical Problem 1 is an empirical exercise calculating velocity from a money-demand equation.

3. Plot of velocities for M1 and M2 (text Figure 7.2) shows fairly stable velocity for M2, erratic velocity for M1 beginning in early 1980s 4. Plot of money growth (text Figure 7.3) shows that instability in velocity translates into erratic movements in money growth Analytical Problem 2 asks for explanations for the upward trend in M1 velocity prior to the 1980s.

5. Quantity theory of money: Real money demand is proportional to real income a. If so, Md/P = kY

(7.5)

b. Assumes constant velocity, where velocity isn’t affected by income or interest rates c. But velocity of M1 is not constant; it rose steadily from 1960 to 1980 and has been erratic since then (1) Part of the change in velocity is due to changes in interest rates in the 1980s (2) Financial innovations also played a role in velocity’s decline in the early 1980s d. M2 velocity is closer to being a constant, but not over short periods

Data Application Using the idea that M2 velocity is stable, economists at the Federal Reserve Board developed an inflation model based on M2 growth. The model suggested that the price level would adjust to an equilibrium level, P*, that was determined mainly by the level of M2. See Jeffrey J. Hallman, Richard D. Porter, and David H. Small, “Is the Price Level Tied to the M2 Monetary Aggregate in the Long Run?” American Economic Review, September 1991, pp. 841–858. However, almost immediately after this article came out, M2 velocity began behaving very unpredictably, and the Federal Reserve deemphasized the use of M2 for policy purposes.

Policy Application The Federal Reserve’s job of conducting monetary policy is made more complicated by sweep programs. For an introduction to these problems, see “Sweep Accounts Lower Reserve Balances, Complicate Fed Funds Targeting” in the Federal Reserve Bank of Atlanta Financial Update, July–September 1999.

IV. Asset Market Equilibrium (Sec. 7.4) A. Asset market equilibrium—an aggregation assumption 1. Assume that all assets can be grouped into two categories, money and nonmonetary assets a. Money includes currency and checking accounts (1) Pays interest rate im (2) Supply is fixed at M b. Nonmonetary assets include stocks, bonds, land, etc.

(1) Pays interest rate i = r + p e (2) Supply is fixed at NM

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2. Asset market equilibrium occurs when quantity of money supplied equals quantity of money demanded a. md + nmd = total nominal wealth of an individual b. Md + NMd = aggregate nominal wealth (from adding up individual wealth) (7.6) c. M + NM = aggregate nominal wealth (supply of assets) (7.7) d. Subtracting (7.7) from (7.6) gives (Md - M) + (NMd - NM) = 0 (7.8) d e. So the excess demand for money (M - M) plus the excess demand for nonmonetary assets (NMd - NM) equals 0. f. So if money supply equals money demand, nonmonetary asset supply must equal nonmonetary asset demand; then the entire asset market is in equilibrium B. The asset market equilibrium condition 1. M/P = L(Y, r + p e) (7.9) real money supply = real money demand a. M is determined by the central bank b. p e is fixed (for now) c. The labor market determines the level of employment; using employment in the production function determines Y d. Given Y, the goods market equilibrium condition determines r Numerical Problem 2 is an exercise in calculating the equilibrium interest rate.

2. With all the other variables in Eq. (7.9) determined, the asset market equilibrium condition determines the price level a. P = M/L(Y, r + pe) (7.10) b. The price level is the ratio of nominal money supply to real money demand c. For example, doubling the money supply would double the price level For exercises dealing with price level determination, see Numerical Problems 3 and 5 and Analytical Problem 4.

Theoretical Application You might wonder why we do not show a diagram of money demand and money supply on the horizontal axis and the real interest rate on the vertical axis at this point in the textbook. The reason is that we need to talk about general equilibrium first, so we wait to introduce such a diagram until Chapter 9. Otherwise, students would correctly wonder why the goods market equilibrium diagram determines the real interest rate and at the same time the asset market equilibrium diagram also determines the real interest rate. Instead, for now, we just give them the idea that the asset market equilibrium determines the price level. Later, we will show how both markets come into equilibrium simultaneously.

V.

Money Growth and Inflation (Sec. 7.5) A. The inflation rate is closely related to the growth rate of the money supply 1. Rewrite Eq. (7.10) in growth-rate terms: DP/P = DM/M - DL(Y, r + pe)/L(Y, r + pe)

(7.11)

2. If the asset market is in equilibrium, the inflation rate equals the growth rate of the nominal money supply minus the growth rate of real money demand

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3. To predict inflation we must forecast both money supply growth and real money demand growth a. In long-run equilibrium, we will have i constant, so we look just at growth in Y b. Let hY be the elasticity of money demand with respect to income c. Then from Eq. (7.11),

p = DM/M - hY DY/Y

(7.12)

d. Example: If output grows 3% per year, the income elasticity of money demand is 2/3, and the money supply is growing at a 10% rate, then the inflation rate will be 8% Numerical Problem 4 gives practice in using elasticities to predict inflation.

B. Application: money growth and inflation in the European countries in transition 1. Though the countries of Eastern Europe are becoming more market-oriented, Russia and some others have high inflation because of rapid money growth 2. Both the growth rates of money demand and money supply affect inflation, but (in cases of high inflation) usually growth of nominal money supply is the most important factor a. For example, if the income elasticity of money demand were 2/3 and real output grew 15%, real money demand would grow 10% (= 2/3 ´ 15%); or if income fell 15%, real money demand would fall 10% b. So money demand does not vary much, no matter how well or poorly an economy is doing, but nominal money supply growth differs across countries by hundreds of percentage points, so large inflation differences must be due to money supply, not money demand 3. Text Figure 7.4 shows the link between money growth and inflation in these countries; inflation is clearly positively associated with money growth 4. So why do countries allow money supplies to grow quickly, if they know it will cause inflation? a. They sometimes find that printing money is the only way to finance government expenditures b. This is especially true for very poor countries, or countries in political crisis

Data Application For a review of the causes of inflation in the short run and long run in countries throughout the world, see Larry Ball’s article, “What Causes Inflation?” Federal Reserve Bank of Philadelphia Business Review, March/April 1993, pp. 3–12.

C. The inflation rate and the nominal interest rate 1. Expectations cannot be observed directly, except perhaps through surveys 2. If money growth is not expected to change much and if factors affecting money demand are stable, inflation may not change much, so the expected inflation rate would be approximately equal to the actual inflation rate 3. If the real interest rate is stable, then the nominal interest rate will move one for one with inflation Analytical Problem 3 shows how expected inflation depends on the money supply.

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Data Application There are many surveys of economists’ forecasts for inflation. The most well known monthly survey is Blue Chip Economic Indicators. Two surveys that are available free of charge are the quarterly Survey of Professional Forecasters, which began in 1968, and the semi-annual Livingston Survey, which began in 1946. The Federal Reserve Bank of Philadelphia produces both, and historical datasets on the surveys are available on the Internet at www.philadelphiafed.org/research-and-data/real-time-center.

3. Text Figure 7.5 plots U.S. inflation and nominal interest rates a. Inflation and nominal interest rates have tended to move together b. But the real interest rate is clearly not constant c. The real interest rate was negative in the mid-1970s and then became much higher and positive in the late-1970s to early-1980s; the real interest rate turned negative again following the financial crisis of 2008

Data Application A careful attempt to measure the world real interest rate was undertaken by Robert J. Barro and Xavier Sala-i-Martin, “World Real Interest Rates,” in O. Blanchard and S. Fischer, eds., NBER Macroeconomics Annual, Cambridge, MA: MIT Press, 1990, pp. 15–61.

D. Application: measuring inflation expectations 1. How do we find out people’s expectations of inflation? a. We could look at surveys b. But a better way is to observe implicit expectations from bond interest rates 2. The U.S. government issues nominal bonds and Treasury Inflation-Protected Securities (TIPS) a. TIPS bonds make real interest payments by adjusting interest and principal for inflation b. Compare nominal interest rate with real interest rate (text Figure 7.6) 3. The break-even inflation rate: interest rate on nominal bonds minus real interest rate on TIPS bonds a. The break-even inflation rate is a rough measure of expected inflation b. TIPS bonds have lower inflation risk, so the break-even inflation rate may be too high c. TIPS bonds do not have as liquid a market, so the break-even inflation rate may be too low d. The net effect of the two effects is likely to be small, so the break-even inflation rate may be about right 4. The data show fluctuations in the break-even inflation rate (text Figure 7.7) a. In contrast, the rate of expected inflation measured in surveys has been fairly constant b. Either bond market participants have very different inflation expectations than forecasters, or else the degree of inflation risk and liquidity on TIPS bonds varied substantially from 1998 on

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Additional Issues for Classroom Discussion

1.

How Has Technology Changed Money?

167

Ask your students how they think improved technology has changed the role of money in the economy.

They might mention such things as computer banking, which allow people to pay bills easier and to move money between accounts without difficulty; phone banking, allowing people to deposit checks without going to a bank; improved information systems, which allow banks to target credit cards for particular types of borrowers and which reduce fraud by authorizing transactions instantaneously. Even newer products include e-money, such as Bitcoin.

2.

How Will Money’s Role Change in the Future?

Imagine an age in which the balance in your checking account is invested immediately and automatically in the stock or bond market, earning substantially more interest than is typical today. Suppose all payments become electronic, so we never need to touch a dollar bill. What role would money play in such a payments system?

These questions have been discussed for the past 20 years, and while we are getting closer to such a system, it isn’t here yet. The idea is that we would no longer use currency as a store of value or as a medium of exchange, but it might continue to be used as a unit of account. After all, we have to have some unit in which we measure our investments and price our goods and services.

3.

Should You Buy Indexed Bonds?

Given a choice between buying nominal bonds and indexed bonds, what would you choose? Ask your students to list the pros and cons of buying indexed bonds.

You may need to give them a bit of historical background. Though introduced for the first time in the United States in 1997, bonds whose nominal payments adjust for inflation have been available in other countries for some time, beginning with Finland in 1945. Typically, countries have started issuing indexed bonds after a bout with inflation.

As you discuss the bonds with your students, you may want to note a few special features that prevent the bonds from being as desirable as an economist might like them to be. First, the principal of the bond is adjusted regularly, so that it maintains its real value, but you must pay taxes immediately on the principal adjustment. That is, before receiving the money, you get taxed on it. Also, because the U.S. government didn’t want to allow a tax advantage to the indexed bonds, taxes on principal and interest are both based on the nominal returns to the bonds, not the real returns. So the bonds don’t fully protect you against inflation, since your taxes will be higher as the inflation rate becomes higher.

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Answers to Textbook Problems

Review Questions 1. Money is the economist’s term for assets that can be used in making payments, such as cash and checking accounts. In everyday speech, people often use the term “money” to refer to their income or wealth, but in economics money means only those assets that are widely used and accepted as payment.

2. The three functions of money are (1) the medium of exchange function, which contributes to a betterfunctioning economy by allowing people to make trades at a lower cost in time and effort than in a barter economy; (2) the unit of account function, which provides a single, uniform measure of value; and (3) the store of value function, by which money is a way of holding wealth that has high liquidity and little risk.

3. The size of the nation’s money supply is determined by its central bank; in the United States, the central bank is the Federal Reserve System. If all money is in the form of currency, the money supply can be expanded if the central bank uses newly minted currency to buy financial assets from the public or directly from the government itself. To reduce the money supply, the central bank can sell financial assets to the public or the government, taking currency out of circulation.

4. The four characteristics of assets that are most important to wealth holders are (1) expected return, (2) risk, (3) liquidity; and (4) time to maturity. Money has a low expected return compared with other assets, low risk since it always maintains its nominal value, is the most liquid of all assets, and has the lowest (zero) time to maturity.

5.

The expectations theory of the term structure of interest rates originates in the idea that investors compare bonds with different times to maturity and choose the ones that yield the highest return. In equilibrium, the theory implies that the expected rate of return on an N-year bond should equal the average of the expected rates of return on one-year bonds during the current year and the N – 1 succeeding years.

The expectations theory is not sufficient because on average, long-term interest rates exceed shortterm interest rates, in violation of the theory’s implications. To form a more accurate theory, a risk premium must be added to the analysis.

6.

The macroeconomic variables that have the greatest impact on money demand are the price level, real income, and the nominal interest rate on other assets. The higher the price level, the higher the demand for money, since more units of money are needed to carry out transactions. The higher the level of real income, the higher the need for liquidity, and so the higher is money demand. When the nominal interest rate on other assets is high, the quantity of money demanded is low, because the opportunity cost of holding money (i.e., the interest you forgo on other assets because you are holding money instead) is high.

7. Velocity is a measure of how often money “turns over” in a period. It is equal to nominal GDP divided by the nominal money supply. The quantity theory of money assumes that velocity is constant, which implies that real money demand is proportional to real income and is unaffected by the real interest rate.

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8. Equilibrium in the asset market is described by the condition that real money supply equals real money demand because when supply equals demand for money, demand must also equal supply for nonmonetary assets. The aggregation assumption that is needed for this is that we can lump all wealth into two categories: (1) money and (2) nonmonetary assets.

9. In equilibrium, the price level is proportional to the nominal money supply; in particular it equals the nominal money supply divided by real money demand. Similarly, the inflation rate is equal to the growth rate of the nominal money supply minus the growth rate of real money demand.

10. Factors that could increase the public’s expected rate of inflation include a rise in money growth or a decline in income growth. With no effect on the real interest rate, the increase in the expected inflation rate would increase the nominal interest rate by the same amount.

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Numerical Problems 1.

For a two-year bond, according to the expectations theory, the interest rate would be the average of the two one-year bonds, which is (6% + 4%)/2 = 5%. Adding the risk premium of 0.5% gives an interest rate on the two-year bond of 5.5%.

For the three-year bond, according to the expectations theory, the interest rate would be the average of the three one-year bonds, which is (6% + 4% + 3%)/3 = 4.33%. Adding the risk premium of 1.0% gives an interest rate on the three-year bond of 5.33%.

The yield curve would show the interest rate on a one-year bond of 6%, the interest rate on a two-year bond of 5.55%, and the interest rate on a three-year bond of 5.33%, so it would be downward sloping, which is called “inverted” in the market.

2.

(a) Real money demand is Md/P = 500 + 0.2Y - 1000i = 500 + (0.2 ´ 1000) - (1000 ´ 0.10) = 600.

Nominal money demand is Md = (Md/P) ´ P = 600 ´ 100 = 60,000.

Velocity is V = PY/Md = 100 ´ 1000/60,000 = 1 2/3. (b) Real money demand is unchanged, because neither Y nor i has changed.

Nominal money demand is Md = (Md/P) ´ P = 600 ´ 200 = 120,000.

Velocity is unchanged, because neither Y nor Md/P has changed, and we can write the equation for velocity as V = PY/Md = Y/(Md/P). (c) It is useful to use the last expression for velocity, V = Y/(Md/P) = Y/(500 + 0.2Y - 1000i).

(1) Effect of increase in real income: When i = 0.10, V = Y/[500 + 0.2Y – (1000 ´ 0.10)] = Y/(400 + 0.2Y) = 1/[(400/Y) + 0.2].

When Y increases, 400/Y decreases, so V increases. For example, if Y = 2000, then V = 2.5, which is an increase over V = 1 2/3 that we got when Y = 1000.

(2) Effect of increase in the nominal interest rate: When Y = 1000, V = 1000/[500 + (0.2 ´ 1000) - 1000i] = 1000/(700 - 1000i) = 1/(0.7 - i).

(3)

When i increases, 0.7 - i decreases, so V increases. For example, if i = 0.20, then V = 2, which is an increase over V = 1 2/3 that we got when i = 0.10.

Effect of increase in the price level: There is no effect on velocity, since we can write velocity as a function just of Y and i.

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Nominal money demand changes proportionally with the price level, so that real money demand, and hence velocity, is unchanged.

3.

(a) Md = $100,000 - $50,000 - [$5000 ´ (i - im) ´ 100]. (Multiplying by 100 is necessary since i and im are in decimals, not percent.) Simplifying this expression, we get Md = $50,000 - $500,000(i - im). (b) Bd = $50,000 + $500,000(i - im).

Adding these together we get Md + Bd = $100,000, which is Mr. Midas’s initial wealth. (c) This can be solved either by setting money supply equal to money demand, or by setting bond supply equal to bond demand.

Md = Ms, so $50,000 - $500,000(i - im) = $20,000 $30,000 = $500,000 i

[Setting im = 0]

i = 0.06 = 6% Bd = Bs, so $50,000 + $500,000i = $80,000 $500,000i = $30,000 i = 0.06 = 6% 4.

(a) From the equation MV = PY, we get M/P = Y/V. At equilibrium, Md = M, so Md/P = Y/V = 10,000/5 = 2000. Md = P ´ (Md/P) = 2 ´ 2000 = 4000. (b) From the equation MV = PY, P = MV/Y. When M = 5000, P = (5000 ´ 5)/10,000 = 2.5.

When M = 6000, P = (6000 ´ 5)/10,000 = 3.

5.

(a) DP/P = - hY DY/Y = - 0.5 ´ 6% = -3%. The price level will be 3% lower. (b) DP/P = - hr Dr/r = -(-0.1) ´ 0.1 = 1%. The price level will be 1% higher. (c) With changes in both income and the real interest rate, to get an unchanged price level would require hY DY/Y + hr Dr/r = 0, so [0.5 ´ (Y – 100)/100] - [0.1 ´ 0.1] = 0, so Y = 102.

6.

(a) p e = DM/M = 10%. i = r + pe = 15%. M/P = L = 0.01 ´ 150/0.15 = 10. P = 300/10 = 30. (b) p e = DM/M = 5%. i = r + pe = 10%. M/P = L = 0.01 ´ 150/0.10 = 15. P = 300/15 = 20. The slowdown in money growth reduces expected inflation, increasing real money demand, thus lowering the price level.

7.

(a) With a constant real interest rate and zero expected inflation, inflation is given by the equation p = DM/M - hY DY/Y. To get inflation equal to zero, the central bank should set money growth so that DM/M = hY DY/Y = 2/3 ´ 0.045 = 0.03 = 3%. Note that the interest elasticity is not relevant, since interest rates don’t change. (b) Since V = PY/M, DV/V = DP/P + DY/Y – DM/M = 0 + 0.045 - 0.03 = 0.015 So velocity should rise 1.5% over the next year.

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Analytical Problems 1.

(a) People would probably take money out of checking accounts and put it into money market mutual funds and money market deposit accounts. Money market mutual funds and money market deposit accounts are included in M2 but are not part of M1. The result is a decrease in M1, but no change in M2. M2 does not increase because M1 is part of M2, so the decrease in M1 offsets the increase in the rest of M2. (b) This would reduce both M1 and M2, as people would have reduced need for money in checking accounts, and home equity lines of credit are not included in either M1 or M2. (c) If people fear a stock market collapse, they will want greater liquidity, so they will hold more money. Also, since stocks are an alternative asset to money, and the expected return to stocks has fallen, money demand will increase. Both effects will lead to people investing less in stocks and more in cash, checking accounts, and other items that provide liquidity and safety, so M1 and M2 will both rise. (d) People would have less need for money in checking accounts, and would put more in savings deposits. So M1 will decrease, while M2 will remain unchanged. (Again, M1 is part of M2, so reducing the amount that is in M1, and increasing the amount that is in M2 but not in M1, has no effect on M2.) (e) If currency demand falls, this decreases M1, thus also decreasing M2.

2. The general rise in velocity from 1959 to 1980 is most likely due to changes in income, in interest rates, and in financial institutions. Higher income led to a less than proportional rise in real money demand, so velocity increased. Rising inflation and rising nominal interest rates in this period led people to seek alternatives to non–interest-bearing money, such as money market mutual funds.

The result was lower money demand, and thus higher velocity. Financial innovations also reduced the need for money. Examples include the development of cash management accounts and the use of automated teller machines.

3.

(a) New cigarettes mean an increase in the money supply. With higher nominal money supply and no change in real money demand, the equilibrium price level must rise. (b) If people anticipate prices rising when the new cigarettes arrive, they will hold less money so that they will not lose purchasing power when prices go up. But if their real money demand is reduced, with the same nominal money supply the equilibrium price level must rise. The result is that when prices are anticipated to rise in the future, people may take actions that cause prices to rise immediately.

4.

(a) A temporary increase in government purchases reduces national saving, causing the real interest rate to rise for a fixed level of income. If the real interest rate is higher, then real money demand will be lower. So prices must rise to make money supply equal money demand. The result is that output is unchanged, the real interest rate increases, and the price level increases. (b) When expected inflation falls, real money demand increases. With no effect on employment or saving and investment, output and the real interest rate remain unchanged. With higher real money demand and an unchanged nominal money supply, the equilibrium price level must decline. So output and the real interest rate are unchanged and prices decline. (c) When labor supply rises, full-employment output increases. Also, with higher output, saving will increase, so the real interest rate will decline. Both higher output and a lower real interest rate increase real money demand. The price level must decline to equate money supply with money demand. The result is an increase in output and a decrease in both the real interest rate and the price level.

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(d) When the interest rate paid on money increases, real money demand rises. With no effect on employment or saving and investment, output and the real interest rate remain unchanged. With higher real money demand and an unchanged nominal money supply, the equilibrium price level must decline. So output and the real interest rate are unchanged and prices decline.

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Working with Macroeconomic Data 1.

Answers vary, depending on recent data.

2.

In the 1960s and early 1970s, M1 growth was more closely related to inflation. In the 1980s, M2 growth was more closely related to inflation. The relationships are stronger in the long run than in the short run. The relationship between M2 growth and inflation weakened after 1990.

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3.

a.

In general, interest rates move in the same direction as inflation. That is not surprising because if real interest rates do not change too much, and because the nominal interest rate equals the real interest rate plus the inflation rate (if actual and expected inflation rates are similar), then nominal interest rates will move in the same direction as inflation.

b.

Because the inflation measure is a short-term one, 3-month T-Bill rates move more in tandem with inflation than the 10-year T-bond. The ten-year rate would be sensitive to long-run changes in inflation, but many inflation movements are short-lived.

4.

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Net worth as a percentage of income was generally rising from 1975 to 1983, from 1984 to 1987, from 1995 to 2000, from 2002 to 2006, and from 2011 to 2018. It was generally falling from 1960 to 1975, 1983 to 1984, 2000 to 2002, and 2006 to 2011. From the fourth quarter of 2007 to the second quarter of 2009, it declined by 17 percent.

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Chapter 8 Business Cycles n

Learning Objectives

I.

Goals of Part 3 A. What causes business cycles?

B. How should policymakers respond to cyclical fluctuations?

1. Classical economists see little need for government action 2. Keynesian economists think government intervention can smooth the business cycle C. Coverage of Chapters 8 to 11 1. Business cycle facts and features (Ch. 8) 2. The basic IS–LM model (Ch. 9) 3. The classical model of the business cycle (Ch. 10) 4. The Keynesian model of the business cycle (Ch. 11)

II. Goals of Chapter 8 A. Define and describe the business cycle (Sec. 8.1) B. Summarize the history of the American business cycle (Sec. 8.2) C. Describe the behavior of various variables over the course of the business cycle (Sec. 8.3) D. Use aggregate demand and aggregate supply to describe the impact on business cycles of various shocks (Sec. 8.4) III. Notes to Ninth Edition Users A. This is a chapter with a lot of data, so the main change is to update all the data B. We add two key terms defining aggregate demand and aggregate supply more carefully than before C. We add a new application, “Do economic expansions die of old age?”

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Teaching Notes

I.

What Is a Business Cycle? (Sec. 8.1) A. U.S. research on cycles began in 1920 at the National Bureau of Economic Research (NBER) 1. NBER maintains the business cycle chronology—a detailed history of business cycles 2. NBER sponsors business cycle studies

Data Application A major compendium of studies on the business cycle was produced by the NBER in 1986, The American Business Cycle: Continuity and Change, edited by Robert J. Gordon, Chicago: University of Chicago Press. It contains general discussions of the then-current state of knowledge of the business cycle, research on components of expenditure and how they change over the cycle, discussions of the role of fiscal and monetary policies, and research on how the cycle has changed over time.

Another NBER volume that is a great resource on business cycle information is Victor Zarnowitz’s book, Business Cycles: Theory, History, Indicators, and Forecasting, Chicago: University of Chicago Press, 1992. Zarnowitz discusses theories and evidence on the business cycle, including the NBER’s research role, research on the cyclical characteristics of cycles, an evaluation of coincident and leading indicators, and a broad discussion of many aspects of business cycle forecasting.

B. Burns and Mitchell (Measuring Business Cycles, 1946) make five main points about business cycles: 1. Business cycles are fluctuations of aggregate economic activity, not a specific variable 2. There are expansions and contractions a. Aggregate economic activity declines in a contraction or recession until it reaches a trough (Figure 8.1)

Figure 8.1 b. Then activity increases in an expansion or boom until it reaches a peak

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c. A particularly severe recession is called a depression d. The sequence from one peak to the next, or from one trough to the next, is a business cycle e. Peaks and troughs are turning points f. Turning points are officially designated by the NBER Business Cycle Dating Committee Data Application The NBER Business Cycle Dating Committee must wait for some time to pass before they can declare the start or end of a recession. For example, in the latest recession, the committee announced in November 2008 that the recession had begun in December 2007; that’s 11 months after the recession began. And they announced in September 2012 that the recession had ended in June 2009; that’s 15 months later. The long time lags are necessary because data are often revised and because the committee wants to ensure that there is truly a turning point in the economy, not just a temporary change in direction.

For a discussion of the committee’s reasons for picking the dates that begin and end recessions, see the NBER web site at www.nber.org.

3. Economic variables show comovement—they have regular and predictable patterns of behavior over the course of the business cycle 4. The business cycle is recurrent, but not periodic a. Recurrent means the pattern of contraction–trough–expansion–peak occurs again and again b. Not being periodic means that it doesn’t occur at regular, predictable intervals 5. The business cycle is persistent a. Declines are followed by further declines; growth is followed by more growth b. Because of persistence, forecasting turning points is quite important

Theoretical Application Should we even care about the business cycle? Robert Lucas does not think so. In his provocative book, Models of Business Cycles, Oxford: Basil Blackwell, 1987, he suggests that the cost of business cycle instability since World War II is very low; in particular, the cost is one-fifth the cost of having an inflation rate of 10%. So, if faced with the choice of eliminating all recessions and having a 10% inflation rate, or having recessions the size we’ve had since 1945 and having no inflation at all, Lucas argues we should take the latter. He suggests that we should move toward a microeconomic view of the business cycle.

Data Application New economic theories and statistical techniques may change somewhat the way in which we look at data on the business cycle. The real business cycle (RBC) approach, which will be discussed in more detail in Chapter 10, suggests alternative interpretations of business cycle data, as Finn Kydland and Ed Prescott show in their article, “Business Cycles: Real Facts and a Monetary Myth,” Federal Reserve Bank of Minneapolis Quarterly Review, Spring 1990, pp.

3–18. They provide a basic set of facts (viewed through the lens of RBC theory) about the movement of economic variables over the business cycle. They also suggest that inflation is not procyclical in the United States since World War II, but seems to be countercyclical.

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II. The American Business Cycle: The Historical Record (Sec. 8.2) A. Text Table 8.1 gives the NBER business cycle chronology B. The pre–World War I period 1. Recessions were common from 1865 to 1917, with 338 months of contraction and 382 months of expansion [compared with 642 months of expansion and 122 months of contraction from 1945 to 2009] 2. The longest contraction on record was 65 months, from October 1873 to March 1879 C. The Great Depression and World War II 1. The worst economic contraction was the Great Depression of the 1930s a. Real GDP fell nearly 30% from the peak in August 1929 to the trough in March 1933 b. The unemployment rate rose from 3% to nearly 25% c. Thousands of banks failed, the stock market collapsed, many farmers went bankrupt, and international trade was halted d. There were really two business cycles in the Great Depression (1) A contraction from August 1929 to March 1933, followed by an expansion that peaked in May 1937 (2) A contraction from May 1937 to June 1938 e. By May 1937, output had nearly returned to its 1929 peak, but the unemployment rate was high (14%) f. In 1939 the unemployment rate was over 17% 2. The Great Depression ended with the start of World War II a. Wartime production brought the unemployment rate below 2% b. Real GDP almost doubled between 1939 and 1944 D. Post–World War II business cycles 1. From 1945 to 1970 there were five mild contractions 2. A very long expansion (106 months, from February 1961 to December 1969) made some economists think the business cycle was dead 3. But the OPEC oil shock of 1973 caused a sharp recession, with real GDP declining 3%, the unemployment rate rising to 9%, and inflation rising to over 10% 4. The 1981–1982 recession was also severe, with the unemployment rate over 11%, but inflation declining from 11% to less than 4% 5. The 1990–1991 recession was mild and short, but the recovery was slow and erratic E. The long boom 1. From 1982 to 2001, there was only one brief recession, from July 1990 to March 1991, which was not very severe 2. The volatility of many macroeconomic variables declined sharply, so the Long Boom was the first part of the period known as the Great Moderation

Data Application When the expansion of the 1990s became the longest in U.S. history in early 2000, the Wall Street Journal ran a special series of articles, “A Century of Booms, and How They Ended” in its February 1, 2000 issue.

F.

The Great Recession 1.

The longest and deepest recession since the Great Depression; began in December 2007

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a. b.

The Great Recession began with a housing crisis (described in Chapter 7) The housing crisis was followed by a financial crisis that rivaled that of the Great Depression (described in greater detail in Chapter 14) 2. The unemployment rose above 10% for the first time since 1982 and the Fed reduced interest rates to near zero 3. Economic growth was sluggish even after the recession ended in 2009

Data Application For an examination of how various macroeconomic variables, especially consumer spending, performed during the Great Recession, see the article by Mariacristina DeNardi, Eric French, and David Benson, “Consumption and the Great Recession,” Federal Reserve Bank of Chicago Economic Perspectives First Quarter 2012, pp. 1–16.

G. Have American business cycles become less severe?

1. Economists believed that business cycles were not as bad after World War II as they were before 2. The average contraction before 1929 lasted 21 months compared with 11 months after 1945 3. The average expansion before 1929 lasted 25 months compared with 50 months after 1945 4. Romer’s 1986 article sparked a strong debate, as it argued that pre-1929 data was not measured well, and that business cycles were not that bad before 1929 5. New research has focused on the reasons for the decline in the volatility of U.S. output a. Stock and Watson’s research showed that the decline came from a sharp drop in volatility around 1984 for many economic variables; dubbed the Great Moderation b. A plot of real GDP growth (text Figure 8.2) shows that the quarterly growth rate of GDP was more stable after 1984 c. A plot of the standard deviations of GDP, consumption, and investment (text Figure 8.3) confirms the decline in volatility d. Stock and Watson found that the change from manufacturing to services was not a major cause of the reduction in volatility e. Stock and Watson showed that evidence that changes in how firms managed their inventories, which some researchers thought was the main source of the drop in volatility, was sensitive to the empirical method used, and thus not a convincing explanation f. Improvements in housing markets may have contributed to the decline in volatility, but cannot explain the sudden drop in volatility, as those changes occurred gradually over time g. Reduced volatility in oil prices was also not an important factor in reducing the volatility of output 6. After showing that many theories for the reduced volatility in output were not convincing, Stock and Watson found three factors that were important a. Reductions in the volatility of food and other commodity prices account for about 15% of the volatility in output b. Reduced fluctuations in productivity were responsible for another 15% of the reduction in output’s volatility c. Improvements in monetary policy were the most important factor, accounting for 20% to 30% of the reduction in the volatility of output d. The remaining reduction in output’s volatility remains unexplained–some unknown form of good luck in terms of smaller shocks to the economy

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7. It is not yet clear if the Great Recession implies that the Great Moderation has ended, though the decline in volatility in 2014 suggests that perhaps the Great Moderation is continuing H. Application “Do economic expansions die of old age?”

1.

Does the probability that an expansion will end rise as the expansion ages? a.

Rudebusch uses survival analysis to look at the probabilities b.

Prior to World War II, the probability of an expansion ending rose a lot as an expansion went on c.

But after World War II, the probability of an expansion ending no longer rises as the expansion continues (text Fig. 8.4)

Data Application Frank Diebold and Glenn Rudebusch argue that although the debate between Romer and others about the volatility of business cycles before 1929 compared to after 1945 is unsettled, there is clear and convincing evidence that the duration of expansions and contractions has changed. The average length of the business cycle remains about the same, but expansions have become much longer and contractions much shorter. See their article, “Shorter Recessions and Longer Expansions,” Federal Reserve Bank of Philadelphia Business Review, November/December 1991, pp. 13–20.

III. Business Cycle Facts (Sec. 8.3) A. All business cycles have features in common B. The cyclical behavior of economic variables—direction and timing 1. What direction does a variable move relative to aggregate economic activity? a. Procyclical: in the same direction b. Countercyclical: in the opposite direction c. Acyclical: with no clear pattern 2. What is the timing of a variable’s movements relative to aggregate economic activity? a. Leading: in advance b. Coincident: at the same time c. Lagging: after

Data Application Your students may enjoy looking at macro data on their own to see what is out there. Some good Internet sites that can be used for free are: (1) Federal Reserve Bank of St. Louis FRED database (research.stlouisfed.org/fred2); (2) Economic Report of the President (fraser.stlouisfed.org/title/45); and (3) National Bureau of Economic Research (www.nber.org).

C. Cyclical behavior of key macroeconomic variables (text Figures 8.5 to 8.13) 1. Procyclical a. Coincident: industrial production, consumption, business fixed investment, and employment b. Leading: residential investment, inventory investment, average labor productivity, money growth, and stock prices c. Lagging: inflation, nominal interest rates d. Timing not designated: government purchases, real wage

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Analytical Problem 3 looks at whether output or total hours worked is more volatile, given that average labor productivity is procyclical.

2. Countercyclical: unemployment (timing is unclassified) 3. Acyclical: real interest rates (timing is not designated) 4. Volatility: durable goods production is more volatile than nondurable goods and services; investment spending is more volatile than consumption 5. Application: the job finding rate and the job loss rate a. The probability that someone finds or loses a job in a given month changes over time b. The job finding rate is the probability that someone who is unemployed will find a job during the month, but that probability declines in recessions and increases in expansions (text Figure 8.9) c. The job loss rate is the probability that someone who is employed one month will become unemployed the next month (text Figure 8.10); it declines in expansions and rises in recessions d. An example (text Table 10.2) shows that small changes in the job loss rate may lead to larger changes in the unemployment rate than larger changes in the job finding rate e. But since the job loss rate applies to many more people, job loss is the main force in increased unemployment rates during recessions Analytical Problem 2 asks for an explanation of why expenditures on durable goods are more volatile over the business cycle than expenditures on nondurables and services.

D. International aspects of the business cycle 1. The cyclical behavior of key economic variables in other countries is similar to that in the United States 2. Major industrial countries frequently have recessions and expansions at about the same time 3. Text Figure 8.14 illustrates common cycles for Japan, Canada, the United States, France, Germany, and the United Kingdom 4. In addition, each economy faces small fluctuations that are not shared with other countries

Data Application For a basic set of facts about business cycles across countries, see the article by Mario J. Crucini, M. Ayhan Kose, and Christopher Otrok, “What Are the Driving Forces of International Business Cycles?” Review of Economic Dynamics, 2011, pp. 156–175.

E.

In touch with data and research—coincident and leading indexes 1. Coincident indexes are designed to help figure out the current state of the economy, while leading indicators are designed to help predict peaks and troughs 2. The first index was developed by Mitchell and Burns of the NBER in the 1930s 3. The CFNAI is a coincident index produced by the Federal Reserve Bank of Chicago based on 85 macroeconomic variables; it is a coincident index that turns significantly negative in recessions (text Figure 8.15) 4. The ADS Business Conditions Index is a coincident index based on variables of different frequencies (text Figure 8.16)

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5. The CFNAI and ADS index perform similarly; the ADS is available more frequently but does not have a long track record 6. The Conference Board produces an index of leading economic indicators; a decline in the index for two or three months in a row warns of recession danger 7. Problems with the leading indicators a. Data are available promptly, but often revised later, so the index may give misleading signals b. The index has given a number of false warnings c. The index provides little information on the timing of the recession or its severity d. Structural changes in the economy necessitate periodic revision of the index 8. Research by Diebold and Rudebusch showed that the index does not help forecast industrial production in real time 9. In real time, the index sometimes gave no warning of recessions a. The index gave no advance warning of the recession that began in December 1970 b. The index was late in calling the recession that began in November 1973; the index did not turn down two months in a row until September 1974 10. After the fact, the index of leading indicators is revised and appears to have predicted the recessions well 11. Stock and Watson attempted to improve the index by creating some new indexes based on newer statistical methods, but the results were disappointing as the new index failed to predict the recessions that began in 1990 and 2001 12. Because recessions may be caused by sudden shocks, the search for a good index of leading indicators may be fruitless F.

In touch with data and research: the seasonal cycle and the business cycle 1. Output varies over the seasons: highest in the fourth quarter, lowest in the first quarter 2. Most economic data is seasonally adjusted to remove regular seasonal movements 3. Barsky and Miron’s 1989 study shows that the movements of variables across the seasons are similar to the movements of variables over the business cycle

Data Application A further discovery made by Barsky and Miron in looking at the seasonal cycle is surprising: they found little production smoothing. Economic theory suggests that even if demand changes over the seasons, production need not. Firms could instead produce steadily through the year, building up inventories of goods in the first three quarters of the year and selling them off in the fourth quarter. But Barsky and Miron find that this doesn’t happen; production and sales tend to move together.

4. If the seasonal cycle is like the business cycle, and the seasonal cycle represents desirable responses to various factors (Christmas, the weather) for which government intervention is inappropriate, should government intervention be used to smooth out the business cycle?

Policy Application Some economists have gone so far as far as to challenge the need for the Fed to change the money supply over the seasons. If the Fed did not increase the money supply in the fall, for example, the seasonal demand for currency due to holiday shopping would cause interest rates to rise. Some economists see the rise in interest rates as a natural phenomenon that the Fed should not prevent. But the case for seasonal monetary policy is based on preventing bank panics (as occurred frequently from 1890 to 1910) and reducing transactions costs (which arise because .

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people expend effort to reduce money balances when interest rates rise). For a good discussion of these issues, see the article by Satyajit Chatterjee. “Leaning Against the Seasonal Wind: Is There a Case for Seasonal Smoothing of Interest Rates?” Federal Reserve Bank of Philadelphia Business Review, March/April 1993, pp. 13–24.

IV. Business Cycle Analysis: A Preview (Sec. 8.4) A. What explains business cycle fluctuations?

1. Two major components of business cycle theories a. A description of the shocks b. A model of how the economy responds to shocks 2. Two major business cycle theories a. Classical theory b. Keynesian theory 3. Study both theories in aggregate demand-aggregate supply (AD–AS) framework B. Aggregate demand and aggregate supply: a brief introduction 1. The model (along with the building block IS–LM model) will be developed in Chapters 9–11 2. The model has three main components; all plotted in (P, Y) space a. Aggregate demand curve b. Short-run aggregate supply curve c. Long-run aggregate supply curve 3. Aggregate demand curve a. Shows quantity of goods and services demanded (Y) for any price level (P); the quantity is called aggregate demand b. Higher P means less aggregate demand (lower Y), so the aggregate demand curve slopes downward; reasons why discussed in chapter 9 c. An increase in aggregate demand for a given P shifts the aggregate demand curve up and to the right; and vice versa (1) Example: a rise in the stock market increases consumption, shifting the aggregate demand curve up and to the right (2) Example: a decline in government purchases shifts the aggregate demand curve down and to the left 4. Aggregate supply curve a. The aggregate supply curve shows how much output producers are willing to supply at any given price level; the quantity is called aggregate supply b. The short-run aggregate supply curve is horizontal; prices are fixed in the short run c. The long-run aggregate supply curve is vertical at the full-employment level of output d. Equilibrium (Figure 8.2; like text Figure 8.17)

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Figure 8.2 (1) Short-run equilibrium: the aggregate demand curve intersects the short-run aggregate supply curve (2) Long-run equilibrium: the aggregate demand curve intersects the long-run aggregate supply curve C. Aggregate demand shocks 1. An aggregate demand shock is a change that shifts the aggregate demand curve 2. Example: a negative aggregate demand shock (Figure 8.3; like text Figure 8.18)

Figure 8.3 a. The aggregate demand curve shifts down and to the left b. Short-run equilibrium occurs where the aggregate demand curve intersects the short-run aggregate supply curve; output falls, price level is unchanged c. Long-run equilibrium occurs where the aggregate demand curve intersects the long-run aggregate supply curve; output returns to its original level, price level has fallen 3. How long does it take to get to the long run? a. Classical theory: prices adjust rapidly (1) So recessions are short-lived (2) No need for government intervention b. Keynesian theory: prices (and wages) adjust slowly (1) Adjustment may take several years

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(2) So the government can fight recessions by taking action to shift the aggregate demand curve D. Aggregate supply shocks 1. Classicals view aggregate supply shocks as the main cause of fluctuations in output a. An aggregate supply shock is a shift of the long-run aggregate supply curve b. Factors that cause aggregate supply shocks are things like changes in productivity or labor supply 2. Example: a negative aggregate supply shock (Figure 8.4, like text Figure 8.19)

Figure 8.4 a. Initial long-run equilibrium at intersection of LRAS1 and AD, with full-employment output level Y1 b. Aggregate supply shock reduces full-employment output from Y1 to Y2 , causing long-run aggregate supply curve to shift left from LRAS1 to LRAS2 c. New equilibrium has lower output and higher price level d. So recession is accompanied by higher price level 3. Keynesians also recognize the importance of supply shocks; their views are discussed further in Chapter 11

Policy Application In his article, “Productivity Growth and the American Business Cycle,” Federal Reserve Bank of Philadelphia Business Review, Sept./Oct. 1995, Satyajit Chatterjee examines the role of monetary policy when supply shocks are the major causes of recessions.

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n

Additional Issues for Classroom Discussion

1.

Should the Government Try to Prevent Recessions?

Ask your class if they think the government should try to prevent recessions. Most people do, but some economists are not convinced that the government knows enough to take the right action at the right time.

If the timing of government policies are wrong, or the magnitude of government policies are wrong, then the government’s attempts to prevent recessions may in fact make the business cycle worse than if they had done nothing at all.

2.

Should Government Policy Prevent the Seasonal Cycle?

Most of the data that economists look at have been adjusted to remove seasonal influences. For example, the fourth quarter of the year has the largest amount of production, because of the holiday gift buying in that quarter. And the first quarter of the year has the smallest amount of production, thanks to winter shutdowns. But why do we object to fluctuations in output caused by the business cycle, yet we don’t try to prevent fluctuations in output over the seasons?

3.

Do Recessions Have Any Positive Economic Effects?

Recessions cause hardships to many people who lose their jobs or whose incomes decline. The entire economy slows down, making it harder for people to change jobs or for college and high-school graduates to find jobs. Many small businesses fail, and people who had planned to open businesses wait until times are better.

Are there any benefits to recessions? Can you think of any ways in which recessions help consumers?

What about corporations? Small business firms? Workers?

Your students may have trouble coming up with anything positive about recessions. But some new theories about recessions suggest that they may be beneficial in terms of allowing older capital stock to be discarded and giving managers the chance to think strategically about the future. Reorganizations take place in recessions, representing a cleansing of firms, with preparation being made for new and better future production. Consumers may find that they can eliminate bad spending habits (because they are forced to). Workers may find that they must seek jobs in other professions, or acquire more human capital by returning to school—either of which may pay off in the long run.

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Answers to Textbook Problems

Review Questions 1.

Figure 8.7 illustrates both the recurrence and persistence of the business cycle. The business cycle is recurrent, as there are repeated episodes of contractions and expansions over time. The business cycle also displays persistence, as declines in economic activity tend to be followed by further declines for some time, while growth in economic activity tends to be followed by further growth for some time.

Figure 8.7 2.

Comovement means that many economic variables move together in a predictable way over the business cycle. The business cycle facts presented in the chapter illustrate comovement among all the variables listed in text Summary Table 10 that are either procyclical (moving in the same direction as aggregate economic activity) or countercyclical (moving in the opposite direction as aggregate economic activity). Only those variables listed as acyclical do not show comovement.

3.

There is some question as to whether or not the business cycle has become less volatile over time.

Originally it was thought that the cycle had been moderated, especially since World War II, but Romer challenged this notion. Further examination of the data by Balke and Gordon, however, shows that there has been some moderation of the business cycle.

Whether the business cycle has become less severe or not is important, especially to economic policymakers. Since World War II, both fiscal policy and monetary policy have been used to try to smooth out business cycles to reduce their severity. If it were found that business cycles are no less severe than they used to be, it would point to the failure of government policy to achieve its objectives.

4.

A variable that moves in the same direction as aggregate economic activity is said to be procyclical, while a variable that moves in the opposite direction is countercyclical. If the peaks and troughs of a variable occur before the peaks and troughs in aggregate economic activity, it is said to be a leading variable. If a variable’s peaks and troughs occur at the same time as the peaks and troughs in aggregate economic activity, it is said to be a coincident variable. If a variable’s peaks and troughs come after the peaks and troughs of aggregate economic activity, it is said to be a lagging variable.

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5.

If the economy were entering a recession, you would expect production, investment, average labor productivity, and the real wage to decline because they are all procyclical, and the unemployment rate to rise because it’s countercyclical.

6.

The fact that some economic variables are known to lead the business cycle is used to develop an index of leading economic indicators. The index is used to forecast economic turning points.

7.

The two components of a theory of business cycles are: (1) A description of the types of factors (called “shocks”) that have major impacts on the economy, such as wars, new inventions, harvest failures, and changes in government policy; and (2) a model of how the economy responds to the various shocks.

8.

Keynesians and classicals differ sharply in their beliefs about how long it takes the economy to reach a long-run equilibrium. Classical economists believe that prices adjust rapidly (within a few months) to restore equilibrium in the face of a shock, while Keynesians believe that prices adjust slowly, taking perhaps several years.

Because of the time it takes for the economy’s equilibrium to be restored, Keynesians see an important role for the government in fighting recessions. But because classicals believe that equilibrium is restored quickly, there’s no need for government policy to fight recessions.

Since classicals think equilibrium is restored quickly in the face of shocks, aggregate demand shocks cannot cause recessions, since they can’t affect output for very long. So classical economists think recessions are caused by aggregate supply shocks. Keynesians, however, think that both aggregate demand and aggregate supply shocks are capable of causing recessions.

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Analytical Problems 1.

Figure 8.8 illustrates the business cycle. The current NBER method picks peaks and troughs in the level of aggregate economic activity, which are points on the figure where the slope of the line is zero. These are shown in Figure 8.8 as P1 (at the peak of the cycle) and T1 (at the trough of the cycle).

However, the older method picks peaks and troughs in detrended economic activity. This means the peaks and troughs occur at points that are the farthest away from the trend line, which means those points at which the slope of the line showing aggregate economic activity is the same as the slope of the trend line. These points are shown in Figure 8.8 as P2 and T2. Note that the point P2 occurs before P1, meaning that peaks in detrended economic activity are earlier than peaks in the level of economic activity. Note also that the point T2 occurs later than T1, which means that troughs in detrended economic activity are later than troughs in the level of economic activity. Since under the old method, troughs occur later and peaks occur earlier, contractions appear to be longer and expansions appear to be shorter using the pre-1927 method than using the current method. Thus the fact that after World War II expansions were longer and contractions were shorter than before World War I is somewhat illusory, since it’s based on two different accounting mechanisms. If expansions and contractions were in fact equally long in both periods, the change in accounting method would mean that our official dating of the business cycle would show longer expansions and shorter contractions after World War II than before World War I.

Figure 8.8 2.

Expenditure on durable goods is more sensitive to the business cycle than expenditure on nondurable goods and services, because people can more easily change the timing of their expenditure on durables.

When economic activity is weak, and people face the danger of losing their jobs, they avoid making durable goods purchases. Instead, they may drive their cars a little longer before buying new ones, get the old washing machine repaired instead of buying a new one, and put off buying new furniture until a new expansion indicates greater income security. So in a recession, durable purchases decline a lot, but when an expansion begins, durable purchases pick up substantially. The exception was in the business cycle that began in March 2001, when very low interest rates supported expenditures on durable goods.

3.

(a) In symbols, let A = average labor productivity, Y = output, and H = total hours worked. By definition, A = Y/H, so in growth terms, DA/A = DY/Y - DH/H. Since all three are procyclical, they all move in the same direction over the business cycle. If total hours worked varied more than output in an expansion, then DH/H would be greater than DY/Y, so that DA/A would be negative, and average labor productivity would be countercyclical. So it must be the case that

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output varies more than total hours worked in an expansion. A similar argument holds in a contraction. (b) That average labor productivity is procyclical helps explain why the Okun’s Law coefficient is 2, not 1. A one-percentage point increase in unemployment is approximately a one percent fall in employment. Thus, if there were no change in average labor productivity, we might expect the percentage fall in output to equal the number of percentage points that the unemployment rate rises. But since average labor productivity moves in the same direction as output, it magnifies the output effect of a given amount of unemployment.

4.

Figure 8.9 illustrates the effects of a demand shock. The economy begins in equilibrium at point A, where the LRAS, SRAS, and AD curves intersect. The demand shock shifts the aggregate demand curve to the left to AD¢. In the short run, the equilibrium is at point B, where AD¢ intersects SRAS. This is a point at which output has declined (a recession), but the price level is unchanged. Over time, the short-run aggregate supply curve shifts down to SRAS¢, restoring long-run equilibrium at point C. At this point, output is back at its full-employment level and the price level has declined. Thus the result of a demand shock on the price level is that the price level is unchanged in the short run and declines in the long run. Since the 1973–1975 recession was one in which the price level rose sharply, it must not have been due to a demand shock.

Figure 8.9 Figure 8.10 illustrates the effects of a supply shock. The economy begins in equilibrium at point A, where the LRAS, SRAS, and AD curves intersect. The supply shock shifts the long-run aggregate supply curve to the left to LRAS¢. The new equilibrium is at point B, where AD intersects LRAS¢. This is a point at which output has declined (a recession), but the price level has risen. This matches what happened in the 1973–1975 recession. Thus we conclude that the 1973–1975 recession was the result of a supply shock, not a demand shock.

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Figure 8.10 5.

Growth that is “too rapid” most likely refers to a situation in which the aggregate demand curve has shifted to the right and, in the short run, intersects the SRAS curve at a level of output that is greater than the full-employment level of output (Figure 8.11). This situation is associated with inflation because, in the long run, prices will rise, shifting the SRAS curve up to intersect with the LRAS and AD curves. The shock that is implicitly assumed to be hitting the economy is an aggregate demand shock, since that is the only shock that increases output in the short run and inflation in the long run.

Figure 8.11

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Working with Macroeconomic Data 1. The unemployment rate is a persistent variable because most changes by 0.2 percentage points or more were followed in the subsequent quarter by another change in the same direction. From 1961Q1 to 2018Q3, 82% of all changes of 0.2 percentage points or more in a quarter were followed by a change in the following quarter in the same direction, versus 13% in the opposite direction and 2% no change.

2. a.

Real imports are procylical and coincident. b.

Federal government receipts are procylical and coincident.

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c.

Housing starts are procylical and leading. d.

Capacity utilization in manufacturing is procylical and coincident.

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e.

Average weekly hours in manufacturing are procylical and coincident.

3.

Real stock prices often decline in the middle of economic expansions, so not every decline in real stock prices is followed by a recession.

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4.

The business cycles of the United States and Canada are most closely related. Business cycles are somewhat related for the United States and Germany but not as closely as the United States and Canada.

5. Many answers are possible depending on the variable chosen.

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Learning Objectives

I.

Goals of Chapter 9 A. Combine the labor market (Chapter 3), the goods market (Chapter 4), and the asset market (Chapter 7) into a complete macroeconomic model (for a closed economy) B. Although the IS–LM model was originally a Keynesian model because it assumes prices are fixed, by allowing prices to adjust, it is possible to use the IS–LM framework to discuss the classical approach C. Using one model for both approaches (the classical model in Chapter 10 and the Keynesian model in Chapter 11) avoids the need to learn two different models and helps show clearly both the similarities and the differences of the two approaches D. Section goals 1.

Discuss factors that explain the full-employment (FE) line (Sec. 9.1) 2.

Discuss factors that affect the IS curve, which represents equilibrium in the goods market (Sec. 9.2) 3.

Discuss factors that affect the LM curve, which represents equilibrium in the asset market (Sec. 9.3) 4.

Describe the conditions necessary for general equilibrium using the IS–LM model (Sec. 9.4) 5.

Discuss the role of price adjustment in achieving general equilibrium (Sec. 9.5) 6.

Explain the fundamentals and implications of the AD–AS model (Sec. 9.6)

II.

Notes to Ninth Edition Users A. We use the distinction between endogenous variables and exogenous variables, introduced in Chapter 6, in more places than before

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Teaching Notes

I.

The FE Line: Equilibrium in the Labor Market (Sec. 9.1) A. In the discussion of the labor market in Chapter 3, we showed how equilibrium in the labor market leads to employment at its full-employment level N and output at Y

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B. If we plot output against the real interest rate, we get a vertical line at Y = Y , since labor market equilibrium is unaffected by changes in the real interest rate (Figure 9.1)

Figure 9.1 C. Factors that shift the FE line 1. Y is determined by the full-employment level of employment and the current levels of capital and productivity; any change in these variables shifts the FE line 2. Summary Table 11 lists the factors that shift the full-employment line a. The full-employment line shifts right because of (1) a beneficial supply shock (2) an increase in labor supply (3) an increase in the capital stock b. The full-employment line shifts left when the opposite happens to the three factors above II. The IS Curve: Equilibrium in the Goods Market (Sec. 9.2) A. The goods market clears when desired investment equals desired national saving 1. Adjustments in the real interest rate bring about equilibrium 2. For any level of output Y, the IS curve shows the real interest rate r for which the goods market is in equilibrium

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3. Derivation of the IS curve from the saving-investment diagram (Figure 9.2)

Figure 9.2 a. Key features (1) The saving curve slopes upward because a higher real interest rate increases saving (2) An increase in output shifts the saving curve to the right, because people save more when their income is higher (3) The investment curve slopes downward because a higher real interest rate reduces the desired capital stock, thus reducing investment b. Consider two different levels of output (1) At the higher level of output, the saving curve is shifted to the right compared to the situation at the lower level of output (2) Since the investment curve is downward sloping, equilibrium at the higher level of output has a lower real interest rate (3) Thus a higher level of output must lead to a lower real interest rate, so the IS curve slopes downward (4) The IS curve shows the relationship between the real interest rate and output for which investment equals saving c. Alternative interpretation in terms of goods market equilibrium (1) Beginning at a point of equilibrium, suppose the real interest rate rises (2) The increased real interest rate causes people to increase saving and thus reduce consumption, and causes firms to reduce investment (3) So the quantity of goods demanded declines (4) To restore equilibrium, the quantity of goods supplied would have to decline (5) So higher real interest rates are associated with lower output, that is, the IS curve slopes downward B. Factors that shift the IS curve 1. Any change that reduces desired national saving relative to desired investment shifts the IS curve up and to the right

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a. Intuitively, imagine constant output, so a reduction in saving means more investment relative to saving; the interest rate must rise to reduce investment and increase saving b. Example of temporary increase in government purchases (Figure 9.3)

Figure 9.3 2. Similarly, a change that increases desired national saving relative to desired investment shifts the IS curve down and to the left 3. An alternative way of stating this is that a change that increases aggregate demand for goods shifts the IS curve up and to the right a. In this case, the increase in aggregate demand for goods exceeds the supply b. The real interest rate must rise to reduce desired consumption and investment and restore equilibrium 4. Summary Table 12 lists the factors that shift the IS curve a. The IS curve shifts up and to the right because of (1) an increase in expected future output (2) an increase in wealth (3) a temporary increase in government purchases (4) a decline in taxes (if Ricardian equivalence doesn’t hold) (5) an increase in the expected future marginal product of capital (6) a decrease in the effective tax rate on capital b. The IS curve shifts down and to the left when the opposite happens to the six factors above Numerical Problem 1 asks students to find the IS curve, given equations for consumption and investment, and looks at how a change in government purchases shifts the curve.

III. The LM Curve: Asset Market Equilibrium (Sec. 9.3) A. The interest rate and the price of a nonmonetary asset 1. The price of a nonmonetary asset is inversely related to its interest rate or yield a. Example: A bond pays $10,000 in one year; its current price is $9615, and its interest rate is 4%, since ($10,000 - $9615)/$9615 = 0.04 = 4% b. If the price of the bond in the market were to fall to $9524, its yield would rise to 5%, since ($10,000 - $9524)/$9524 = 0.05 = 5% 2. For a given level of expected inflation, the price of a nonmonetary asset is inversely related to the real interest rate B. The equality of money demanded and money supplied .

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1. Equilibrium in the asset market requires that the real money supply equal the real quantity of money demanded 2. Real money supply is determined by the central bank and isn’t affect by the real interest rate 3. Real money demand falls as the real interest rate rises 4. Real money demand rises as the level of output rises 5. The LM curve (Figure 9.4) is derived by plotting real money demand for different levels of output and looking at the resulting equilibrium

Figure 9.4 6. By what mechanism is equilibrium restored? a. Starting at equilibrium, suppose output rises, so real money demand increases b. The rise in people’s demand for money makes them sell nonmonetary assets, so the price of those assets falls and the real interest rate rises c. As the interest rate rises, the demand for money declines until equilibrium is reached 7. The LM curve shows the combinations of the real interest rate and output that clear the asset market a. Intuitively, for any given level of output, the LM curve shows the real interest rate necessary to equate real money demand and supply b. Thus the LM curve slopes upward from left to right C. Factors that shift the LM curve 1. Any change that reduces real money supply relative to real money demand shifts the LM curve up a. For a given level of output, the reduction in real money supply relative to real money demand causes the equilibrium real interest rate to rise b. The rise in the real interest rate is shown as an upward shift of the LM curve 2. Similarly, a change that increases real money supply relative to real money demand shifts the LM curve down and to the right 3. Summary Table 13 lists the factors that shift the LM curve a. The LM curve shifts down and to the right because of (1) an increase in the nominal money supply (2) a decrease in the price level (3) an increase in expected inflation (4) a decrease in the nominal interest rate on money

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(5) a decrease in wealth (6) a decrease in the risk of alternative assets relative to the risk of holding money (7) an increase in the liquidity of alternative assets (8) an increase in the efficiency of payment technologies b. The LM curve shifts up and to the left when the opposite happens to the eight factors listed above 4. Changes in the real money supply a. An increase in the real money supply shifts the LM curve down and to the right (Figure 9.5)

Figure 9.5 b. Similarly, a drop in real money supply shifts the LM curve up and to the left c. The real money supply changes when the nominal money supply changes at a different rate than the price level 5. Changes in real money demand a. An increase in real money demand shifts the LM curve up and to the left (Figure 9.6)

Figure 9.6 b. Similarly, a drop in real money demand shifts the LM curve down and to the right

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Numerical Problem 2 shows the derivation of the LM curve from a money demand equation and looks at how changes in money demand and supply shift the curve.

IV.

General Equilibrium in the Complete IS–LM Model (Sec. 9.4) A. When all markets are simultaneously in equilibrium there is a general equilibrium 1. This occurs where the FE, IS, and LM curves intersect (Figure 9.7)

Figure 9.7 B. Applying the IS–LM framework: A temporary adverse supply shock 1. Suppose the productivity parameter in the production function falls temporarily 2. The supply shock reduces the marginal productivity of labor, hence labor demand a. With lower labor demand, the equilibrium real wage and employment fall b. Lower employment and lower productivity both reduce the equilibrium level of output, thus shifting the FE line to the left 3. There is no effect of a temporary supply shock on the IS or LM curves 4. Since the FE, IS, and LM curves don’t intersect, the price level adjusts, shifting the LM curve until a general equilibrium is reached a. In this case the price level rises to shift the LM curve up and to the left to restore equilibrium (Figure 9.8)

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Figure 9.8 5. The inflation rate rises temporarily, not permanently 6. Summary: The real wage, employment, and output decline, while the real interest rate and price level are higher a. There is a temporary burst of inflation as the price level moves to a higher level b. Since the real interest rate is higher and output is lower, consumption and investment must be lower C. Application: The 2008 oil price shock 1. In 2008, oil prices increased sharply in first half of year 2. In theory, this would make real interest rates increase 3. But housing crisis and financial crisis led Fed to cut interest rates sharply, causing real interest rates to become negative 4. The financial crisis led demand for oil to fall, so oil prices fell sharply in late 2008 5. So adverse supply shock became beneficial supply shock 6. But damage from housing crisis and financial crisis dominated effect of beneficial supply shock Analytical Problem 2 examines the effect on the real interest rate of a permanent oil price shock compared to a temporary oil price shock.

D. In touch with data and research: Econometric models and macroeconomic forecasts 1. Many models that are used for macroeconomic research and analysis are based on the IS–LM model 2. There are three major steps in using an economic model for forecasting a. An econometric model estimates the parameters of the model (slopes, intercepts, elasticities) through statistical analysis of the data b. Projections are made of exogenous variables (variables outside the model), such as oil prices and changes in productivity c. The model is solved for the values of endogenous variables, such as output, employment, and interest rates

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3. The Federal Reserve Board’s FRB/US model, introduced in 1996, improves on the old model by better handling of expectations, improved modeling of reactions to shocks, and use of newer statistical techniques 4. The FRB/US model is the workhorse for policy analysis by the Fed’s staff economists 5. Board of Governor’s staff adjust the FRB/US forecasts with their judgment; the subsequent forecasts reported in the Tealbook (formerly the Greenbook) have been found to be superior to private-sector forecasts, especially for inflation

Theoretical Application For an overview of the current state of the art in macroeconomic forecasting, see the article by Graham Elliott and Allan Timmermann, “Economic Forecasting,” Journal of Economic Literature, March 2008, pp. 3–56.

V.

Price Adjustment and the Attainment of General Equilibrium (Sec. 9.5) A. The effects of a monetary expansion 1. An increase in money supply shifts the LM curve down and to the right 2. Because financial markets respond most quickly to changes in economic conditions, the asset market responds to the disequilibrium a. The FE line is slow to respond, because job matching and wage renegotiation take time b. The IS curve responds somewhat slowly c. We assume that the labor market is temporarily out of equilibrium, so there’s a short-run equilibrium at the intersection of the IS and LM curves Analytical Problem 3 looks at this short-run equilibrium.

3. The increase in the money supply causes people to try to get rid of excess money balances by buying assets, driving the real interest rate down a. The decline in the real interest rate causes consumption and investment to increase temporarily b. Output is assumed to increase temporarily to meet the extra demand 4. The adjustment of the price level a. Since the demand for goods exceeds firms’ desired supply of goods, firms raise prices b. The rise in the price level causes the LM curve to shift up c. The price level continues to rise until the LM curve intersects with the FE line and the IS curve at general equilibrium (Figure 9.9)

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Figure 9.9 d. The result is no change in employment, output, or the real interest rate e. The price level is higher by the same proportion as the increase in the money supply f. So all real variables (including the real wage) are unchanged, while nominal values (including the nominal wage) have risen proportionately with the change in the money supply Numerical Problems 3 and 4 and Analytical Problem 1 look at the complete IS–LM model, including adjustment of the price level to restore equilibrium.

5. Trend money growth and inflation a. This analysis also handles the case in which the money supply is growing continuously b. If both the money supply and price level rise by the same proportion, there is no change in the real money supply, and the LM curve does not shift c. If the money supply grew faster than the price level, the LM curve would shift down and to the right d. Often, then, we will discuss things in relative terms (1) The examples can often be thought of as a change in M or P relative to the expected or trend growth of money and inflation (2) Thus when we talk about “an increase in the money supply,” we have in mind an increase in the growth rate relative to the trend (3) Similarly, a result that the price level declines can be interpreted as the price level declining relative to a trend; for example, inflation may fall from 7% to 4% B. Classical versus Keynesian versions of the IS–LM model 1. There are two key questions in the debate between classical and Keynesian approaches a. How rapidly does the economy reach general equilibrium? b. What are the effects of monetary policy on the economy?

2. Price adjustment and the self-correcting economy a. The economy is brought into general equilibrium by adjustment of the price level b. The speed at which this adjustment occurs is much debated c. Classical economists see rapid adjustment of the price level (1) So the economy returns quickly to full employment after a shock

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(2) If firms change prices instead of output in response to a change in demand, the adjustment process is almost immediate d. Keynesian economists see slow adjustment of the price level (1) It may be several years before prices and wages adjust fully (2) When not in general equilibrium, output is determined by aggregate demand at the intersection of the IS and LM curves, and the labor market is not in equilibrium 3. Monetary neutrality a. Money is neutral if a change in the nominal money supply changes the price level proportionately but has no effect on real variables b. The classical view is that a monetary expansion affects prices quickly with at most a transitory effect on real variables c. Keynesians think the economy may spend a long time in disequilibrium, so a monetary expansion increases output and employment and causes the real interest rate to fall d. Keynesians believe in monetary neutrality in the long run but not the short run, while classicals believe it holds even in the relatively short run VI. Aggregate Demand and Aggregate Supply (Sec. 9.6) A. Use the IS–LM model to develop the AD–AS model 1. The two models are equivalent 2. Depending on the issue, one model or the other may prove more useful a. IS–LM relates the real interest rate to output b. AD–AS relates the price level to output B. The aggregate demand curve 1. The AD curve shows the relationship between the quantity of goods demanded and the price level when the goods market and asset market are in equilibrium a. So the AD curve represents the price level and output level at which the IS and LM curves intersect (Figure 9.10)

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Figure 9.10 b. The AD curve is unlike other demand curves, which relate the quantity demanded of a good to its relative price; the AD curve relates the total quantity of goods demanded to the general price level, not a relative price c. The AD curve slopes downward because a higher price level is associated with lower real money supply, shifting the LM curve up, raising the real interest rate, and decreasing output demanded

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2. Factors that shift the AD curve a. Any factor that causes the intersection of the IS and LM curves to shift to the left causes the AD curve to shift down and to the left; any factor causing the IS–LM intersection to shift to the right causes the AD curve to shift up and to the right b. For example, a temporary increase in government purchases shifts the IS curve up and to the right, so it shifts the AD curve up and to the right as well (Figure 9.11)

Figure 9.11

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c. Summary Table 14: Factors that shift the AD curve (1) Factors that shift the IS curve up and to the right and thus the AD curve up and to the right as well (a) Increases in future output (Y f ), wealth, government purchases (G), or the expected future marginal productivity of capital (MPK f ) (b) Decreases in taxes (T) if Ricardian equivalence doesn’t hold, or the effective tax rate on capital (t ) (2) Factors that shift the LM curve down and to the right and thus the AD curve up and to the right as well (a) Increases in the nominal money supply (M) or in expected inflation (p e) (b) Decreases in the nominal interest rate on money (im) or the real demand for money C. The aggregate supply curve 1. The aggregate supply curve shows the relationship between the price level and the aggregate amount of output that firms supply 2. In the short run, prices remain fixed, so firms supply whatever output is demanded a. The short-run aggregate supply curve is horizontal (Figure 9.12)

Figure 9.12 3. Full-employment output is not affected by the price level, so the long-run aggregate supply curve (LRAS) is a vertical line at Y = Y in Figure 9.12 4. Factors that shift the aggregate supply curves a. The SRAS curve shifts whenever firms change their prices in the short run (1) Factors like increased costs of producing goods lead firms to increase prices, shifting SRAS up (2) Factors leading to reduced prices shift SRAS down b. Anything that increases Y shifts the LRAS curve right; anything that decreases Y shifts LRAS left c. Examples include changes in the labor force or productivity changes that affect labor demand

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D. Equilibrium in the AD–AS model 1. Short-run equilibrium: AD intersects SRAS (text Fig. 9.13a) 2. Long-run equilibrium: AD intersects LRAS a. Also called general equilibrium b. AD, LRAS, and SRAS all intersect at same point (Fig. 9.13; text Fig. 9.13b)

Figure 9.13 c. If the economy is not in general equilibrium, economic forces work to restore general equilibrium both in AD–AS diagram and IS–LM diagram E. Monetary neutrality in the AD–AS model (Figure 9.14 and key diagram 7)

Figure 9.14 1. Suppose the economy begins in general equilibrium, but then the money supply is increased by 10% 2. This shifts the AD curve upward by 10% (from AD1 to AD2) because to maintain the aggregate quantity demanded at a given level, the price level would have to rise by 10% so that real money supply would not change and would remain equal to real money demand 3. In the short run, with the price level fixed, equilibrium occurs where AD2 intersects SRAS1, with a higher level of output

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4. Since output exceeds Y , over time firms raise prices and the short-run aggregate supply curve shifts up to SRAS2, restoring long-run equilibrium 5. The result is a higher price level—higher by 10% 6. Money is neutral in the long run, as output is unchanged F. The key question is: How long does it take to get from the short run to the long run?

1. The answer to this question is what separates classicals from Keynesians Numerical Problem 5 illustrates the effects of monetary and fiscal policy using the model.

Numerical Problem 6 and Analytical Problems 4 and 5 deal with various aspects of the algebraic version of the IS–LM model.

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Additional Issues for Classroom Discussion

1.

Where Would We Be Without Equilibrium Forces?

Economists generally take for granted that markets work so that powerful economic forces return the economy to general equilibrium. But you may want to discuss with your class what the forces are that bring the economy back to equilibrium. What would happen if such forces were absent? What would determine where the economy is heading? Would the economy be characterized by chaos (in the scientific sense)? Would sunspot equilibria be pervasive? Ask your students if they think the world is fundamentally an equilibrium mechanism, or ultimately random or chaotic.

2.

What Assumptions Are Unrealistic?

In developing our model of the economy, we make a number of assumptions about what variables are affected by which other variables. Some of those assumptions are pretty obvious, but the reasons for others are more subtle. Your students may be curious to know how much it matters which variables are affected by which other ones. Does the precise structure of the model matter a lot for the qualitative exercises that we do?

A good exercise is to take the IS–LM model and change some of the assumptions to see what might happen to the model. This can be especially interesting when done to examine the impacts of monetary and fiscal policy. Differing assumptions may completely change what the model says about policy. For example, you can change the variables that are considered to be exogenous and endogenous, or add or take out variables representing wealth effects. This is the type of exercise that students do at the graduate level, for example, in Macroeconomic Theory, 2nd ed., by Thomas J. Sargent, chapter II.

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Answers to Textbook Problems

Review Questions 1.

The position of the FE line is determined by the labor market and the production function. Labor supply and demand determine equilibrium employment. Using equilibrium employment in the production function gives the full-employment level of output. The FE line is vertical at that point.

The FE line shifts to the right if there is an increase in labor supply or the capital stock or if there is a beneficial supply shock.

2.

The IS curve shows combinations of the real interest rate (r) and output (Y) that leave the goods market in equilibrium. Equilibrium in the goods market occurs when the aggregate supply of goods (Y) equals the aggregate demand for goods (C d + I d + G). Since desired national saving (S d) is Y - C d - G, an equivalent condition is S d = I d. Equilibrium is achieved by the adjustment of the real interest rate to make the desired level of saving equal to the desired level of investment. For different levels of output, there are different desired saving curves, with different equilibrium interest rates.

When plotted on a figure showing output and the real interest rate, this forms the IS curve, as shown in Figure 9.15. The curve slopes downward because as output rises, the saving curve shifts along the investment curve and the real interest rate declines.

Figure 9.15 The IS curve could shift down and to the left if: (1) expected future output falls, because this increases desired saving; (2) government purchases fall, because this increases desired saving; (3) the expected future marginal product of capital falls, because this decreases desired investment; or (4) corporate taxes increase, because this decreases desired investment.

3.

The LM curve shows the combinations of output and the real interest rate that maintain equilibrium in the asset market. Equilibrium in the asset market occurs when real money demand equals the real money supply.

Figure 9.16 shows the derivation of the LM curve and why it slopes upward. An increase in output from Y1 to Y2 raises money demand, shifting the money demand curve from MD(Y1) to MD(Y2). With money supply fixed at MS, there must be a higher real interest rate to get equilibrium in the asset market. This gives two points of the LM curve, plotted on the right half of the figure. The result is that higher output increases the real interest rate along the LM curve, so the LM curve slopes upward.

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Figure 9.16 The LM curve would shift down and to the right if the nominal money supply or expected inflation increased or if the price level or nominal interest rate on money decreased. In addition, the curve would shift down and to the right if there were a decrease in wealth, a decrease in the risk of alternative assets relative to the risk of holding money, an increase in the liquidity of alternative assets, or an increase in the efficiency of payment technologies.

4.

For constant output, if real money supply exceeds the real quantity of money demanded, the real interest rate will decline to increase the real quantity of money demanded until equilibrium is reached. This process occurs because people who find themselves with excess money balances purchase nonmonetary assets, thus increasing the market price of the nonmonetary assets and reducing the real interest rate.

5.

General equilibrium is a situation in which all markets in an economy are simultaneously in equilibrium. This is shown in Figure 9.17 as the point at which the FE line and the IS and LM curves intersect. If the economy is not initially in general equilibrium, output and the real interest rate are determined by the intersection of the IS and LM curves. Then adjustment of the price level moves the LM curve until it intersects the FE line and IS curve.

Figure 9.17

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6.

There is monetary neutrality if a change in the nominal money supply changes the price level but has no effect on real variables. Once prices adjust, money is neutral in the IS–LM model, because a change in the money supply that shifts the LM curve is matched by a proportional change in the price level that returns the real money supply back to its original level and moves the LM curve back to its original location. Classical economists believe that money is neutral in the short run, but Keynesians believe that there may be sluggish adjustment of the price level, so that changes in the money supply affect output and the real interest rate in the short run. Both classicals and Keynesians believe money is neutral in the long run.

7.

The aggregate demand curve relates the price level to the aggregate demand for goods and services. It is downward sloping, because with a fixed nominal money supply, an increase in the price level shifts the LM curve up, so the level of output at the IS–LM intersection is lower.

Factors that shift the aggregate demand curve up and to the right include (1) an increase in expected future output, which reduces desired saving, raises desired consumption, and shifts the IS curve up and to the right; (2) an increase in government purchases, which reduces desired saving and shifts the IS curve up and to the right; (3) an increase in expected future MPK, which increases desired investment and shifts the IS curve up and to the right; (4) a decrease in corporate taxes, which increases desired investment and shifts the IS curve up and to the right; (5) an increase in the nominal money supply, which raises the real money supply and shifts the LM curve down and to the right; (6) a decrease in the interest rate on money, which decreases the demand for money and shifts the LM curve down and to the right; and (7) an increase in the expected inflation rate, which reduces the demand for money and shifts the LM curve down and to the right.

8.

The short-run aggregate supply curve is horizontal and the long-run aggregate supply curve is vertical. The short-run aggregate supply curve is horizontal because prices remain fixed in the short run. The long-run aggregate supply curve is vertical because the aggregate amount of output supplied is the full-employment level, regardless of the price level.

9.

In the short run, money is not neutral, but in the long run it is neutral. Suppose the economy is initially in general equilibrium, as shown in Figure 9.18, where LRAS, SRAS1, and AD1 intersect.

Now suppose the money supply declines by 10%, so the aggregate demand curve shifts down and to the left to AD2. In the short run, the equilibrium occurs at the intersection of AD2 and SRAS1, so output declines and the price level is unchanged. Since output declines, money is not neutral. In the long run, however, the price level will decline so the short-run aggregate supply curve shifts down to SRAS2.

The long-run equilibrium occurs at the intersection of AD2, SRAS2, and LRAS, at which output has been restored to its original level and the price level is lower. Since output is back at its original level in the long run, money is neutral in the long run.

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Figure 9.18

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Numerical Problems 1.

(a) S d = Y - C d - G = Y - (4000 - 4000r + 0.2Y) - 2000 = -6000 + 4000r + 0.8Y. (b) (1) Using the equation that goods supplied equals goods demanded gives Y = Cd + Id + G = (4000 - 4000r + 0.2Y) + (2400 - 4000r) + 2000 = 8400 - 8000r + 0.2Y. So 0.8Y = 8400 - 8000r, or 8000r = 8400 - 0.8Y. (2) Using the equivalent equation that desired saving equals desired investment gives S d = Id -6000 + 4000r + 0.8Y = 2400 - 4000r 0.8Y = 8400 - 8000r, or 8000r = 8400 - 0.8Y. So we can use either equilibrium condition to get the same result.

When Y = 10,000, 8000r = 8400 - (0.8 ´ 10,000) = 400, so r = 0.05.

When Y = 10,200, 8000r = 8400 - (0.8 ´ 10,200) = 240, so r = 0.03. (c) When G = 2400, desired saving becomes S d = -6400 + 4000r + 0.8Y. S d is now 400 less for any given r and Y. Setting S d = I d, we get -6400 + 4000r + 0.8Y = 2400 - 4000r 8000r = 8800 - 0.8Y. Similarly, using the equation that goods supplied equals goods demanded gives: Y = Cd + Id + G = (4000 - 4000r + 0.2Y) + (2400 - 4000r) + 2400 = 8800 - 8000r + 0.2Y. So 0.8Y = 8800 - 8000r, or 8000r = 8800 - 0.8Y.

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At Y = 10,000, this is 8000r = 8800 - (0.8 ´ 10,000) = 800, so r = 0.10. The market-clearing real interest rate increases from 0.05 to 0.10. Thus the IS curve shifts up and to the right from IS1 to IS2 in Figure 9.19.

Figure 9.19 2.

(a) M d/P = 3000 + 0.1Y - 10,000i = 3000 + 0.1Y – 10,000(r + p e) = 3000 + 0.1Y – 10,000(r + .02) = 2800 + 0.1Y – 10,000r.

Setting M/P = Md/P: 6000/2 = 2800 + 0.1Y - 10,000r 10,000r = -200 + 0.1Y r = -0.02 + (Y/100,000).

When Y = 8000, r = 0.06.

When Y = 9000, r = 0.07.

These points are plotted as line LMa in Figure 9.20.

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Figure 9.20 (b) M = 6600, so M/P = 3300. Setting money supply equal to money demand: 3300 = 2800 + 0.1Y – 10,000r 10,000r = –500 + 0.1Y r = –0.05 + (Y/100,000).

When Y = 8000, r = 0.03.

When Y = 9000, r = 0.04.

The LM curve is shifted down and to the right from LMa to LMb in Figure 9.20, since the same level of Y gives a lower r at equilibrium. (c) M d/P = 3000 + 0.1Y - 10,000(r + pe) = 3000 + 0.1Y - 10,000r - (10,000 ´ .03) = 2700 + 0.1Y - 10,000r.

Setting money supply equal to money demand: 3000 = 2700 + 0.1Y - 10,000r 10,000r = - 300 + 0.1Y r = - 0.03 + (Y/100,000).

When Y = 8000, r = 0.05.

When Y = 9000, r = 0.06.

The LM curve is shifted down and to the right from LMa to LMc in Figure 9.20, since there is a higher real interest rate for every given level of output. The LM curve shifts down and to the right by one percentage point (the increase in p e ) because for any given Y, the same nominal interest rate clears the asset market. With an unchanged nominal interest rate, the increase in p e is matched by an equal decrease in r.

3.

(a) First, we’ll find the IS curve.

S d = Y – C d – G = Y - [200 + 0.8(Y - T) - 500r] - G = Y - [200 + (0.6Y - 16) - 500r] - G = -184 + 0.4Y + 500r - G Setting S d = I d gives -184 + 0.4Y + 500r - G = 200 - 500r.

Solving this for Y in terms of r gives Y = (960 + 2.5G) - 2500r.

When G = 196, this is Y = 1450 - 2500r.

Next, we will find the LM curve. Setting money demand equal to money supply gives 9890/P = 0.5Y - 250r - 25, which can be solved for Y = 19,780/P + 50 + 500 r.

With full-employment output of 1000, using this in the IS curve and solving for r gives r = 0.18.

Using Y = 1000 and r = 0.18 in the LM curve and solving for P gives P = 23. Plugging these results into the consumption and investment equations gives C = 694 and I = 110. (b) With G = 216, the IS curve becomes Y = 1500 - 2500r. With Y = 1000, the IS curve gives r = 0.20, the LM curve gives P = 23.27, the consumption equation gives C = 684, and the investment equation gives I = 100.

4.

(a) First, look at labor market equilibrium.

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Labor supply is NS = 55 + 10(1 - t)w. Labor demand (ND) comes from the equation w = 5A (0.005A ´ ND). Substituting the latter equation into the former, and equating labor supply and labor demand gives N = 100. Using this in either the labor supply or labor demand equation then gives w = 9. Using N in the production function gives Y = 950. (b) Next, look at goods market equilibrium and the IS curve.

Sd = Y - Cd - G = Y - [300 + 0.8(Y - T) - 200r] - G = Y - [300 + (0.4Y - 16) – 200r] - G = - 284 + 0.6Y + 200r - G. Setting S d = I d gives - 284 + 0.6Y + 200r - G = 258.5 - 250r.

Solving this for r in terms of Y gives r = (542.5 + G)/450 - 0.004/3Y. When G = 50, this is r = 1.317 - 0.004/3 Y. With full-employment output of 950, using this in the IS curve and solving for r gives r = 0.05.

Plugging these results into the consumption and investment equations gives C = 654 and I = 246. (c) Next, look at asset market equilibrium and the LM curve.

Setting money demand equal to money supply gives 9150/P = 0.5Y - 250(r + 0.02), which can be solved for r = [0.5Y - (5 + 9150/P)]/250. With Y = 950 and r = 0.05, solving for P gives P = 20. (d) With G = 72.5, the IS curve becomes r = 1.367 – 0.004/3 Y. With Y = 950, the IS curve gives r = 0.10, the LM curve gives P = 20.56, the consumption equation gives C = 644, and the investment equation gives I = 233.5. The real wage, employment, and output are unaffected by the change.

5.

The IS curve is found by setting desired saving equal to desired investment. Desired saving is S d = Y - C d - G = Y - [1275 + 0.5(Y - T) - 200r] - G. Setting S d = I d gives Y - [1275 + 0.5(Y - T) 200r] - G = 900 - 200r, or Y = 4350 - 800r + 2G - T. The LM curve is M/P = L = 0.5Y - 200i = 0.5Y - 200(r + p ) = 0.5Y - 200r. (a) T = G = 450, M = 9000. The IS curve gives Y = 4350 - 800r + 2G - T = 4350 - 800r + (2 ´ 450) -450 = 4800 - 800r. The LM curve gives 9000/P = 0.5Y - 200r. To find the aggregate demand curve, eliminate r in the two equations by multiplying the LM curve through by 4 and rearrange the resulting equation and the IS curve.

LM: 9000/P = 0.5Y - 200r. Multiplying by 4 gives 36,000/P = 2Y - 800r. Rearranging gives 800r = 2Y - 36,000/P. IS: Y = 4800 - 800r. Rearranging gives 800r = 4800 - Y. Setting the righthand sides of these two equations to each other (since both equal 800r) gives: 2Y - (36,000/P) = 4800 - Y, or 3Y = 4800 + (36,000/P), or Y = 1600 + (12,000/P); this is the AD curve.

With Y = 4600 at full employment, the AD curve gives 4600 = 1600 + (12,000/P), or P = 4. From the IS curve Y = 4800 - 800r, so 4600 = 4800 - 800r, or 800r = 200, so r = 0.25. Consumption is C = 1275 + 0.5(Y - T) - 200r = 1275 + 0.5(4600 - 450) - (200 ´ 0.25) = 3300. Investment is I = 900 - 200r = 900 - (200 ´ 0.25) = 850. (b) Following the same steps as above, with M = 4500 instead of 9000, gives the aggregate demand curve AD: Y = 1600 + (6000/P). With Y = 4600, this gives P = 2. Nothing has changed in the IS equation, so it still gives r = 0.25. And nothing has changed in either the consumption or investment equations, so we still get C = 3300 and I = 850. Money is neutral here, as no real variables are affected and the price level changes in proportion to the money supply. (c) T = G = 330, M = 9000. The IS curve is Y = 4350 - 800r + 2G - T = 4350 - 800r + (2 ´ 330) 330 = 4680 - 800r.

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LM: 36,000/P = 2Y - 800r, or 800r = 2Y - 36,000/P. IS: Y = 4680 - 800r, or 800r = 4680 - Y. AD: 2Y - (36,000/P) = 4680 - Y, or (36,000/P) + 4680 = 3Y, or Y = 1560 + (12,000/P).

With Y = 4600 at full employment, the AD curve gives 4600 = 1560 + (12,000/P), or P = 3.95.

From the IS curve, Y = 4680 - 800r, so 4600 = 4680 - 800r, or 800r = 80, so r = 0.10.

Consumption is C = 1275 + 0.5(Y - T) - 200r = 1275 + 0.5(4600 - 330) - (200 ´ 0.10) = 3390.

Investment is I = 900 - 200r = 900 - (200 ´ 0.10) = 880.

6.

(a) A = 2, f1 = 5, f2 = 0.005, n0 = 55, nw = 10, c0 = 300, cY = 0.8, cr = 200, t0 = 20, t = 0.5, i0 = 258.5, ir = 250, l0 = 0, lY = 0.5, lr = 250. (b) These values are all calculated directly, using the equations in the Appendix. They should match the results in Numerical Problem 4, above. (c) See the answer to part b.

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Analytical Problems 1.

(a) The increase in desired investment shifts the IS curve up and to the right, as shown in Figure 9.21.

The price level rises, shifting the LM curve up and to the left to restore equilibrium. Since the real interest rate rises, consumption declines. In summary, there is no change in the real wage, employment, or output; there is a rise in the real interest rate, the price level, and investment; and there is a decline in consumption.

Figure 9.21 (b) The rise in expected inflation shifts the LM curve down and to the right, as shown in Figure 9.22.

The price level rises, shifting the LM curve up and to the left to restore equilibrium. Since the real interest rate is unchanged, consumption and investment are unchanged. In summary, there is no change in the real wage, employment, output, the real interest rate, consumption, or investment; and there is a rise in the price level.

Figure 9.22 (c) The increase in labor supply is shown as a shift in the labor supply curve in Figure 9.23 (a).

This leads to a decline in the real wage rate and an increase in employment. The rise in employment causes an increase in output, shifting the FE line to the right in Figure 9.23 (b).

To restore equilibrium, the price level must decline, shifting the LM curve down and to the right.

Since output increases and the real interest rate declines, consumption and investment increase.

In summary, the real wage, the real interest rate, and the price level decline; and employment, output, consumption, and investment rise.

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Figure 9.23 (d) The reduction in the demand for money gives results identical to those in part (b).

2.

The increase in the price of oil reduces the marginal product of labor, causing the labor demand curve to shift to the left from ND1 to ND2 in Figure 9.24. Since households’ expected future incomes decline, labor supply increases, shifting the labor supply curve from NS1 to NS2 (but by assumption, the shift to the left in labor demand is larger than the shift to the right in labor supply). At equilibrium, there is a reduced real wage and lower employment. The productivity shock results in a shift to the left of the full-employment line from FE1 to FE2 in Figure 9.25, as both employment and productivity decline.

Because the shock is permanent, it reduces future output and reduces the future marginal product of capital, both of which result in a downward shift of the IS curve. The new equilibrium is located at the intersection of the new IS curve and the new FE line. If, as shown in the figure, this intersection lies above and to the left of the original LM curve, the price level will increase and shift the LM curve upward (from LM1 to LM2) to pass through the new equilibrium point. The result is an increase in the price level, but an ambiguous effect on the real interest rate. Since output is lower, consumption is lower. Since the effect on the real interest rate is ambiguous, the effect on saving and investment are ambiguous as well, though the fall in the future marginal product of capital would tend to reduce investment.

Figure 9.24

Figure 9.25

The result is different from that of a temporary supply shock; when the shock is temporary there is no impact on future output or the marginal product of capital, so the IS curve does not shift. In that case, the price level increases to shift the LM curve up and to the left from LM1 to LM2 in Figure 9.26 to restore equilibrium. In that case, the real interest rate unambiguously increases. Under a permanent

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shock, the IS curve shifts down and to the left, so the rise in the real interest rate is less than in the case of a temporary shock, and the real interest rate can even decline.

Figure 9.26 3.

(a) The decrease in expected inflation increases real money demand, shifting the LM curve up, as shown in Figure 9.27. The real interest rate rises and output declines.

Figure 9.27 (b) The increase in desired consumption shifts the IS curve up and to the right, as shown in Figure 9.28. This causes the real interest rate and output to rise.

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Figure 9.28 (c) The increase in government purchases shifts the IS curve up and to the right, with the same result as in part (b). (The FE line also shifts, as the increase in government expenditures reduces people’s wealth and leads them to increase labor supply, but this shift will not affect the short-run equilibrium, as the economy will be off the FE line.) (d) If Ricardian equivalence holds, the increase in taxes has no effect on either the IS or LM curves, so there is no change in either the real interest rate or output. If Ricardian equivalence does not hold, so that the increase in taxes reduces consumption spending, the IS curve shifts down and to the left, as shown in Figure 9.29. Both the real interest rate and output decline.

Figure 9.29 (e) An increase in the expected future marginal productivity of capital shifts the IS curve up and to the right, with the same result as in part (b).

4.

The change in Eq. (9.B.10) has no effect on employment, the real wage, or output. The only effect this has is on the term bIS, which is now bIS = [1 - (1 - t)cY - iY]/(cr + ir). Since iY is positive, the new bIS is lower than it was before. The real interest rate and price level are still determined by Eqs. (9.B.22) and (9.B.23), respectively. Given the equation for the real interest rate, Equation (9.B.22), the equilibrium value of the real interest rate is now higher it was before because 𝑟 = 𝛼$% − 𝛽$% 𝑌) and bIS is lower than it was before. Given the equation for the price level, Equation (9.B.22), the equilibrium value of the price level is now higher it was before. Because P = M/[l0 + lY - lr(aIS - bIS + p e)] and bIS is lower than it was before, so the term in parentheses is higher than it was before, so the denominator is lower than it was before, so the entire fraction is larger than it was before.

5.

The change in the money demand function affects only the equation determining the price level, Eq. (9.B.23). It is now .

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P = M/[l0 + lY Y - lr(aIS - bIS Y + p e - im)].

Given the equation for the price level, the equilibrium value of the price level is now lower than it was before because the term in parentheses is lower than it was before, so the denominator is higher than it was before, so the entire fraction is smaller than it was before.

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Chapter 10 Classical Business Cycle Analysis: Market-Clearing Macroeconomics n

Learning Objectives

I.

Goals of Chapter 10 A. Summarize the real business cycle theory and describe how well it accounts for the business cycle facts (Sec. 10.1) B. Discuss the effects of fiscal policy shocks in the classical model (Sec. 10.2) C. Discuss unemployment in the classical model (Sec. 10.3) D. Explain the roles of money and monetary policy in the classical model (Sec. 10.4) E. Summarize the fundamentals and implications of the misperceptions theory (Sec. 10.5)

II.

Notes to Ninth Edition Users A. We added greater detail about lags in fiscal policy (recognition lag, legislative lag, implementation lag, and impact lag)

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n

Teaching Notes

I.

The Real Business Cycle Theory (Sec. 10.1) A. Introduction to real business cycle theory 1. Two key questions about business cycles a. What are the underlying economic causes? b. What should government policymakers do about them?

2. Any business cycle theory has two components a. A description of the types of shocks believed to affect the economy the most b. A model that describes how key macroeconomic variables respond to economic shocks 3. Real business cycle (RBC) theory (Kydland and Prescott) a. Real shocks to the economy are the primary cause of business cycles (1) Examples: Shocks to the production function, the size of the labor force, the real quantity of government purchases, the spending and saving decisions of consumers (affecting the IS curve or the FE line) (2) Nominal shocks are shocks to money supply or demand (affecting the LM curve) b. The largest role is played by shocks to the production function, which the text has called supply shocks, and RBC theorists call productivity shocks (1) Examples: Development of new products or production techniques, introduction of new management techniques, changes in the quality of capital or labor, changes in the availability of raw materials or energy, unusually good or bad weather, changes in government regulations affecting production (2) Most economic booms result from beneficial productivity shocks; most recessions are caused by adverse productivity shocks c. The recessionary impact of an adverse productivity shock (1) Results from Chapter 3: Real wage, employment, output, consumption, and investment decline, while the real interest rate and price level rise (2) So an adverse productivity shock causes a recession (output declines), whereas a beneficial productivity shock causes a boom (output increases); but output always equals full-employment output d. Real business cycle theory and the business cycle facts (1) The RBC theory is consistent with many business cycle facts (a) If the economy is continuously buffeted by productivity shocks, the theory predicts recurrent fluctuations in aggregate output, which we observe (b) The theory correctly predicts procyclical employment and real wages Numerical Problem 1 looks at the relationship between real wages and employment over the business cycle and the issue of whether the labor supply curve should be flat or steep to be consistent with the data. (c) The theory correctly predicts procyclical average labor productivity. If booms were not due to productivity shocks, we would expect average labor productivity to be countercyclical because of diminishing marginal productivity of labor (2) The theory predicts countercyclical movements of the price level, which seems to be inconsistent with the data

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(a) But Kydland and Prescott, when using some newer statistical techniques for calculating the trends in inflation and output, find evidence that the price level is countercyclical. (b) Although the Great Depression appears to have been caused by a sequence of large, adverse aggregate demand shocks, Kydland and Prescott argue that since World War II, large adverse supply shocks have caused the price level to rise while output fell (c) The surge in inflation during the recessions associated with the oil price shocks of 1973–1974 and 1979–1980 is consistent with RBC theory

Data Application The “bible” of empirical work on RBC models is by Robert King, Charles Plosser, and Sergio Rebelo of the University of Rochester, “Production, Growth and Business Cycles: Technical Appendix,” May 1987. This is an appendix to two articles published in the Journal of Monetary Economics in 1989 that have become the cornerstone for subsequent empirical work using the RBC approach. The appendix explains in detail how the RBC model is analyzed and calibrated, and it describes computer programs written for the software package MATLAB. 4. Application: Calibrating the business cycle a. A major element of RBC theory is that it attempts to make quantitative, not just qualitative, predictions about the business cycle b. RBC theorists use the method of calibration to work out a detailed numerical example of the theory (1) First they write down specific functions explaining the behavior of people in the economy; for example, they might choose as the production function for the economy, Y = AKaN1–a (2) Then they use existing studies of the economy to choose numbers for parameters like a in the production function; for example, a = 0.3 (3) Next they simulate what happens when the economy is hit by various shocks to different sectors of the economy (4) Prescott’s computer simulations (text Figures. 10.1 and 10.2) match post–World War II data fairly well

Data Application The work on calibration has led to a major scientific debate within the economics profession about how to do empirical work. Economists working on RBC models, led by Prescott, believe strongly in calibration as the only way to do empirical work in macroeconomics. Others disagree, just as vehemently. An illuminating debate by many of the leading antagonists can be found in the symposium on “Computational Experiments in Macroeconomics” in the Journal of Economic Perspectives, Winter 1996.

5. Are productivity shocks the only source of recessions? a. Critics of the RBC theory suggest that except for the oil price shocks of 1973, 1979, and 1990, there are no productivity shocks that one can easily identify that caused recessions b. One RBC response is that it does not have to be a big shock; instead, the cumulation of many small shocks can cause a business cycle (text Figure 10.3)

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Numerical Problem 6 is a coin-flipping exercise to show that random shocks can lead to big aggregate movements.

6. Does the Solow residual measure technology shocks? a. RBC theorists measure productivity shocks as the Solow residual (1) Named after Robert Solow, the originator of modern growth theory (2) Given a production function, Y = AKaN1–a, and data on Y, K, and N, the Solow residual is A = Y/(KaN1–a)

(10.1)

(3) It is called a residual because it cannot be measured directly b. The Solow residual is strongly procyclical in U.S. data (1) This accords with RBC theory, which says the cycle is driven by productivity shocks c. But should the Solow residual be interpreted as a measure of technology?

(1) If it is a measure of technology, it should not be related to factors that do not directly affect scientific and technological progress, such as government purchases or monetary policy (2) But statistical studies show a correlation between these d. Measured productivity can vary even if the actual technology does not change (1) Capital and labor are used more intensively at times (2) More intensive use of inputs leads to higher output (3) Define the utilization rate of capital uK and the utilization rate of labor uN (4) Define capital services as uK K and labor services as uN N (5) Rewrite the production function as Y = AF(uK K, uN N) = A(uK K)a (uN N)1–a

(10.2)

(6) Use this to substitute for Y in Eq. (10.1) to get Solow residual = AuKa u1N- a

(10.3)

(7) So the Solow residual is not just A, but depends on uK and uN (8) Utilization is procyclical, so the measured Solow residual is more procyclical than is the true productivity term A (a) Burnside–Eichenbaum–Rebelo evidence on procyclical utilization of capital (b) Fay–Medoff and Braun–Evans evidence on procyclical utilization of labor (i) Labor hoarding: firms keep workers in recessions to avoid incurring hiring and firing costs (ii) Hoarded labor does not work as hard, or performs maintenance (iii) The lower productivity of hoarded labor does not reflect technological change, just the rate of utilization e. Conclusion: Changes in the measured Solow residual do not necessarily reflect changes in technology 7. Also, the critics suggest that shocks other than productivity shocks, such as wars and military buildups, have caused business cycles 8. Models allowing for other shocks are DSGE models (dynamic, stochastic, general equilibrium models)

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Theoretical Application For more on criticisms of the RBC theory and the RBC response to the critics, see the discussion in the Federal Reserve Bank of Minneapolis Quarterly Review, Fall 1986, and the Journal of Economic Perspectives, Summer 1989.

II. Fiscal Policy Shocks in the Classical Model (Sec. 10.2) A. The effects of a temporary increase in government expenditures (Figure 10.1; like text Figure 10.4) 1. The current or future taxes needed to pay for the government expenditures effectively reduce people’s wealth, causing an income effect on labor supply 2. The increased labor supply leads to a fall in the real wage and a rise in employment 3. The rise in employment increases output, so the FE line shifts to the right 4. The temporary rise in government purchases shifts the IS curve up and to the right as national saving declines 5. It is reasonable to assume that the shift of the IS curve is bigger than the shift of the FE line, so prices must rise to shift the LM curve up and to the left to restore equilibrium 6. Since employment rises, average labor productivity declines; this helps match the data better, since without fiscal policy the RBC model shows a correlation between output and average labor productivity that is too high 7. So adding fiscal policy shocks to the model increases its ability to match the actual behavior of the economy

Figure 10.1 Analytical Problems 2, 3, and 4 deal with various aspects of the classical IS-LM model.

B. Should fiscal policy be used to dampen the cycle?

1. Classical economists oppose attempts to dampen the cycle, since prices and wages adjust quickly to restore equilibrium 2. Besides, fiscal policy increases output by making workers worse off, since they face higher taxes

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3. Instead, government spending should be determined by cost-benefit analysis 4. Also, there may be lags in enacting the correct policy and in implementing it a. Recognition lag, legislative lag, implementation lag, impact lag b. So choosing the right policy today depends on where you think the economy will be in the future c. This creates problems, because forecasts of the future state of the economy are imperfect 5. It is also not clear how much to change fiscal policy to get the desired effect on employment and output III. Unemployment in the Classical Model (Sec. 10.3) A. In the classical model, there is no unemployment; people who are not working are voluntarily not in the labor force B. In reality, measured unemployment is never zero, and it is the problem of unemployment in recessions that concerns policymakers the most C. Classical economists have a more sophisticated version of the model to account for unemployment 1. Workers and jobs have different requirements, so there is a matching problem 2. It takes time to match workers to jobs, so there is always some unemployment 3. Unemployment rises in recessions because productivity shocks cause increased mismatches between workers and jobs 4. A shock that increases mismatching raises frictional unemployment and may also cause structural unemployment if the types of skills needed by employers change 5. So the shock causes the natural rate of unemployment to rise; there is still no cyclical unemployment in the classical model

Theoretical Application A nice discussion of the classical view of unemployment is by Robert E. Lucas, Jr., Models of Business Cycles, Chapter V, New York: Basil Blackwell, 1987.

D. Davis and Haltiwanger show that there is a tremendous amount of churning of jobs both within and across industries (text Fig. 10.5)

Data Application For everything you’ve ever wanted to know but were afraid to ask about how jobs change over the business cycle, see the book by Davis, Haltiwanger, and Schuh, Job Creation and Destruction (Cambridge: MIT Press, 1996).

E. But this worker match theory cannot explain all unemployment 1. Many workers are laid off temporarily; there is no mismatch, just a change in the timing of work 2. If recessions were times of increased mismatch, there should be a rise in help-wanted ads in recessions, but in fact, they fall

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Data Application Classical economists believe that unemployment is often affected by institutional factors that encourage unemployment. Many unemployed workers find jobs once their unemployment benefits run out, so the government should not (according to classical economists) be very generous with unemployment benefits because doing so leads to higher unemployment. But in the recession that began in December 2007, unemployment benefits were extended much longer than the usual six months. However, economists at the Federal Reserve Bank of San Francisco found that the extension of unemployment benefits did not explain much of the unemployment rate or the increase in the duration of unemployment during the recession. See Rob Valetta and Katherine Kuang, “Extended Unemployment and UI Benefits,” FRBSF Economic Letter, 2010–12, April 19, 2010. However, the rise of long-term unemployment can be explained by a sharp decline in the rate of transition from unemployment to employment, with a small portion explained by extensions to unemployment benefits, according to Daniel Aaronson, Bhashkar Mazumder, and Shani Schechter, “What Is Behind the Rise in Long-Term Unemployment?” Federal Reserve Bank of Chicago Economic Commentary, 2Q/2010, pp. 28–51.

F. So can the government use fiscal policy to reduce unemployment?

1. Doing so does not improve the mismatch problem 2. A better approach is to eliminate barriers to labor-market adjustment by reducing burdensome regulations on businesses or by getting rid of the minimum wage Numerical Problem 7 looks at the behavior of the unemployment rate due to a temporary productivity shock when there are many people in transition between being employed and unemployed.

G. Jobless recoveries 1. After each of the last three recessions, employment continued to decline during the recovery, so the recoveries have come to be known as “jobless recoveries” 2. The previous 5 recessions (before 1990) all featured a sharp rebound in employment as soon as the recession ended (text Fig. 10.6) 3. For the recoveries that followed the 1990–1991 and 2001 recessions, one theory was that the recessions were so mild that the recovery was weak because employment did not fall very much in the recession; but the 2007–2009 recession was very deep and still employment growth in the recovery was weak 4. It appears that productivity growth has been strong in the jobless recoveries, so GDP has grown even as employment declined; but this explanation does not explain why the same thing didn’t happen previously

Data Application Economists have been working hard to come up with good explanations for the jobless recoveries. Many ideas have been developed but nothing is totally convincing yet. Some promising ideas come from the literature on labor economics, and how labor markets may be undergoing structural change. Jason Faberman (“Job Flows, Jobless Recoveries, and the Great Moderation.” Federal Reserve Bank of Chicago working paper, February 2012) suggests that both job creation and job destruction have become less volatile since the mid-1980s, and they respond less to shocks to the economy. Faberman’s results are consistent with those of Nir Jaimovich and Henry Siu (“The Trend is the Cycle: Job Polarization and Jobless Recoveries” Duke University working paper, 2012), who find that in mid-level occupations, employees are being replaced by technology or by outsourcing, so that middle-wage workers are becoming a smaller share of the labor force. .

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Theoretical Application In most macroeconomic models, including the IS–LM and AD–AS models, the key variables are economy-wide averages of income, the wage rate, wealth, money holdings, and so on. But some issues in macroeconomics are better addressed in models in which agents in the model (agents are decision-makers such households and business firms that decide how much to consume or invest) act in different ways or face different wages or have differing amounts of wealth; such models are heterogeneous-agent models. For example, to understand how the unemployment rate changes over time, a model of the demographics of the labor force (the number of workers of different ages, different levels of experience, and different levels of education) is useful. In recent years, more macroeconomists have begun building heterogeneous-agent models. (For a description of such models and how they are developed, see José-Víctor Ríos-Rull, “Models with Heterogeneous Agents,” in Thomas F. Cooley, ed., Frontiers of Business Cycle Research (Princeton: Princeton University Press, 1995), pp. 98–125.)

Some researchers have used heterogeneous-agent models to study the costs of business cycles, in terms of the reduced well-being of the agents. In recessions, people who do not lose their jobs are not affected as much as people who lose their jobs; heterogeneous-agent models can account for the differential impact on the well-being of different people. In addition, people who lose their jobs may not be able to borrow, so their consumption spending declines, making them worse off. Research shows that when people cannot borrow, the costs of business cycles are significantly larger than if people were able to borrow whenever they lose their jobs, and thus not have to reduce their spending.

Researchers have also used heterogeneous-agent models to see if they can calibrate the real interest rate better than in other models. The real interest rate generated by RBC models is often several percentage points higher than is true in the data. But in RBC models with heterogeneous agents in which people face risk, such as the risk of becoming unemployed, and cannot borrow if they become unemployed, then the real interest rate is somewhat lower than in other RBC models without heterogeneous agents. The risk in such models also leads people to save more than they would if there were no such risk.

So, RBC models with heterogeneous agents are able to match certain aspects of the economic data better than standard RBC models.

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Theoretical Application Some researchers have found that the RBC model can better match the U.S. data on business cycles if the model explicitly accounts for household production, which is output produced at home instead of in a market. Household production includes such goods and services as cooking, child care, sewing, and food grown in a home garden.

The U.S. national income accounts described in Chapter 2 count mainly the output of businesses, not households. But people clearly switch between the two. For example, when times are good and a person is employed, she may hire someone else to mow her lawn. Because those lawnmowing services are paid for in a market, they count in GDP. But if times are bad, someone losing her job may mow the lawn herself; such services are not counted in GDP but nonetheless represent output.

When household production is incorporated into an RBC model, the match between the model and the data improves, as shown by Jeremy Greenwood of the University of Pennsylvania, Richard Rogerson of Arizona State University, and Randall Wright of the University of Wisconsin (“Putting Home Economics into Macroeconomics,” Quarterly Review, Federal Reserve Bank of Minneapolis, Summer 1993, pp. 2–11). A household-production model has a higher standard deviation of (market) output than a standard RBC model and more closely matches the U.S. data.

Models with household production may also be used to improve our understanding of foreign economies, especially those not as well developed as the United States. In less-developed countries, a greater proportion of output is produced at home, such as home-sewn clothes and food grown in a home garden. In their study of development, Stephen L. Parente of the University of Illinois, Richard Rogerson, and Randall Wright (“Household Production and Development,” Economic Review, Federal Reserve Bank of Cleveland, Third Quarter 1999, pp. 21–35) show that once household production is accounted for, income differences across countries are not as big as the GDP data suggest. So, modeling household production is vital in understanding differences in the well-being of people in different countries.

IV. Money in the Classical Model (Sec. 10.4) A. Monetary policy and the economy Money is neutral in both the short run and the long run in the classical model, because prices adjust rapidly to restore equilibrium B. Monetary nonneutrality and reverse causation 1. If money is neutral, why does the data show that money is a leading, procyclical variable? a. Increases in the money supply are often followed by increases in output b. Reductions in the money supply are often followed by recessions 2. The classical answer: Reverse causation a. Just because changes in money growth precede changes in output does not mean that the money changes cause the output changes b. Example: People put storm windows on their houses before winter, but it is the coming winter that causes the storm windows to go on, the storm windows do not cause winter c. Reverse causation means money growth is higher because people expect higher output in the future; the higher money growth doesn’t cause the higher future output d. If so, money can be procyclical and leading even though money is neutral

Data Application An early review of empirical work testing the RBC theory of reverse causation is Shaghil Ahmed, “Does Money Affect Output?” Federal Reserve Bank of Philadelphia Business Review, July/August 1993. He finds mixed support for reverse causation, but does suggest that money growth is unlikely to be a major factor causing business cycles.

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3. Why would higher future output cause people to increase money demand? a. Firms, anticipating higher sales, would need more money for transactions to pay for materials and workers b. The Fed would respond to the higher demand for money by increasing money supply; otherwise, the price level would decline

Theoretical Application The early theoretical RBC models did not include a monetary sector at all—they assumed that money was unimportant for the business cycle. Since then, RBC theorists have been trying to incorporate money into their models. The focus so far has been trying to get the models to produce a liquidity effect, in which an increase in the money supply temporarily reduces nominal interest rates. See Lawrence J. Christiano, “Modeling the Liquidity Effect of a Money Shock,” Federal Reserve Bank of Minneapolis Quarterly Review, Winter 1991.

Analytical Problem 5 works out another example of how reverse causation could occur through firms’ demand for money for transactions and the Fed’s money supply response.

C. The nonneutrality of money: Additional evidence 1. Friedman and Schwartz have extensively documented that often monetary changes have had an independent origin; they weren’t just a reflection of changes or future changes in economic activity a. These independent changes in money supply were followed by changes in income and prices b. The independent origins of money changes include such things as gold discoveries, changes in monetary institutions, and changes in the leadership of the Fed 2. More recently, Romer and Romer documented additional episodes of monetary nonneutrality since 1960 a. One example is the Fed’s tight money policy begun in 1979 that was followed by a minor recession in 1980 and a deeper one in 1981 b. That was followed by monetary expansion in 1982 that led to an economic boom

Theoretical Application For a thorough overview of how money works to affect the economy in various models, see the symposium on “The Monetary Transmission Mechanism,” in the Journal of Economic Perspectives, Fall 1995.

3. So money does not appear to be neutral 4. There is a version of the classical model in which money is not neutral—the misperceptions theory discussed next Numerical Problems 2 and 3 examine price level effects in the classical model.

V.

The Misperceptions Theory and the Nonneutrality of Money (Sec. 10.5) A. Introduction to the misperceptions theory 1. In the classical model, money is neutral since prices adjust quickly a. In this case, the only relevant supply curve is the long-run aggregate supply curve

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b. So movements in aggregate demand have no effect on output 2. But if producers misperceive the aggregate price level, then the relevant aggregate supply curve in the short run is not vertical a. This happens because producers have imperfect information about the general price level b. As a result, they misinterpret changes in the general price level as changes in relative prices c. This leads to a short-run aggregate supply curve that is not vertical d. But prices still adjust rapidly B. The misperceptions theory is that the aggregate quantity of output supplied rises above the fullemployment level Y when the aggregate price level P is higher than expected 1. This makes the AS curve slope upward 2. Example: A bakery that makes bread a. The price of bread is the baker’s nominal wage; the price of bread relative to the general price level is the baker’s real wage b. If the relative price of bread rises, the baker may work more and produce more bread c. If the baker cannot observe the general price level as easily as the price of bread, he or she must estimate the relative price of bread d. If the price of bread rises 5% and the baker thinks inflation is 5%, there is no change in the relative price of bread, so there is no change in the baker’s labor supply e. But suppose the baker expects the general price level to rise by 5%, but sees the price of bread rising by 8%; then the baker will work more in response to the wage increase 3. Generalizing this example, if everyone expects prices to increase 5% but they actually increase 8%, they will work more 4. So, an increase in the price level that is higher than expected induces people to work more and thus increases the economy’s output 5. Similarly, an increase in the price level that is lower than expected reduces output 6. The equation Y = Y + b(P - Pe) [Eq. (10.4)] summarizes the misperceptions theory 7. In the short run, the aggregate supply (SRAS) curve slopes upward and intersects the long-run aggregate supply (LRAS) curve at P = Pe (Figure 10.2; like text Figure 10.7)

Figure 10.2 Analytical Problem 1 contracts the effects of a change in the future marginal product of capital in an RBC model to that in a misperceptions model.

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C. Monetary policy and the misperceptions theory 1. Because of misperceptions, unanticipated monetary policy has real effects; but anticipated monetary policy has no real effects because there are no misperceptions 2. Unanticipated changes in the money supply (Figure 10.3; like text Figure 10.8)

Figure 10.3 a. Initial equilibrium where AD1 intersects SRAS1 and LRAS b. Unanticipated increase in money supply shifts AD curve to AD2 c. The price level rises to P2 and output rises above Y , so money is not neutral d. As people get information about the true price level, their expectations change, and the SRAS curve shifts left to SRAS2, with output returning to Y e. So unanticipated money is not neutral in the short run, but it is neutral in the long run 3. Anticipated changes in the money supply a. If people anticipate the change in the money supply and thus in the price level, they aren’t fooled, there are no misperceptions, and the SRAS curve shifts immediately to its higher level b. So anticipated money is neutral in both the short run and the long run

Data Application Do the data support the misperceptions theory? Robert Barro, “Unanticipated Money, Output, and the Price Level in the United States,” Journal of Political Economy, August 1978, pp. 549–580, found support for the misperceptions theory; his results suggested that output was affected only by unanticipated money growth. But others challenged these results and found that both anticipated and unanticipated money growth seem to affect output. See Frederic S. Mishkin, “Does Anticipated Monetary Policy Matter? An Econometric Investigation,” Journal of Political Economy, February 1982, pp. 22–51.

D. Rational expectations and the role of monetary policy 1. The only way the Fed can use monetary policy to affect output is to surprise people 2. But people realize that the Fed would want to increase the money supply in recessions and decrease it in booms, so they will not be fooled 3. The rational expectations hypothesis suggests that the public’s forecasts of economic .

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variables are well reasoned and use all the available data 4. If the public has rational expectations, the Fed will not be able to surprise people in response to the business cycle; only random monetary policy has any effects 5. So even if smoothing the business cycle were desirable, the combination of misperceptions theory and rational expectations suggests that the Fed cannot systematically use monetary policy to stabilize the economy Numerical Problems 4 and 8 look at the misperceptions theory and unanticipated compared to anticipated changes in the money supply.

6. Propagating the effects of unanticipated changes in the money supply a. It does not seem like people could be fooled for long, since money supply figures are reported weekly and inflation is reported monthly b. Classical economists argue that propagation mechanisms allow short-lived shocks to have long-lived effects c. Example of propagation: The behavior of inventories (1) Firms hold a normal level of inventories against their normal level of sales (2) An unanticipated increase in the money supply increases sales (3) Since the firm cannot produce many more goods immediately, it draws down its inventories (4) Even after the money supply change is known, the firm must produce more to restore its inventory level (5) Thus the short-term monetary shock has a long-lived effect on the economy

Theoretical Application Although the text presents the theories in the reverse order, the misperceptions theory came first (being developed in the 1970s) and the RBC theory came later (in the 1980s). Many classical economists moved away from the misperceptions theory because they were not convinced by its arguments for monetary non-neutrality; in particular, the information lag in observing money and prices didn’t seem long enough to cause much effect. For a broad review of how classical macroeconomic theory developed, as well as its relationship to Keynesian theory, see Robert J. Barro, “New Classicals and Keynesians, or the Good Guys and the Bad Guys, ” National Bureau of Economic Research Working Paper No. 2982, May 1989. Also, Bennett McCallum discusses the development of the classical approach in “New Classical Macroeconomics: A Sympathetic Account,” Scandinavian Journal of Economics, 1989, pp. 223–252.

E. In touch with data and research: Are price forecasts rational?

1. Economists can test whether price forecasts are rational by looking at surveys of people’s expectations 2. The forecast error of a forecast is the difference between the actual value of the variable and the forecast value 3. If people have rational expectations, forecast errors should be unpredictable random numbers; otherwise, people would be making systematic errors and thus not have rational expectations

Data Application If you examine a survey of forecasters, like the Livingston Survey, you will see that the forecasters

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made very bad forecasts of inflation around 1973 to 1974 and again around 1979 to 1980. Both periods are associated with large rises in oil prices.

Looking at data on interest rates, if you take nominal interest rates and subtract the expected inflation rate (using the Livingston Survey forecasts of inflation), the resulting real interest rates are nearly always positive. But if you subtract actual inflation rates from nominal interest rates, you will find negative realized real interest rates around the time of the oil price shocks. In fact, the real interest rate was as low as negative 5 percent at one point. So making bad inflation forecasts has expensive consequences in financial markets.

4. Many statistical studies suggest that people do not have rational expectations 5. But people who answer surveys may not have a lot at stake in making forecasts, so could not be expected to produce rational forecasts 6. Instead, professional forecasters are more likely to produce rational forecasts 7. Keane and Runkle, using a survey of professional forecasters, find evidence that these forecasters do have rational expectations 8. Croushore used inflation forecasts made by the general public, as well as economists, and found evidence broadly consistent with rational expectations, though expectations tend to lag reality when inflation changes sharply

Data Application The survey used by Keane and Runkle was begun by Victor Zarnowitz of the University of Chicago in 1968 and was run by the American Statistical Association and National Bureau of Economic Research until 1990. At that time the survey was taken over by the Federal Reserve Bank of Philadelphia and christened the “Survey of Professional Forecasters,” See the article by Dean Croushore, “Introducing: The Survey of Professional Forecasters,” Federal Reserve Bank of Philadelphia Business Review, November/December 1993.

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Additional Issues for Classroom Discussion

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Do Wages Adjust to Clear the Labor Market?

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One of the key assumptions of classical macroeconomic theory is that wages adjust rapidly to bring about equilibrium in the labor market in a relatively short period of time. Is this a reasonable assumption?

Some economists look at the labor-market statistics, which show large swings in unemployment and not much change in wages over the business cycle. They believe this indicates sluggish wage adjustment, supporting the Keynesian model over the classical model.

One reason for wages to adjust sluggishly is the hypothesis of downward nominal wage rigidity. Under this theory, employers do not want to reduce workers’ nominal wages, because doing so is bad for morale and they fear a decline in productivity. If firms cannot reduce nominal wages, they will lay off workers in recessions.

There is some evidence, however, that many firms reduce workers’ nominal wages. In “Inflation, Nominal Wage Rigidity, and the Efficiency of Labor Markets” (Federal Reserve Board FEDS working paper 95-45, October 1995), David Lebow, David Stockton, and William Wascher, economists at the Federal Reserve Board, found that the distribution of real wages that people earn is about the same when inflation is low as when it is high. If nominal wages did not adjust downward very well, we would expect instead the distribution of wages to be skewed upward when inflation is low relative to when it is high because high inflation allows a real wage cut without a nominal wage cut. When inflation is low, real wages cannot be reduced unless nominal wages are reduced. Lebow, Stockton, and Wascher find that nominal wage reductions are not all that rare for workers. This supports the classical assumption that wages can adjust to bring about equilibrium in the labor market.

2.

Are People’s Inflation Forecasts Rational?

When the misperceptions theory was developed in the late 1970s, a number of economists began testing people’s forecasts to see how rational they were. The theory implies that on average, people should not make systematic errors in forecasting. Of special importance are people’s forecasts of inflation, since these affect the aggregate supply curve.

One way to test these theories is to examine the forecasts collected by surveys to see if people make serious forecasting errors. When this was done in the early 1980s, the results were pretty convincing— people’s inflation forecasts were clearly biased. People seemed to be making forecasts of inflation that were far too low. Even when inflation turned out to be higher than expected, people were slow to change their forecasts. This was bad news for the misperceptions theory, which relies on people forming rational expectations.

In response, some classical economists simply argued that the surveys of forecasts were not adequate.

There were several surveys used in these studies, the most well-known being the Livingston Survey, which was started in 1946 by economic columnist Joe Livingston of the Philadelphia Inquirer and is now run by the Federal Reserve Bank of Philadelphia. Classical economists argued that the people who provided their forecasts for surveys did not have a strong incentive to forecast rationally. They were not investors with money at risk if their forecasts turned out to be wrong. And even if they did have money on the line, they might not have provided their true forecasts to the surveys.

But these complaints about the surveys by classical economists were not necessary, as there is an alternative explanation for the lack of rationality in the survey forecasts. The result that forecasts are not rational is entirely because of the experience of the 1970s. For example, if you look at forecast survey data from the 1980s and beyond, the forecasts look quite good. But in the 1970s, the U.S. economy was hit by two major oil price shocks, which caught everyone by surprise. Then-current economic theories had no

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predictions about the response of output and inflation to an oil price shock, so forecasters did not forecast well. But the economic theories were then extended to deal with oil price shocks, and if you look at forecasts in 1986 and 1990 when there were substantial changes in the price of oil, the forecasts performed very well.

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Answers to Textbook Problems

Review Questions 1. The main feature of the classical IS–LM model that distinguishes it from the Keynesian IS–LM model is the classical model’s assumption that prices adjust quickly to restore equilibrium. Keynesians assume that prices are slow to adjust to restore equilibrium. The distinction is of practical importance because classicals are less likely than Keynesians to recommend government intervention to restore equilibrium.

2. The two main components of any theory of the business cycle are (1) a specification of the types of shocks or disturbances that are believed to be the most important in affecting the economy and (2) a model of the macroeconomy that describes how key variables respond to these economic shocks. In the real business cycle theory, productivity shocks are the primary source of cyclical fluctuations.

The model of the economy is the classical IS–LM model.

3. A real shock is a disturbance to the real side of the economy that affects the IS curve or the FE line.

A nominal shock is a disturbance to money supply or money demand that affects the LM curve. Real shocks include changes in the production function, in the size of the labor force, in the real quantity of government purchases, or in the spending and saving decisions of consumers. Real business cycle theorists consider shocks to the production function to be the most important. These include the development of new products or production methods, the introduction of new management techniques, changes in the quality of capital or labor, changes in the availability of raw materials or energy, unusually good or unusually bad weather, and changes in government regulations affecting production.

4. RBC theory is successful at explaining that employment is procyclical, that average labor productivity is procyclical, that the real wage is mildly procyclical, and that investment is more volatile than consumption. It is not so successful at measuring or identifying the productivity shocks that have caused business cycle fluctuations, or at explaining why unemployment occurs in downturns.

5. The Solow residual is the most common measure of productivity shocks. It is strongly procyclical, rising in expansions and declining in contractions. The Solow residual changes when total factor productivity changes, when capital utilization changes, and when labor utilization changes.

6. The increase in government purchases does not affect labor demand, but causes an increase in labor supply at any given real wage. This occurs because workers are poorer due to the current or future taxes they must pay to finance the increased government spending. Since labor demand is unchanged but labor supply increases, the real wage declines and employment rises. The rise in employment raises output in the economy. If the shift in the FE line is much smaller than the shift in the IS curve, the combination of shifts to the right in the FE line and IS curve also leads to a rise in the real interest rate and the price level.

According to classical economists, fiscal policy should not be used to smooth out the business cycle because free markets produce efficient outcomes without government intervention, and because imperfect knowledge of the economy, political constraints on policy actions, and time lags make such stabilization policies impractical.

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Reverse causation means that expected future increases in output cause increases in the current money supply, and expected future decreases in output cause decreases in the current money supply.

It may occur, for example, because businesses increase their money demand for transactions before they increase output. It is intended to explain the fact that money is procyclical and a leading variable in the context of a model in which money is neutral.

8. According to the misperceptions theory, an increase in the price level fools producers of goods into producing more, because they are unable to tell whether the increase in prices is a relative price increase or a rise in the general price level. The change in prices must be unexpected for this to occur, because to the extent that the price change was expected, producers would not be fooled into changing production.

9. In the classical model, money is neutral in both the short run and the long run. This is modified in the misperceptions theory in that anticipated monetary changes are neutral in the short run, but unanticipated monetary changes are not neutral in the short run. Both anticipated and unanticipated monetary changes are neutral in the long run.

10. Rational expectations mean that the public’s forecasts of various economic variables are based on reasoned and intelligent examination of available economic data. If the public has rational expectations, the central bank will not be able to surprise the public systematically, and so it cannot use monetary policy to stabilize output.

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Numerical Problems 1.

(a) Labor supply is given by the equation NS = 45 + 0.1w. Before the shock, labor demand is determined by the equation w = 1.0(100 - N). Setting labor supply equal to labor demand by substituting the labor demand equation into the labor supply equation gives N = 45 + 0.1 w = 45 + [0.1 ´ 1.0(100 - N)] = 45 + 10 - 0.1N, or 1.1 N = 55, so N = 50. Then w = 1.0(100 - N) = 50.

Output is Y = 1.0[(100 ´ 50) - (0.5 ´ 502)] = 3750.

After the shock, repeating the above steps gives N = 45 + 0.1 w = 45 + [0.1 ´ 1.1(100 - N)] = 45 + 11 - 0.11N, or 1.11 N = 56, so N = 50.45. Then w = 1.1(100 - N) = 54.505. Output is Y = 1.1[(100 ´ 50.45) - (0.5 ´ 50.452)] = 4150. (b) Now NS = 10 + 0.8w. Before the shock, N = 10 + 0.8 w = 10 + [0.8 ´ 1.0(100 - N)] = 10 + 80 - 0.8N, or 1.8 N = 90, so N = 50. Then w = 1.0(100 – N) = 50. Output is Y = 1.0[(100 ´ 50) - (0.5 ´ 502)] = 3750.

After the shock, N = 10 + 0.8 w = 10 + [0.8 ´ 1.1(100 - N)] = 10 + 88 - 0.88N, or 1.88 N = 98, so N = 52.13. Then w = 1.1(100 - N) = 52.66. Output is Y = 1.1[(100 ´ 52.13) - (0.5 ´ 52.132)] = 4240. (c) If the real wage is only slightly procyclical, then a flat labor supply curve, as in part (b) is necessary, rather than a steep labor supply curve as in part (a). Figure 10.4 illustrates the difference in slopes of the two labor supply curves. When labor demand increases from ND1 to ND2, the real wage rises a lot (from w1a to w2a ) with a steep labor supply curve, but the real wage rises only a little bit (from w1b to w2b ) if the labor supply curve is fairly flat. A calibrated RBC model would fit the facts better if the labor supply curve were fairly flat, that is, labor supply is sensitive to the real wage, as in part (b).

Figure 10.4 2.

The IS curve gives Y = C + I + G = 600 + 0.5(Y - T) - 50r + 450 - 50r + G = 1050 - 100r + 0.5Y 0.5T + G, or 0.5Y = 1050 - 100r - 0.5T + G, or Y = 2100 - 200r - T + 2G. The LM curve gives M/P = L = 0.5Y - 100i = 0.5Y - 100(r + p ) = 0.5Y - 100(r + 0.05) = 0.5Y - 100r - 5. (a) M = 4320, G = T = 150. The IS curve is Y = 2100 - 200r - T + 2G = 2100 - 200r - 150 + (2 ´ 150) = 2250 - 200r. Output must be at its full-employment level of 2210. From the IS curve, 2210 = 2250 - 200r, or 200r = 40, so r = 0.20. Using this in the LM curve to find the price level gives M/P = 0.5Y - 100r - 5, or 4320/P = (0.5 ´ 2210) - (100 ´ 0.20) - 5, so P = 4320/(1105 - 20 - 5) = 4320/1080 = 4. Then consumption is C = 600 + 0.5(Y - T) – 50r = 600 + 0.5(2210 - 150) (50 ´ 0.20) = 600 + 1030 - 10 = 1620. Investment is I = 450 - 50r = 450 - (50 ´ 0.20) = 440. .

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(b) When M increases to 4752, nothing in the IS curve is affected, so Y and r are the same as in part (a), as are C and I. The LM curve becomes 4752/P = 1080, or P = 4.4. No real variables are affected, and the price level rises 10% just as the money supply did, so money is neutral. (c) When G = T = 190, the IS curve shifts. It becomes Y = 2100 - 200r - T + 2G = 2100 - 200r 190 + (2 ´ 190) = 2290 - 200r. With Y = 2210, this gives 2210 = 2290 - 200r, or 200r = 80, so r = 0.40. From the LM curve, 4320/P = 0.5Y - 100r - 5 = (0.5 ´ 2210) - (100 ´ 0.40) - 5 = 1105 - 40 - 5 = 1060, so P = 4320/1060 = 4.075. C = 600 + 0.5(Y - T) – 50r = 600 + 0.5(2210 190) - (50 ´ 0.40) = 600 + 1010 - 20 = 1590. I = 450 - 50r = 450 - (50 ´ 0.40) = 430. Fiscal policy is not neutral since the change in policy has real effects on the interest rate, consumption, and investment.

3.

The IS curve is found by setting desired saving equal to desired investment. Desired saving is Sd = Y - Cd - G = Y - [250 + 0.5(Y - T) - 500r] - G. Setting Sd = Id gives Y - [250 + 0.5(Y - T) - 500r] - G = 250 - 500r, or Y = 1000 - 2000r + 2G - T. The LM curve is M/P = L = 0.5Y - 500i = 0.5Y 500(r + p e) = 0.5Y - 500r. (a) T = G = 200, M = 7650. The IS curve gives Y = 1000 - 2000r + 2G - T = 1000 - 2000r + (2 ´ 200) - 200 = 1200 - 2000r. The LM curve gives 7650/P = 0.5Y - 500r. To find the aggregate demand curve, eliminate r in the two equations by multiplying the LM curve through by 4 and rearrange the resulting equation and the IS curve.

LM: 7650/P = 0.5Y - 500r. Multiplying by 4 gives 30,600/P = 2Y - 2000r. Rearranging gives 2000r = 2Y - 30,600/P. IS: Y = 1200 - 2000r. Rearranging gives 2000r = 1200 - Y. Setting the right-hand sides of these two equations to each other (since both equal 2000r) gives: 2Y (30,600/P) = 1200 - Y, or 3Y = 1200 + (30,600/P), or Y = 400 + (10,200/P); this is the AD curve.

With Y = 1000 at full employment, the AD curve gives 1000 = 400 + (10,200/P), or P = 17.

From the IS curve Y = 1200 - 2000r, so 1000 = 1200 - 2000r, or 2000r = 200, so r = 0.10.

Consumption is C = 250 + 0.5(Y - T) - 500r = 250 + 0.5(1000 - 200) - (500 ´ 0.10) = 600.

Investment is I = 250 - 500r = 250 - (500 ´ 0.10) = 200. (b) Following the same steps as above, with M = 9000 instead of 7650, gives the aggregate demand curve AD: Y = 400 + (12,000/P). With Y = 1000, this gives P = 20. Nothing has changed in the IS equation, so it still gives r = 0.10. And nothing has changed in either the consumption or investment equations, so we still get C = 600 and I = 200. Money is neutral here, as no real variables are affected and the price level changes in proportion to the money supply. (c) T = G = 300, M = 7650. The IS curve is Y = 1000 - 2000r + 2G - T = 1000 - 2000r + (2 ´ 300) - 300 = 1300 - 2000r. IS: Y = 1300 - 2000r, or 2000r = 1300 - Y. LM: 30,600/P = 2Y - 2000r, or 2000r = 2Y - 30,600/P. AD: 2Y - (30,600/P) = 1300 - Y, or (30,600/P) + 1300 = 3Y, or Y = 433 1/3 + (10,200/P).

With Y = 1000 at full employment, the AD curve gives 1000 = 433 1/3 + (10,200/P), or P = 18.

From the IS curve, Y = 1300 - 2000r, so 1000 = 1300 - 2000r, or 2000r = 300, so r = 0.15.

Consumption is C = 250 + 0.5(Y - T) - 500r = 250 + 0.5(1000 - 300) - (500 ´ 0.15) = 525.

Investment is I = 250 - 500r = 250 - (500 ´ 0.15) = 175.

4.

AD: Y = 300 + 30(M/P), AS: Y = 500 + 10(P – Pe), M = 400. (a) P e = 60. Setting AD = AS to eliminate Y, we get 300 + 30(M/P) = 500 + 10(P - P e ). Plugging in the values of M and Pe gives 300 + (30 ´ 400/P) = 500 + 10(P - 60), or 300 + (12,000/P) = 500 + 10P - 600, or 400 + (12,000/P) = 10P. Multiplying this equation through by P/10 gives 40P + 1200 = P 2, or P 2 - 40P - 1200 = 0. This can be factored into (P - 60)(P + 20) = 0. P can’t be

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negative, so the only solution to this equation is P = 60. At this equilibrium P = P e, so Y = 500, and the economy is at full-employment output. (b) With an unanticipated increase in the money supply to M = 700, the expected price level is unchanged at Pe = 60. The aggregate demand curve is Y = 300 + 30(M/P) = 300 + (30 ´ 700/P) = 300 + (21,000/P). The aggregate supply curve is Y = 500 + 10(P - Pe) = 500 + 10(P - 60) = 10P - 100. Setting AD = AS to eliminate Y gives 300 + (21,000/P) = 10P - 100, or 400 + (21,000/P) = 10P, or P - 40 - (2100/P) = 0. Multiplying through by P gives P2 - 40P - 2100 = 0. This can be factored as (P - 70)(P + 30) = 0, which has the positive solution P = 70. From the AD curve, Y = 300 + (21,000/P) = 300 + (21,000/70) = 600. (c) When M = 700 and is anticipated, P = Pe. Then the AD curve is Y = 300 + (21,000/P) and the AS curve is Y = 500. Setting AD = AS gives 500 = 300 + (21,000/P), which has the solution P = 105.

5.

6.

(a) To find the Solow residual, use the equation for the production function, dividing through to solve for A: A = Y/K 0.3N 0.7. Assuming there is no change in utilization rates, this is the measured Solow residual. Given that equation, plugging in the values for Y, K, and N, gives the Solow residual as 1.435 in 2015 and 1.507 in 2016. The growth rate of the Solow residual is [(1.507/1.435) - 1] ´ 100% = 5.0%. (b) With no change in utilization rates, the growth rate of the Solow residual equals the growth rate of productivity (A), 5.0%. (c) With a change in utilization rates, the production function is modified, as shown in Eq. (10.2).

Now productivity is measured as A = Y/(uKK) 0.3(uNN) 0.7 but the Solow residual is still measured as in part (a). Setting uN = 1 in year 2015 and 1.03 in year 2016, we calculate the value of A as 1.435 in 2015 (as in part a), and 1.476 in 2016. This is an increase in productivity of [(1.476/1.435) - 1] ´ 100% = 2.9%, significantly less than the 5.0% increase in the Solow residual. (d) Setting uN = 1 in year 2015 and 1.03 in year 2016, and uK = 1 in year 2015 and 1.03 in year 2016, we calculate the value of A as 1.435 in 2015 (as in part a), and 1.463 in 2016. This is an increase in productivity of [(1.463/1.435) - 1] ´ 100% = 2.0%, again significantly less than the 5.0% increase in the Solow residual.

This problem illustrates the idea that the measured Solow residual grows faster than productivity when the utilization rates of capital and labor increase.

An example is shown in Figure 10.5. There are several long cycles in output.

Figure 10.5

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7.

(a) With an unemployment rate of 5%, there are initially 5 million unemployed and 95 million employed. Since 1% of the employed become unemployed, 95 million ´ 0.01 = 950,000 move from employment to unemployment each month. Since 19% of the unemployed become employed, 5 million ´ 0.19 = 950,000 from unemployment each month. Since the same number move from employed to unemployed as the number moving from unemployed to employed, the unemployment rate remains 5% in February and March. (b) Note: All amounts are in millions.

April: Employed (E) to Unemployed (U): 95 ´ 0.03 = 2.85. U to E is 5 ´ 0.19 = 0.95.

So U = 5 + 2.85 - 0.95 = 6.9. The unemployment rate (u) = 6.9%.

May: E to U: 93.1 ´ 0.01 = 0.931. U to E is 6.9 ´ 0.19 = 1.311.

So U = 6.9 + 0.931 - 1.311 = 6.52 and u = 6.52%.

June: E to U: 93.48 ´ 0.01 = 0.9348. U to E is 6.52 ´ 0.19 = 1.2388.

So U = 6.52 + 0.9348 - 1.2388 = 6.216 and u = 6.216%.

July: E to U: 93.784 ´ 0.01 = 0.93784. U to E is 6.216 ´ 0.19 = 1.18104.

So U = 6.216 + 0.93784 - 1.18104 = 5.9728 and u = 5.9728%.

8.

(a) aIS = 2.47, bIS = 0.0004, aLM = 0, bLM = 0.001, lr = 500, b = 100. (b) Y = [2.47 + 88,950/(P ´ 500)]/(.0004 + .001) = (2.47 + 177.9/P)/.0014 (c) Y = 6000 + 100P - 2915 = 3085 + 100P; use this in the AD curve to eliminate Y. 3085 + 100P = (2.47 + 177.9/P)/.0014; multiply through by P and .0014 to get 4.319P + .14P 2 = 2.47P + 177.9, or .14P 2 + 1.849P - 177.9 = 0; use quadratic formula: P = 29.65. Y = 3085 + 100P = 6050. (d) Long run: Y = 6000; 6000 = (2.47 + 177.9/P)/0.0014, so P = 30.

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Analytical Problems 1.

(a) The increase in MPK f leaves aggregate supply unchanged, since expected future labor income and expected future wages are unchanged. But aggregate demand increases, because firms increase investment, shifting the IS curve up and to the right. There is no shift in either the LM curve or the FE line.

Figure 10.6(a) shows that the increase in aggregate demand causes no change in output, since the AS curve is vertical, but the price level increases. Figure 10.6(b) shows the shift up and to the right of the IS curve from IS 1 to IS 2. To get the economy to equilibrium, the price level rises so that the LM curve shifts from LM 1 to LM 2. The real interest rate increases as a result. In the labor market, there is no change in labor demand or supply, so employment and output are unchanged. Since the real interest rate rises, saving increases and consumption declines. Since investment equals saving, investment also rises. (b) The misperceptions theory gets a different result. As shown in Figure 10.7, the shift in the aggregate demand curve from AD1 to AD2 increases both output and the price level as the economy moves along the short-run aggregate supply curve SRAS. The difference in this result compared to the result in part (a) comes from producers misperceiving the change in the price level as a change in relative prices, and increasing their labor demand and output.

2.

(a) In the case of a permanent increase in government purchases, the income effect on labor supply, which arises because the present value of taxes increases to pay for the added government spending, is much higher than in the case of a temporary increase in government spending. So workers increase their labor supply more when the government spending change is permanent than when it is temporary. (b) Desired national saving is unaffected by the change in government spending if the change in consumption is just equal to the change in taxes, so there is no shift in the saving curve. If investment is also unaffected by the change in government spending, then the IS curve does not shift. (c) Figure 10.8 shows the effect of the increase in government purchases on the economy. The FE line shifts to the right from FE1 to FE2 due to the increase in labor supply. To restore equilibrium, the price level must decline to shift the LM curve from LM 1 to LM 2. So output rises and the real interest rate declines.

If consumption falls less than the increase in government purchases, the IS curve shifts up and to the right from IS1 to IS2 in Figure 10.9. As a result of the shift in the IS curve, the real interest rate and the price level will fall by less than in the case in which current consumption falls by 100, and in fact, the real interest rate and the price level may even rise if the IS curve shifts by a lot, as shown in the figure.

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Figure 10.6

Figure 10.7

Figure 10.8

Figure 10.9

The temporary increase in government purchases causes an income effect that increases workers’ labor supply. This results in an increase in the full-employment level of output from FE1 to FE2 in

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Figure 10.10. The increase in government purchases also shifts the IS curve up and to the right from IS1 to IS2, as it reduces national saving. Assuming that the shift up of the IS curve is so large that it intersects the LM curve to the right of the FE line, the price level must rise to get back to equilibrium at full employment, by shifting the LM curve up and to the left from LM1 to LM2. The result is an increase in output and the real interest rate.

Figure 10.10 Figure 10.11 shows the impact on the labor market. Labor supply shifts from NS1 to NS2, leading to a decline in the real wage and a rise in employment. Average labor productivity declines, since employment rises while capital is fixed. Investment declines, since the real interest rate rises.

Figure 10.11 To summarize, in response to a temporary increase in government purchases, output, the real interest rate, the price level, and employment rise, while average labor productivity and investment decline. (a) The business cycle fact is that employment is procyclical. The model is consistent with this fact, since employment rises when government purchases rise, causing output to rise. (b) The business cycle fact is that the real wage is mildly procyclical. The model is inconsistent with this fact, since it shows a decline in the real wage when government purchases rise and output rises. (c) The business cycle fact is that average labor productivity is procyclical. The model is inconsistent with this fact, since it shows a decline in average labor productivity when government purchases rise and output rises. .

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(d) The business cycle fact is that investment is procyclical. The model is not consistent with this fact, as investment falls when government purchases rise and output rises. (e) The business cycle fact is that the price level is procyclical. The model is consistent with this fact, as the price level rises when government purchases increase and output increases.

4.

The temporary wage tax has a small income effect but a large substitution effect, so labor supply is reduced. As Figure 10.12 shows, this increases the (pretax) real wage rate and reduces employment.

The reduction in employment shifts the FE line from FE1 to FE2 in Figure 10.13, while the increase in government purchases shifts the IS curve from IS1 to IS2. To restore equilibrium, where IS, LM, and FE intersect, the price level must rise, so that the LM curve shifts from LM1 to LM2. The result is an increase in the real interest rate and a decline in output.

Figure 10.12

Figure 10.13 5.

(a) An increase in expected future output increases money demand, so the LM curve shifts up and to the left. As shown in Figure 10.14, the LM curve shifts from LM1 to LM2. General equilibrium in the economy can be restored by shifting the LM curve from LM2 to LM3, which occurs as the price level declines. .

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Figure 10.14 (b) If the Fed wants to stabilize the price level, then it increases the money supply in response to the increase in money demand, so that the LM curve shifts from LM2 to LM3 without a decline in the price level. This represents reverse causation, because the rise in future output causes the current money supply to increase. It might appear that the rise in the current money supply caused the rise in future output because of this timing, but in fact the reverse is true.

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Working with Macroeconomic Data 1.

Generally, sharp changes up and down in productivity are correlated with business cycles.

Productivity often declines in recessions and rises faster in expansions.

2.

a. Unanticipated money growth usually declines before recessions in the 1960s, 1970s, and 1980s.

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b. The nominal interest rate declines when there is an upward spike in unanticipated money growth in the 1960s.

c. In the 1973–1975 recession, unanticipated money growth rises sharply and the real interest rate is negative.

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3.

The plots show that the forecasts are fairly rational, as they lie along a 45-degree line, as we would expect with rational forecasts. There are some deviations from the 45-degree line, but they do not appear systematic.

4.

The Michigan survey of households shows inflation expectations consistently below those of the Survey of Professional Forecasters in the early 1980s but consistently above the SPF forecasts after 2000.

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Comparing both forecasts with the realized inflation rate, we see that the SPF was generally more accurate, though not in the 1980s.

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Chapter 11 Keynesianism: The Macroeconomics of Wage and Price Rigidity n

Learning Objectives

I.

Goals of Chapter 11 A. Summarize the Keynesian explanations for real-wage rigidity (Sec. 11.1) B. Describe the causes and effects of price stickiness according to the Keynesian model (Sec. 11.2) C. Analyze the effects of monetary and fiscal policy in the Keynesian model (Sec. 11.3) D. Explain Keynesian theories about business cycles and macroeconomic stabilization (Sec. 11.4)

II. Notes to Ninth Edition Users A. We added a summary box comparing the Keynesian view with the classical view on many dimensions

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Teaching Notes

I.

Real-Wage Rigidity (Sec. 11.1)

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A. Wage rigidity is important in explaining unemployment 1. In the classical model, unemployment is due to mismatches between workers and firms 2. Keynesians are skeptical, believing that recessions lead to substantial cyclical unemployment 3. Keynesians view equilibrium as a situation in which there is no upward or downward pressure on wages 4. To get a model in which unemployment persists, Keynesian theory posits that the real wage is slow to adjust to equilibrate the labor market B. Some reasons for real-wage rigidity 1. For unemployment to exist, the real wage must exceed the market-clearing wage 2. If the real wage is too high, why don’t firms reduce the wage? a. One possibility is that the minimum wage and labor unions prevent wages from being reduced (1) But most U.S. workers are not minimum wage workers, nor are they in unions (2) The minimum wage would explain why the nominal wage is rigid, but not why the real wage is rigid (3) This might be a better explanation in Europe, where unions are far more powerful b. Another possibility is that a firm may want to pay high wages to get a stable labor force and avoid turnover costs—costs of hiring and training new workers c. A third reason is that workers’ productivity may depend on the wages they’re paid—the efficiency wage model C. The Efficiency Wage Model 1. Workers who feel well treated will work harder and more efficiently (the “carrot”); this is Akerlof’s gift exchange motive 2. Workers who are well paid will not risk losing their jobs by shirking (the “stick”) 3. Both the gift exchange motive and shirking model imply that a worker’s effort depends on the real wage (Figure 11.1)

Figure 11.1

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4. The effort curve, plotting effort against the real wage, is S-shaped a. At low levels of the real wage, workers make hardly any effort b. Effort rises as the real wage increases c. As the real wage becomes very high, effort flattens out as it reaches the maximum possible level D. Wage determination in the efficiency wage model 1. Given the effort curve, what determines the real wage firms will pay?

2. To maximize profit, firms choose the real wage that gets the most effort from workers for each dollar of real wages paid 3. This occurs at point B in Figure 11.1, where a line from the origin is just tangent to the effort curve 4. The wage rate at point B is called the efficiency wage 5. The real wage is rigid, as long as the effort curve does not change E. Employment and Unemployment in the Efficiency Wage Model 1. The labor market now determines employment and unemployment, depending on how far above the market-clearing wage is the efficiency wage (Figure 11.2)

Figure 11.2 2. The labor supply curve is upward sloping, while the labor demand curve is the marginal product of labor when the effort level is determined by the efficiency wage 3. The difference between labor supply and labor demand is the amount of unemployment 4. The fact that there is unemployment puts no downward pressure on the real wage, since firms know that if they reduce the real wage, effort will decline Analytical Problem 5 takes a more sophisticated look at the labor market, dividing it into one sector with an efficiency wage and another sector in which the real wage equates labor demand and supply.

5. Does the efficiency wage theory match up with the data? a. It seems to have worked for Henry Ford in 1914 b. Plants that pay higher wages appear to experience less shirking c. But the theory implies that the real wage is completely rigid, whereas the data suggests that the real wage moves over time and over the business cycle d. It is possible to jazz up the model to allow for the efficiency wage to change over time

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(1) Workers would be less likely to shirk and would work harder during a recession if the probability of losing their jobs increased (2) This would cause the effort curve to rise and may cause the efficiency wage to decline somewhat (3) This would lead to a lower real wage rate in recessions, which is consistent with the data F.

Efficiency wages and the FE line 1. The FE line is vertical, as in the classical model, since full-employment output is determined in the labor market and does not depend on the real interest rate 2. But in the Keynesian model, changes in labor supply do not affect the FE line, since they do not affect equilibrium employment 3. A change in productivity does affect the FE line, since it affects labor demand Numerical Problem 1 looks at the determination of the efficiency wage and employment.

II.

Price Stickiness (Sec. 11.2) A. Price stickiness is the tendency of prices to adjust slowly to changes in the economy 1. The data suggest that money is not neutral, so Keynesians reject the classical model (without misperceptions) 2. Keynesians developed the idea of price stickiness to explain why money is not neutral 3. An alternative version of the Keynesian model (discussed in Appendix 11.A) assumes that nominal wages are sticky, rather than prices; that model also suggests that money is not neutral

Theoretical Application The idea that nominal wage contracts lead to a fixed nominal wage in a theoretical Keynesian model was developed by Stanley Fischer, “Long-term Contracts, Rational Expectations, and the Optimal Money Supply Rule,” Journal of Political Economy, February 1977, pp. 191–205, and John B. Taylor, “Aggregate Dynamics and Staggered Contracts,” Journal of Political Economy, February 1980, pp. 1–23. But empirical analysis casts doubt on the theory, as shown by Shaghil Ahmed, “Wage Stickiness and the Non-neutrality of Money: A Cross-Industry Analysis,” Journal of Monetary Economics, 1987, pp. 25–50.

B. Sources of price stickiness: Monopolistic competition and menu costs 1. Monopolistic competition a. If markets had perfect competition, the market would force prices to adjust rapidly; sellers are price takers, because they must accept the market price b. In many markets, sellers have some degree of monopoly; they are price setters under monopolistic competition c. Keynesians suggest that many markets are characterized by monopolistic competition d. In monopolistically competitive markets, sellers do three things (1) They set prices in nominal terms and maintain those prices for some period (2) They adjust output to meet the demand at their fixed nominal price (3) They readjust prices from time to time when costs or demand change significantly e. Menu costs and price stickiness (1) The term menu costs comes from the costs faced by a restaurant when it changes prices—it must print new menus (2) Even small costs like these may prevent sellers from changing prices often

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(3) Since competition is not perfect, having the wrong price temporarily will not affect the seller’s profits much (4) The firm will change prices when demand or costs of production change enough to warrant the price change

Theoretical Application One of the first articles to present the combination of monopolistic competition and menu costs as the cause of price stickiness was N. Gregory Mankiw, “Small Menu Costs and Large Business Cycles: A Macroeconomic Model of Monopoly,” Quarterly Journal of Economics, May 1985, pp. 529–537. f. Empirical evidence on price stickiness (1) Blinder and his students found a high degree of price stickiness in their survey of firms (a) The main reason for price stickiness was managers’ fear that if they raised their prices, they would lose customers to rivals (2) But catalog prices also do not seem to change much from one issue to the next and often change by only small amounts, suggesting that while prices are sticky, menu costs may not be the reason (Kashyap) (3) Price stickiness may not be pervasive, as prices change on average every 4.3 months (Bils–Klenow)

Empirical Application Following up on the Bils-Klenow observation, economists at the Federal Reserve have developed a sticky-price consumer price index, which might provide improved forecasts of inflation. The index is based on looking at changes in the prices of goods that change less often, on average, than every 4.3 months. See Michael F. Bryan and Brent Meyer, “Are Some Prices in the CPI More Forward Looking than Others? We Think So.” Federal Reserve Bank of Cleveland Economic Commentary, Number 2010-2, May 19, 2010.

(5) But some of the measured price stickiness is because of sales; when you look at price changes excluding sales, prices change on average every 11 months (Nakamura– Steinsson) (6) Relative prices may respond quickly to supply or demand shocks for a particular good, but the price level may change slowly to changes in monetary policy (Boivin– Giannoni–Mihov), so in our macroeconomic model, the assumption of price stickiness is useful g. Meeting the demand at the fixed nominal price (1) Since firms have some monopoly power, they price goods at a markup over their marginal cost of production: P = (1 + h)MC

(11.1)

(2) If demand turns out to be larger at that price than the firm planned, the firm will still meet the demand at that price, since it earns additional profits due to the markup (3) Since the firm is paying an efficiency wage, it can hire more workers at that wage to produce more goods when necessary (4) This means that the economy can produce an amount of output that is not on the FE line during the period in which prices have not adjusted

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Theoretical Application Modern Keynesian theory depends on monopoly power and the markup. Recently, however, this view of the markup has been challenged. Empirical work has suggested that the markup is not countercyclical, as the Keynesian model of the business cycle suggests, and is instead procyclical or acyclical. See Christopher J. Nekerda and Valerie A. Ramey, “The Cyclical Behavior of the Price-Cost Markup,” University of California at San Diego manuscript, 2013. h. Effective labor demand (1) The firm’s labor demand is thus determined by the demand for its output (2) The effective labor demand curve, NDe(Y ), shows how much labor is needed to produce the output demanded in the economy (Figure 11.3)

Figure 11.3 (3) It slopes upward from left to right because a firm needs more labor to produce additional output

Empirical Application The theory of price stickiness leads to an empirical method of measuring inflation expectations.

Because some prices are sticky and others are more flexible, prices that are sticky seem likely to reflect inflation expectations. Michael S. Bryan and Brent Meyer, in their article “Are Some Prices in the CPI More Forward Looking than Others? We Think So,” Federal Reserve Bank of Cleveland Economic Commentary 2010-2, May 19, 2010, show how they can extract information on inflation expectations from the subset of prices that are fairly sticky, ignoring more flexible prices. The Federal Reserve Bank of Atlanta maintains an updated measure of the sticky-price CPI at: http://www.frbatlanta.org/research/inflationproject/stickyprice/.

Theoretical Application The major articles underlying Keynesian theory are collected in the volume New Keynesian Economics, edited by N. Gregory Mankiw and David Romer, Cambridge, Massachusetts: MIT Press, 1991. The main topics covered are costly price adjustment, the staggering of wages and

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prices, imperfect competition, coordination failures, the labor market, the credit market, and the goods market.

III. Monetary and Fiscal Policy in the Keynesian Model (Sec. 11.3) A. Monetary policy 1. Monetary policy in the Keynesian IS–LM model a. The Keynesian FE line differs from the classical model in two respects (1) The Keynesian level of full employment occurs where the efficiency wage line intersects the labor demand curve, not where labor supply equals labor demand, as in the classical model (2) Changes in labor supply do not affect the FE line in the Keynesian model; they do in the classical model b. Since prices are sticky in the short run in the Keynesian model, the price level does not adjust to restore general equilibrium (1) Keynesians assume that when not in general equilibrium, the economy lies at the intersection of the IS and LM curves, and may be off the FE line (2) This represents the assumption that firms meet the demand for their products by adjusting employment Numerical Problem 2 and Analytical Problems 1 and 2 use the Keynesian IS–LM model. c. Analysis of an increase in the nominal money supply (Figure 11.4) (1) LM curve shifts down from LM1 to LM2 (2) Output rises and the real interest rate falls (3) Firms raise employment and production due to increased demand (4) The increase in money supply is an expansionary monetary policy (easy money); a decrease in money supply is contractionary monetary policy (tight money) (5) Easy money increases real money supply, causing the real interest rate to fall to clear the money market (a) The lower real interest rate increases consumption and investment (b) With higher demand for output, firms increase production and employment (6) Eventually firms raise prices, the LM curve shifts back to its original level, and general equilibrium is restored (7) Thus money is neutral in the long run, but not in the short run

Data Application For a discussion of how monetary policy affects different parts of the economy, see the article by David Reifschneider, Robert Tetlow, and John Williams, “Aggregate Disturbances, Monetary Policy, and the Macroeconomy: The FRB/US Perspective,” Federal Reserve Bulletin, January 1999.

The article discusses the Federal Reserve Board’s model of the economy.

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Figure 11.4 B. Monetary Policy in the Keynesian AD–AS framework 1. We can do the same analysis in the AD–AS framework, as was done in text Figure 9.14 2. The main difference between the Keynesian and classical approaches is the speed of price adjustment a. The classical model has fast price adjustment, so the SRAS curve is irrelevant b. In the Keynesian model, the short-run aggregate supply (SRAS) curve is horizontal, because monopolistically competitive firms face menu costs 3. The effect of a 10% increase in money supply is to shift the AD curve up by 10% a. Thus output rises in the short run to where the SRAS curve intersects the AD curve b. In the long run the price level rises, causing the SRAS curve to shift up such that it intersects the AD and LRAS curves 4. So in the Keynesian model, money is not neutral in the short run, but it is neutral in the long run Numerical Problem 4 uses the Keynesian AD–AS framework.

Theoretical Application Some Keynesians do not agree with the view presented in the textbook that a change in monetary policy has no effect on the long-run aggregate supply curve. J. Bradford DeLong and Lawrence H. Summers, “How Does Macroeconomic Policy Affect Output?” Brookings Papers on Economic Activity 2: 1988, pp. 433–480, argue that macroeconomic stabilization policy, including monetary policy, can change the full-employment rate of output. They cite data showing the asymmetric response of output to policy changes, suggesting that better stabilization policies can increase the average level of output.

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C. Fiscal policy 1. The effect of increased government purchases (Figure 11.5)

Figure 11.5 a. A temporary increase in government purchases shifts the IS curve up b. In the short run, output and the real interest rate increase c. The multiplier, DY/DG, tells how much increase in output comes from the increase in government spending (1) Keynesians think the multiplier is bigger than 1, so that not only does total output rise due to the increase in government purchases, but output going to the private sector increases as well (2) Classical analysis also gets an increase in output, but only because higher current or future taxes caused an increase in labor supply, a shift of the FE line (3) In the Keynesian model, the FE line does not shift, only the IS curve does d. When prices adjust, the LM curve shifts up and equilibrium is restored at the fullemployment level of output with a higher real interest rate than before e. Similar analysis comes from looking at the AD–AS framework (Figure 11.6)

Figure 11.6

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2. The effect of lower taxes a. Keynesians believe that a reduction of (lump-sum) taxes is expansionary, just like an increase in government purchases b. Keynesians reject Ricardian equivalence, believing that the reduction in taxes increases consumption spending, reducing desired national saving and shifting the IS curve up c. The only difference between lower taxes and increased government purchases is that when taxes are lower, consumption increases as a percentage of full-employment output, whereas when government purchases increase, government purchases become a larger percentage of full-employment output IV. The Keynesian Theory of Business Cycles and Macroeconomic Stabilization (Sec. 11.4) A. Keynesian business cycle theory 1. Keynesians think aggregate demand shocks are the primary source of business cycle fluctuations 2. Aggregate demand shocks are shocks to the IS or LM curves, such as fiscal policy, changes in desired investment arising from changes in the expected future marginal product of capital, changes in consumer confidence that affect desired saving, and changes in money demand or supply 3. A recession is caused by a shift of the aggregate demand curve to the left, either from the IS curve shifting down, or the LM curve shifting up (text Fig. 11.7) 4. The Keynesian theory fits certain business cycle facts a. There are recurrent fluctuations in output b. Employment fluctuates in the same direction as output c. Money is procyclical and leading d. Investment and durable goods spending is procyclical and volatile (1) This is explained by the Keynesian model if shocks to investment and durable goods spending are a main source of business cycles (2) Keynes believed in “animal spirits,” waves of pessimism and optimism, as a key source of business cycles e. Inflation is procyclical and lagging (1) The Keynesian model fits the data on inflation, because the price level declines after a recession has begun, as the economy moves toward general equilibrium 5. Procyclical labor productivity and labor hoarding a. As discussed in Sec. 11.1, firms may hoard labor in a recession rather than fire workers, because of the costs of hiring and training new workers b. Such hoarded labor is used less intensively, being used on make-work or maintenance tasks that do not contribute to measured output c. Thus in a recession, measured productivity is low, even though the production function is stable d. So labor hoarding explains why labor productivity is procyclical in the data without assuming that recessions and expansions are caused by productivity shocks

Theoretical Application Several prominent macroeconomists discuss their views of the Keynesian model of business cycles in a symposium in the Journal of Economic Perspectives, Winter 1993.

B. Macroeconomic stabilization 1. Keynesians favor government actions to stabilize the economy

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2. Recessions are undesirable because the unemployed are hurt 3. Suppose there is a shock that shifts the IS curve down, causing a recession (Figure 11.7; like text Figure 11.8)

Figure 11.7 a. If the government does nothing, eventually the price level will decline, restoring general equilibrium. But output and employment may remain below their full-employment levels for some time b. The government could increase the money supply, shifting the LM curve down to move the economy to general equilibrium c. The government could increase government purchases to shift the IS curve back up to restore general equilibrium 4. Using monetary or fiscal policy to restore general equilibrium has the advantage of acting quickly, rather than waiting some time for the price level to decline 5. But the price level is higher in the long run when using policy than it would be if the government took no action 6. The choice of monetary or fiscal policy affects the composition of spending a. An increase in government purchases crowds out consumption and investment spending, because of a higher real interest rate b. Tax burdens are also higher when government purchases increase, further reducing consumption Analytical Problem 4 looks at the benefits of using government purchases to combat recessions.

7. Difficulties of macroeconomic stabilization a. Macroeconomic stabilization is the use of monetary and fiscal policies to moderate the business cycle; also called aggregate demand management b. In practice, macroeconomic stabilization has not been terribly successful c. One problem is in gauging how far the economy is from full employment, since we cannot measure or analyze the state of the economy perfectly d. Another problem is that we do not know the quantitative impact on output of a change in policy e. Also, because policies take time to implement (implementation lag) and take effect (impact lag), using them requires good forecasts of where the economy will be six months or a year in the future; but our forecasting ability is quite imprecise .

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Analytical Problem 3 looks at how lags in the effect of policy can influence decisions about how to use policy. f. These problems suggest that policy should not be used to “fine tune” the economy, but should be used to combat major recessions

Policy Application A general analysis of the possibility of using activist monetary policy, which contrasts the results from classical and Keynesian theories, is Tom Stark and Herb Taylor, “Activist Monetary Policy for Good or Evil? The New Keynesians vs. the New Classicals,” Federal Reserve Bank of Philadelphia Business Review, March/April 1991.

C. Supply shocks in the Keynesian model 1. Until the mid-1970s, Keynesians focused on demand shocks as the main source of business cycles 2. But the oil price shock that hit the economy beginning in 1973 forced Keynesians to reformulate their theory 3. Now Keynesians concede that supply shocks can cause recessions, but they do not think supply shocks are the main source of recessions 4. An adverse oil price shock shifts the FE line left (Figure 11.8; like text Figure 11.9)

Figure 11.8 a. The average price level rises, shifting the LM curve up (from LM1 to LM2), because the large increase in the price of oil outweighs the menu costs that would otherwise hold prices fixed b. The LM curve could shift farther than the FE line, as in the figure, though that is not necessary c. So in the short run, inflation rises and output falls d. There is not much that stabilization policy can do about the decline in output that occurs, because of the lower level of full-employment output e. Inflation is already increased due to the shock; expansionary policy to increase output would increase inflation further

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D. In Touch with Data and Research: DSGE Models and the Classical-Keynesian Debate 1. Until recently, classicals and Keynesians used very different models 2. Recently, each group has incorporated ideas from the other group; Keynesian economists began using DSGE models and classicals began using sticky prices and imperfect competition 3. Research with DSGE models is increasingly being used by central banks for applied policy analysis E. Comparing the Keynesian View with the Classical View 1. Speed of price adjustment 2. Appropriate model 3. Importance of supply shocks 4. Role of government 5. Do inflation expectations matter?

6. Type of model 7. Model of unemployment 8. Labor market equilibrium 9. Labor supply affects FE line?

V.

Appendix 11.A: Labor Contracts and Nominal-Wage Rigidity A. Some Keynesians think the nonneutrality of money is because of nominal-wage rigidity, not nominal-price rigidity 1. Nominal wages could be rigid because of long-term contracts between firms and unions 2. With nominal-wage rigidity, the short-run aggregate supply curve slopes upward instead of being horizontal 3. Even so, the main results of the Keynesian model still hold B. The short-run aggregate supply curve with labor contracts 1. U.S. labor contracts usually specify employment conditions and the nominal wage rate for three to five years 2. Employers decide on workers’ hours and must pay them the contracted nominal wage 3. The result is an upward-sloping short-run aggregate supply curve a. As the price level rises, the real wage declines, since the nominal wage is fixed b. As the real wage declines, firms hire more workers and thus increase output C. Nonneutrality of money 1. Money is not neutral in this model, because as the money supply increases, the AD curve shifts along the fixed (upward-sloping) SRAS curve (Figure 11.9; like text Figure 11.A.1)

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Figure 11.9 2. As a result, output and the price level increase 3. Over time, workers will negotiate higher nominal wages and the SRAS curve will shift left to restore general equilibrium 4. Thus money is nonneutral in the short run but neutral in the long run 5. There are several objections to this theory a. Less than one-sixth of the U.S. labor force is unionized and covered by long-term wage contracts; however, some nonunion workers get wages similar to those in union contracts, and other workers may have implicit contracts that act like long-term contracts b. Some labor contracts are indexed to inflation, so the real wage is fixed, not the nominal wage; however, most contracts aren’t completely indexed c. The theory predicts that real wages will be countercyclical, but in fact they are procyclical; however, if there are both aggregate supply shocks and aggregate demand shocks, real wages may turn out on average to be procyclical, but could still be countercyclical for demand shocks Numerical Problem 5 is an exercise dealing with the rigid nominal-wage version of the Keynesian model.

VI. Appendix 11.C: The Multiplier in the Short-Run Keynesian Model A. The multiplier shows the change in output resulting from a one-unit change in government purchases 1. First, calculate the effect on the intercept of the IS curve, aIS, of a change in G a. aIS = (c0 + i0 + G - cYt0)/(cr + ir) same as (9.A.15) b. If G increases by DG, DaIS = DG/(cr + ir) 2. Second, calculate the effect on Y of a change in aIS a. The AD curve intersects the SRAS curve at Y = [aIS - aLM + (1/

r

)(M/Psr)]/[bIS + bLM]

(11.C.1) (11.C.2)

(11.C.3)

same as (9.A.27) b. From (11.C.3), DY = DaIS/(bIS + bLM)

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(11.C.4)

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3. Finally, combine both effects a. Substituting (11.C.2) in (11.C.4) we get DY/DG = 1/[(cr + ir)(bIS + bLM)]

(11.C.5)

b. This is the government purchases multiplier c. The multiplier is positive, since all the terms in it are positive; it may be greater or less than one d. The multiplier will be large if the LM curve is flat (bLM is zero), since then the shift in the IS curve has a large effect on output (1) In this special case, DY/DG = 1/[1 - (1 - t)cY] (2) For example, if the MPC is cY = 0.8 and t = 0.25, then the multiplier is 2.5 e. The multiplier will be small if the LM curve is steep (bLM is large)

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(11.C.6)

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Additional Issues for Classroom Discussion

1.

Do Lags Eliminate the Effectiveness of Fiscal Policy?

275

Keynesian economists in the past have encouraged the use of fiscal policy to combat recession. They believe that wages and prices do not adjust rapidly enough to bring the economy to full employment in a reasonable period of time without the help of changes in government expenditures. However, fiscal policy takes a long time to be implemented. Can we expect it to be effective in combating recessions?

Fiscal policy cannot be changed rapidly. When the economy goes into a recession, we usually do not know it until several months later (recognition lag). Once a recession has been identified, a program must be devised. The next step is to convince the legislature that the expansionary program is necessary and to gain agreement on its specific provisions (legislative lag). Only once the necessary laws are passed can the program be implemented. Changes in taxes are implemented relatively rapidly, but if changes in expenditures are passed, more time is needed (implementation lag). The government may contract with the private sector, but it must often request and evaluate bids and select someone to administer the program before the funds can be spent. When the government itself supervises the program, new workers must be hired and trained. In either case, a period of several months if not a year or more is required before the program can be implemented.

Since 1950, business cycle contractions have averaged eleven months. To pass through all the stages outlined above and for fiscal policy to take effect seems to exceed the eleven months of an average contraction. Some recessions are even shorter; for example, the 1980 recession lasted only six months, entirely too short a period of time for discretionary fiscal policy to have an impact (impact lag).

In fact, government intervention may actually make the economic situation worse. If a stimulus package is implemented after the recession is over, it may result in upward pressure on prices and encourage a boom and bust cycle rather than long-term sustainable growth.

2.

Do Prices Adjust Slowly?

One of the main differences between Keynesians and classical economists is their disagreement over how quickly prices adjust to changes in the economy. Which point of view seems more in line with what happens in the economy?

In some markets, prices do adjust rapidly. This is particularly true in commodity markets such as those for corn and wheat. It is also true for items such as gasoline. While gas stations are individualized by their location and service, prices still change frequently. On the other hand, many prices are changed only infrequently. The text mentions such items as magazines and items sold through catalogs. While the authors point out that the monetary cost of such price changes is generally small, there may be other costs that are more important. Changing prices may encourage rivals to change their prices, too, and thus set off price wars that damage most competitors. The airline industry is noted for frequent price changes and destructive competition. In addition, an increase in price above the customary cost may cause consumers to rethink old habits and move to other products.

Your students may wish to discuss whether they side with the Keynesians or the classicals on the question of price rigidity. In looking at price movements, it is probably important that discussants explicitly define which goods’ prices are being discussed, since this may be critical in determining an individual’s point of view.

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The Interest Rate Forecast for 1993

In late 1992, private forecasters suggested that the Fed would need to raise interest rates in 1993 as the economy expanded. This can be seen in Figure 11.10, in which the economy is initially in equilibrium with the IS curve at IS 0 and the LM curve at LM 0. The forecast for 1993 was that the IS curve would shift up and to the right to IS1. If the Fed maintained the real interest rate at r0, it would need to expand the money supply to shift the LM curve to LM1, which would increase output beyond the full-employment level. To prevent this, the Fed would have to allow interest rates to rise to r1.

Figure 11.10 However, in early 1993, President Clinton announced a contractionary fiscal policy. This had the effect of shifting the IS curve to IS2. It also meant that the Fed would not need to raise interest rates, because the IS curve would no longer be shifting to the right beyond the full-employment point. Maintaining the initial level of the real interest rate at r0 meant increasing the money supply, so the LM curve shifted to LM2.

Forecasters anticipated this, and responded to President Clinton’s announcement by changing their forecasts of interest rates, holding them constant throughout the year.

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Answers to Textbook Problems

Review Questions 1. The efficiency wage is the real wage that maximizes effort or efficiency per dollar of real wages. It assumes that workers will exert more effort, the higher the real wage. The real wage will remain rigid even if there is an excess supply of labor, because firms will not reduce the wage they pay; doing so would reduce their profits, since workers wouldn’t work as hard.

2. Full-employment output is the amount of output produced by firms with employment determined by the labor demand curve at the point where the marginal product of labor equals the efficiency wage.

A productivity shock does not lead to a change in the efficiency wage, since it does not affect work effort. But it does affect the marginal product of labor, so employment changes. A beneficial productivity shock, for example, leads to an increase in employment. Both the employment increase and the increase in productivity lead to an increase in full-employment output.

Labor supply changes have no effect on the efficiency wage or employment; they simply affect the amount of unemployment. So they have no impact on full-employment output.

3. Price stickiness is the tendency of prices to adjust only slowly to changes in the economy. Keynesians believe it is important to allow for price stickiness to explain why monetary policy is not neutral.

4. Menu costs are the costs of changing prices. Menu costs may lead to price stickiness in monopolistically competitive markets but not in perfectly competitive markets, because a monopolistically competitive firm’s demand is not as sensitive to the price as is a perfectly competitive firm’s demand. Monopolistically competitive firms may meet the demand at a fixed price when demand increases, because price exceeds marginal cost, so that profits still rise, and because the cost of changing prices may exceed the additional profit earned from doing so.

A perfect competitor would lose all of its customers if its price were a little above the price charged by its competitors. But a monopolistically competitive firm would lose only some of its customers in this case.

5. In the Keynesian model, money is not neutral in the short run, but it is neutral in the long run. In the short run, an increase in the money supply increases output and the real interest rate, while the price level and real (efficiency) wage are unchanged. In the long run, however, only the price level is changed, with no change in output, the real interest rate, or the real wage. In the basic classical model, money is neutral in both the short run and the long run, so only the price level is affected by a change in the money supply, just as in the long-run Keynesian model. The extended classical model with misperceptions is similar to the Keynesian model. In the short run, an increase in the money supply increases output and the real interest rate, just as in the Keynesian model. However, unlike the Keynesian model, the price level rises, as does the real wage. The long run of the extended classical model is identical to the classical model or the long run of the Keynesian model—only the price level is affected.

6. In the Keynesian model in the short run, output and the real interest rate increase due to an increase in government purchases. In the long run, the real interest rate is higher, but output returns to its fullemployment level. Since the real interest rate is higher in the long run, investment is lower and consumption is lower.

7.

In response to a recession, policymakers can (1) make no change in macroeconomic policy, (2) increase the money supply, or (3) increase government purchases.

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If they make no change in macroeconomic policy, then during the recession output is below its full-employment level. Over time, the price level will decline to restore equilibrium. In the long run, the price level will be lower and employment will return to the full-employment level.

If policymakers increase the money supply, the economy returns to full employment without a change in the price level. The composition of output is the same as when the economy returns to full employment without monetary or fiscal policy.

If policymakers increase government purchases, again the economy returns to full-employment equilibrium without a change in the price level. However, the higher real interest rate caused by the expansionary fiscal policy reduces consumption and investment, and the higher taxes to pay for the government spending also reduce consumption relative to either the situation in which monetary policy is used, or in which there is no policy response at all.

There are practical difficulties with increasing the money supply or increasing government purchases to return the economy to full employment. It is difficult to tell how far the economy is below full employment to know the right amount of fiscal or monetary stimulus to apply. We do not know exactly how much output will increase in response to a monetary or fiscal expansion. And since these policies take time to implement and more time to affect the economy, we really need to know where the economy will be six months or a year from now, not just where it is today, but such knowledge is very imprecise.

8. Employment is procyclical because a contractionary aggregate demand shock reduces both output and employment. Money is procyclical because price stickiness means that an increase in the money supply increases output as the aggregate demand curve moves along the flat, short-run, aggregate supply curve. Inflation is procyclical, because in a recession the price level declines over time to restore general equilibrium. Investment is procyclical for two reasons. First, shifts in the expected future marginal product of capital are important causes of cycles, shifting the IS and AD curves, thus affecting output in the same direction. Also, a shift in the LM curve leads to a change in the real interest rate, moving investment in the same direction as the change in output.

9. The Keynesian theory assumes that demand shocks cause most cyclical fluctuations. This means that during expansions when employment rises, average labor productivity declines, so it is countercyclical.

But the business cycle fact is that average labor productivity is mildly procyclical. However, if labor hoarding occurs, so that a given measured amount of employment produces less output during recessions and more output during expansions, then measured average labor productivity would be procyclical.

10. In Keynesian analysis, a supply shock may reduce output in two ways: (1) a reduction in output, because the supply shock reduces the marginal product of labor, shifting the FE line to the left; and (2) a further reduction in output if the supply shock is something like an oil price shock that is large enough to cause many firms to raise prices, shifting the LM curve up and to the left so much that it intersects the IS curve to the left of the FE line. Supply shocks create problems for stabilization policy because: (1) policy can do nothing to affect the location of the FE line; and (2) using expansionary policy risks worsening the already-high rate of inflation.

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Numerical Problems 1.

The following table shows the real wage (w), the effort level (E), and the effort per unit of real wages (E/w). w

E

E/w

8 10 12 14 16 18

7 10 15 17 19 20

0.875 1.00 1.25 1.21 1.19 1.11

The firm will pay a wage of 12, since that wage provides the maximum effort per unit of the real wage (E/w = 1.25). The firm will employ 88 workers, since that is the number of workers for which w = MPN. As long as the supply of labor exceeds the demand for labor, labor supply has no effect on the firm’s decision.

2.

(a) The IS curve is found from the equation Y = C d + I d + G = 130 + 0.5(Y - 100) - 500r + 100 500r + 100, or 0.5Y = 280 - 1000r, or Y = 560 - 2000r.

The LM curve comes from the equation M/P = L, which in this case is 1320/P = 0.5Y - 1000r, or Y = (2640/P) + 2000r. (b) At full employment, Y = 500. Using this in the IS curve gives 500 = 560 - 2000r, which has the solution r = 0.03. Plugging the values for Y and r in the LM curve gives 500 = (2640/P) + (2000 ´ 0.03), or 440 = 2640/P, which has the solution P = 6. Then consumption is C = 130 + 0.5(Y - 100) 500r = 130 + 0.5(500 - 100) - (500 ´ 0.03) = 315. Investment is I = 100 - (500 ´ 0.03) = 85. (c) If desired investment increases to 200 - 500r, the IS curve shifts from IS1 to IS2 in Figure 11.11.

This can be seen in the equation Y = C d + I d + G = 130 + 0.5(Y - 100) - 500r + 200 - 500r + 100, or 0.5Y = 380 - 1000r, or Y = 760 - 2000r. In the short run, the price level remains fixed at 6, so the LM curve remains at LM1. With the price level equal to 6, the LM curve has the equation Y = (2640/P) + 2000r = 440 + 2000r. The IS and LM curves intersect where 760 - 2000r = 440 + 2000r, or 320 = 4000r, which has the solution r = 0.08. At r = 0.08, output is given from the IS curve as Y = 760 - 2000r = 760 - (2000 ´ 0.08) = 600. Then consumption is C = 130 + 0.5 (Y - 100) - 500r = 130 + 0.5(600 - 100) - (500 ´ 0.08) = 340. Investment is I = 200 - 500r = 200 - (500 ´ 0.08) = 160.

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Figure 11.11 In the long run, the price level rises to shift the LM curve from LM1 to LM2 to restore equilibrium.

The IS curve is given by the equation Y = 760 - 2000r. At full employment, Y = 500, so the IS curve is 500 = 760 - 2000r, or 2000r = 260, which has the solution r = 0.13. The LM curve is given by the equation Y = (2640/P) + 2000r, or 500 = (2640/P) + (2000 ´ 0.13), or 240 = 2640/P, which has the solution P = 11. Then consumption is C = 130 + 0.5(500 - 100) - (500 ´ 0.13) = 265. Investment is I = 200 - 500r = 200 - (500 ´ 0.13) = 135.

3.

(a) Y = C + I + G = [388 + 0.4(Y - 300) - 600r] + [352 - 400r] + 280 = 900 + 0.4Y - 1000r, so 0.6Y = 900 - 1000r. Therefore, Y = 1500 - (1666 + 2/3)r. Equivalently, r = 0.9 - 0.0006Y. (b) 12600/7 = M/P = L = 1750 + 0.75Y - 8750(r + 0.02), so 1800 = 1750 + 0.75Y - 8750r - 175.

Therefore, 225 = 0.75Y - 8750r, so Y = 300 + (11,666+2/3)r. Equivalently, r = -0.0257143 + 0.0000857143Y or r = -9/350 + (3/35000)Y. (c) IS–LM intersection: 1500 - (1666 + 2/3)r = Y = 300 + (11,666 + 2/3)r, so 1200 = (13,333 + 1/3)r.

Therefore, r = 0.09. Substitute r = 0.09 into the IS curve to obtain Y = 1500 - [(1666+2/3) ´ 0.09], so Y = 1350. As a check, you can substitute r = 0.09 into the equation for the LM curve, to obtain Y = 300 + [(11,666 + 2/3) ´ 0.09] = 1350.

Consumption = C = 388 + 0.4(Y - T) - 600r = 388 + 0.4(1350 - 300) - (600 ´ 0.09) = 388 + 420 - 54, so C = 754.

Investment = I = 352 - 400r = 352 - (400 ´ 0.09), so I = 316.

Note that C + I + G = 754 + 316 + 280 = 1350 = Y. (d) In long-run equilibrium, output equals its full-employment level, so Y = 1400.

Substitute Y = 1400 into the IS curve to obtain r = 0.9 - 0.0006Y = 0.9 - (0.0006 ´ 1400), so r = 0.06.

Consumption = C = 388 + 0.4(Y - T) - 600r = 388 + 0.4(1400 - 300) - (600 ´ 0.06), so C = 792.

Investment = I = 352 - 400r = 352 - (400 ´ 0.06), so I = 328.

Note that C + I + G = 792 + 328 + 280 = 1400 = Y. (e) M/P = L, so P = M/L = 12,600/[1750 + 0.75Y - 8750(r + pe )] = 12,600/{1750 + (0.75 ´ 1400) [8750(0.06 + 0.02)]}= 12,600/2100, so P = 6.

Velocity = real output/real money supply = Y/(M/P), where Y = 1400 and M/P = 12600/6 = 2100.

Therefore, velocity = 1400/2100, so velocity = 2/3.

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Chapter 11 Keynesianism: The Macroeconomics of Wage and Price Rigidity

(f) (1) (2)

(3)

(4)

281

Set I = 320 in the investment equation (I = 352 - 400r) to obtain 320 = 352 - 400r, which implies 400r = 32. Therefore, the real interest rate must be r = 0.08 to attain I = 320.

In long-run equilibrium, output equals its full-employment level, so Y = 1400. Therefore, Y = C + I + G implies 1400 = C + 320 + 350, so C = 730 in long-run equilibrium when I = 320 and G = 350.

In long-run equilibrium with I = 320 and G = 350, Y = 1400 and r = 0.08. Set C = 730 in the consumption function C = 388 + 0.4(Y - T) - 600r to obtain 730 = 388 + 0.4(1400 - T) - (600 ´ 0.08). Therefore, 0.4T = 388 + 560 - 48 - 730 = 170, which implies T = 425 to attain the level of consumption in part (2) in long-run equilibrium with I = 320 and G = 350.

In long-run equilibrium, Y = 1400 and r = 0.08, so L = 1750 + 0.75Y - 8750(r + p e ) = 1750 + (0.75 ´ 1400) - [8750 ´ (0.08 + 0.02)] = 1925. Since M/P = L = 1925, we have M = 1925 ´ P. To attain P = 6 in long-run equilibrium with I = 320 and G = 350, the nominal money supply must be M = 1925 ´ 6, so M = 11,550.

4.

(a) The IS curve is given by Y = C d + I d + G = 300 + 0.5(Y - 100) - 300r + 100 - 100r + 100 = 450 + 0.5Y - 400r. This can be rewritten as 0.5Y = 450 - 400r, or Y = 900 - 800r. The LM curve is M/P = L, or 6300/P = 0.5Y - 200r.

To find the aggregate demand curve, substitute the LM curve into the IS curve to eliminate r.

To do this, multiply both sides of the LM curve by 4 to get 25,200/P = 2Y - 800r, or 800r = 2Y - (25,200/P). Then substitute this in the IS curve: Y = 900 - 800r = 900 - [2Y - (25,200/P)].

This can be rewritten as 3Y = 900 + (25,200/P), or Y = 300 + (8400/P). (b) With P = 15, the AD curve is Y = 300 + (8400/15) = 860. From the IS curve, 860 = 900 - 800r, which has the solution r = 0.05. Consumption is C = 300 + 0.5(860 - 100) - (300 ´ 0.05) = 665.

Investment is I = 100 - (100 ´ 0.05) = 95. (c) In the long run, Y = 700. From the IS equation, 700 = 900 - 800r, which has the solution r = 0.25.

The LM curve then is 6300/P = (0.5 ´ 700) - (200 ´ 0.25) = 300, which has the solution P = 21.

Consumption is C = 300 + 0.5(700 - 100) - (300 ´ 0.25) = 525. Investment is I = 100 - (100 ´ 0.25) = 75.

5.

(a) Setting w = MPN, w = 10/ N . This is the labor demand curve. (b) At W = 20, w = W/P = 20/P. Since labor demand is given by w = 10/ N , then 20/P = 10/ N , or 2 N = P. (c) Y = 20 N = 10P, or P = (1/10) Y, as shown in Figure 11.14 by the SRAS curve.

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Figure 11.14 (d) The IS curve is Y = 120 - 500r. The LM curve is M/P = 0.5Y - 500r, which can be rewritten as 500r = 0.5Y - (M/P). Plugging the LM curve into the IS curve to eliminate r gives Y = 120 500r = 120 - [0.5Y - (M/P)]. This can be rewritten as 1.5Y = 120 + (M/P). This is the AD curve.

With M = 300, the AD curve is 1.5Y = 120 + (300/P), or Y = 80 + (200/P). The AD curve is shown in Figure 11.14. (e) To find the intersection of the SRAS curve (Y = 10P) and the AD curve [Y = 80 + (200/P)], find the price level such that 10P = 80 + (200/P). This can be rewritten as 10P2 - 80P - 200 = 0, or as P2 - 8P - 20 = 0. This can be factored as (P - 10)(P + 2) = 0. The nonnegative root is P = 10. At P = 10, from the SRAS curve, Y = 10 P = 10 ´ 10 = 100. On the IS curve, 100 = 120 - 500r, or r = 0.04. Since P = 2 N , or 10 = 2 N , then N = 5, or N = 25. The real wage is w = 20/P = 20/10 = 2. (f ) When the money supply falls to 135, the AD curve becomes 1.5Y = 120 + (135/P), or Y = 80 + (90/P). The AD curve intersects the SRAS curve where 10P = 80 + (90/P). This can be rewritten as 10P2 - 80P - 90 = 0, or P2 - 8P - 9 = 0. This can be factored as (P - 9)(P + 1) = 0, which has the nonnegative solution P = 9. From the SRAS curve, Y = 10P = 10 ´ 9 = 90. From the IS curve 90 = 120 - 500r, which has the solution r = 0.06. Since P = 2 N , N = (P/2)2 = 4.52 = 20.25.

The real wage is w = W/P = 20/9 = 2 2/9.

6.

(a) Y = C d + I d + G = [325 + 0.5(1000 - 150) - 500r] + [200 - 500r] + 150, so 1000r = 100, so r = 0.10.

M/P = L, so 6000/P = 0.5Y - 1000r = (0.5 ´ 1000) - (1000 ´ 0.10) = 400, so P = 15.

C = 325 + 0.5(Y - T) - 500r = 325 + 0.5(1000 - 150) - (500 ´ .10) = 700.

I = 200 - 500r = 200 - (500 ´ .10) = 150. (b) aIS = (c0 + i0 + G - cYt0)/(cr + ir) = [325 + 200 + 150 - (0.5 ´ 150)]/(500 + 500) = 0.6. bIS = [1 - (1 - t)cY]/(cr + ir) = [1 - (1 - 0) 0.5]/(500 + 500) = .0005. aLM = 0 / r - pe= 0/1000 - 0 = 0.

bLM = r

Y

/ r = 0.5/1000 = .0005.

= 1000.

(c) Since P = 15 at full employment, then Y = 1000 and r = 0.10. (d) aIS = (c0 + i0 + G - cYt0)/(cr + ir) = [325 + 200 + 250 - (0.5 ´ 150)]/(500 + 500) = 0.7.

M/P = 6000/15 = 400.

Y = [aIS - aLM + (1/ r )(M/P)]/[bIS + bLM] = [0.7 - 0 + (400/1000)]/(.0005 + .0005) = 1.1/.001 = 1100. (e) DY/DG = 1/[(cr + ir)(bIS + bLM)] = 1/[(500 + 500)(.0005 + .0005)] = 1.

The result is the same as in part (d). In part (d), DY = 100 when DG =100, so DY/DG = 1.

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Analytical Problems 1.

In Figures 11.15 and 11.16, point A is the starting point, point B shows the short-run equilibrium after the change, and point C shows the long-run equilibrium after the change.

Figure 11.15

Figure 11.16

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(a) In Figure 11.15, the increase in tax incentives increases investment, shifting the IS curve up and to the right from IS1 to IS2 in Figure 11.15(a), and shifting the AD curve from AD1 to AD2 in Figure 11.15(b). The short-run equilibrium is at point B. Output increases, the real interest rate increases, employment increases, and the price level is unchanged.

To restore long-run equilibrium, the price level rises, shifting the LM curve from LM1 to LM2 in Figure 11.15(a) and the short-run aggregate supply curve from SRAS1 to SRAS2 in Figure 11.15(b). The long-run equilibrium is at point C. Compared to the starting point, output is the same, the real interest rate is higher, employment is the same, and the price level is higher. (b) In Figure 11.16, the increase in tax incentives increases saving—shifting the IS curve from IS1 to IS2 in Figure 11.16(a), and shifting the AD curve from AD1 to AD2 in Figure 11.16(b). The shortrun equilibrium is at point B. Output decreases, the real interest rate decreases, employment decreases, and the price level is unchanged.

To restore long-run equilibrium, the price level declines, shifting the LM curve from LM1 to LM2 in Figure 11.16(a) and the short-run aggregate supply curve from SRAS1 to SRAS2 in Figure 11.16(b). The long-run equilibrium is at point C. Compared to the starting point, output is the same, the real interest rate is lower, employment is the same, and the price level is lower. (c) A wave of investor pessimism reduces investment. This shifts the IS curve down and to the left and the AD curve down and to the left, having the same result as in problem part (b). (d) An increase in consumer confidence increases consumption spending, shifting the IS curve up and to the right and the AD curve up and to the right, with the same result as in problem part (a).

2.

In Figures 11.17–11.20, point A is the starting point, point B shows the short-run equilibrium after the change, and point C shows the long-run equilibrium after the change. (a) In Figure 11.17, when banks pay a higher interest rate on checking accounts, the demand for money rises, shifting the LM curve up and to the left from LM1 to LM2 in Figure 11.17(a). As a result, the AD curve shifts down and to the left from AD1 to AD2 in Figure 11.17(b). The new short-run equilibrium occurs at point B, where output is lower, the real interest rate is higher, employment is lower, and the price level is unchanged.

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In the long run, the price level decreases to shift the LM curve from LM2 to LM3, which is the same as LM1, to restore equilibrium at point C. As a result, the short-run aggregate supply curve shifts down from SRAS1 to SRAS2. At the new equilibrium, compared to the starting point, output is the same, the real interest rate is the same, employment is the same, and the price level is lower.

Figure 11.17 (b) In Figure 11.18, the introduction of credit cards reduces the demand for money—shifting the LM curve down and to the right from LM1 to LM2 in Figure 11.18(a). As a result, the AD curve shifts from AD1 to AD2 in Figure 11.18(b). The new short-run equilibrium occurs at point B, where output is higher, the real interest rate is lower, employment is higher, and the price level is unchanged.

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In the long run, the price level increases to shift the LM curve from LM2 to LM3, which is the same as LM1, to restore equilibrium at point C. As a result, the short-run aggregate supply curve shifts up from SRAS1 to SRAS2. At the new equilibrium, compared to the starting point, output is the same, the real interest rate is the same, employment is the same, and the price level is higher.

Figure 11.18 (c) In Figure 11.19, the reduction in agricultural output shifts the FE curve to the left from FE1 to FE2, and shifts the LRAS line from LRAS1 to LRAS2. The rise in agricultural prices increases the price level, so the short-run aggregate supply curve shifts up from SRAS1 to SRAS2. Also, the rise in the price level shifts the LM curve up and to the left from LM1 to LM2. The short-run equilibrium is at point B, assuming that the LM curve shifts so much that it intersects the IS curve to the left

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of the FE line. At point B, compared to the starting point, output is lower, the real interest rate is higher, employment is lower, and the price level is higher.

Figure 11.19 If the water shortage persists, a new long-run equilibrium occurs at point C. To get to this equilibrium, the price level must decline, shifting the LM curve from LM2 to LM3, and the short-run aggregate supply curve from SRAS2 to SRAS3. Relative to point B, the new equilibrium has a higher output level, a lower real interest rate, higher employment, and a lower price level.

(Relative to the initial equilibrium at point A, output and employment are lower, and the real interest rate and the price level are higher.)

When the water shortage is over, then the economy goes back to point A in the long run, with no permanent effects.

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(d) In Figure 11.20, the beneficial supply shock makes more production possible at full employment, so the FE line shifts to the right in Figure 11.20(a) from FE1 to FE2, and the LRAS line shifts from LRAS1 to LRAS2 in Figure 11.20(b). There is no immediate change in the price level, so the LM curve remains at LM1 and the short-run aggregate supply curve remains at SRAS1. The shift of the FE curve does not affect aggregate demand in the short run: output, the real interest rate, and the price level are all unchanged in the short run. The shift in the production function shifts the effective labor demand curve and reduces employment in the short run.

Figure 11.20 If the supply shock persists, prices will decline, so the LM curve will shift from LM1 to LM2 and the SRAS curve will shift from SRAS1 to SRAS2. As shown in the diagrams, the economy reaches a new equilibrium at point C, with a higher output level, a lower real interest rate, and a lower price level.

When the supply shock disappears, the economy returns to its equilibrium at point A.

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A lag in the impact of policy of six months, which is about the time it takes firms to adjust prices, could cause policy to be destabilizing. That is, monetary policy may be pushing the economy away from equilibrium.

To see this, suppose the economy is in a recession at point A in Figure 11.21. The short-run aggregate-supply curve SRAS1 intersects the aggregate demand curve AD1 at point A, to the left of the long-run aggregate supply curve LRAS. Suppose the Fed engages in expansionary monetary policy to try to shift the aggregate demand curve from AD1 to AD2 in six months, to push the economy to point B. But the recession leads firms to reduce their prices, dropping the SRAS curve from SRAS1 to SRAS2. In the absence of monetary policy action, the economy would get back to full employment because of the fall in the price level to point C. But the Fed action leads to a new equilibrium at point D. So the Fed causes the economy to overshoot the equilibrium point. The result may be to exaggerate the business cycle, pushing output too high in expansions. Then if the Fed responds to an expansion by using contractionary monetary policy, it may overshoot on the other side, causing a new recession.

Figure 11.21 If the Fed could forecast recessions well, it could stabilize the economy by using monetary policy appropriately before a recession begins. Or if the Fed’s policy takes effect before firms adjust prices, then it can also help stabilize output by shifting the AD curve before the SRAS curve shifts.

4.

An increase in government purchases shifts the IS curve up and to the right and the AD curve up and to the right to return the economy to full employment, instead of waiting for the price level to fall to get there. The advantage of doing so, according to Keynesians, is that full employment is restored quickly, whereas if the price level must adjust, it may take a long time for full employment to be restored. In the short run, the fiscal expansion does not affect the real wage, since it is an efficiency wage. However, it increases employment and it increases current and future taxes to pay for the higher government spending. The effect on consumption is ambiguous, with the rise in output raising consumption, while the rise in taxes reduces consumption. In the long run, at full employment, the lasting effects of the fiscal expansion are to decrease consumption, because of the higher real interest rate and the higher taxes, with more of the economy’s output devoted to government purchases and less to the private sector. Whether a program of fiscal stimulus in response to a recession is worthwhile depends on the benefits of the government purchases and on how long it takes the economy to return to a full-employment equilibrium by a change in the price level. The more beneficial are government purchases, the more likely such a program is to increase economic welfare.

The longer the free market takes to restore equilibrium, the more likely such a program is to increase economic welfare.

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(a) In response to expansionary monetary policy, aggregate demand increases, increasing output and labor demand. This causes the labor demand curve to shift from ND1 to ND2 in the primary labor market, shown in Figure 11.22. The result is an increase in employment and output with no change in the real wage in the primary labor market. Since more workers are now in the primary labor market, the labor supply in the secondary labor market decreases from NS1 to NS2. This causes an increase in the real wage, a decrease in employment, and a decrease in output in the secondary labor market.

Figure 11.22 (b) Increased immigration has no effect in the primary labor market, since labor supply changes in general have no effect. In the secondary labor market, the immigration shifts the labor supply curve to the right from NS1 to NS2, causing a reduction in the real wage, increased employment, and increased output. However, to some extent these effects may be mitigated by the fact that increased immigration leads to increased aggregate demand, increasing labor demand in both the primary and secondary markets (Figure 11.23).

Figure 11.23

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(c) If there is a shift in the effort curve, the efficiency wage rises in the primary labor market. Since effort exerted at the higher wage is the same as before the change, the shift in the effort curve has no impact on the marginal product of labor, so there is no shift in the labor demand curve. So the effect of the higher real (efficiency) wage is to reduce employment and thus output in the primary labor market. This means that labor supply in the secondary labor market increases, shifting the labor supply curve from NS1 to NS2. The real wage falls, employment rises, and output rises in the secondary labor market, as Figure 11.24 shows.

Figure 11.24 (d) The productivity improvement shifts the labor demand curve to the right, so at the fixed real (efficiency) wage, firms demand more labor. Employment increases, so output increases in the primary labor market. The increase in employment in the primary labor market reduces the labor supply in the secondary labor market, shifting the labor supply curve from NS1 to NS2. This increases the real wage, and reduces employment and output in the secondary labor market.

See Figure 11.25.

Figure 11.25

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(e) The productivity improvement in the secondary labor market has no effect on the primary labor market. In the secondary labor market, increased productivity increases the marginal product of labor so that labor demand increases from ND1 to ND2. The result is a higher real wage, higher employment, and increased output (Figure 11.26).

Figure 11.26

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Working with Macroeconomic Data 1.

In the 1980s, usually the federal government deficit/GDP moved in the opposite direction as the short-term real interest rate and in the 2000s the federal government deficit/GDP moved in the same direction as the short-term real interest rate. In the 1970s and early 1980s, usually the federal government deficit/GDP moved in the opposite direction as the long-term real interest rate and in the 2000s the federal government deficit/GDP moved in the same direction as the long-term real interest rate.

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2.

Between 1960 and 1980, an increase in the money growth rate is followed after several years by an increase in the inflation rate; after 1980, the relationship disappears. The money growth rate rose because of financial innovation and thus became less important in determining the inflation rate.

3.

TPF growth generally declines when oil price growth is high. Classical economists would argue that the supply shock was the sole cause of the decline in TFP. Keynesian economists would say that price stickiness prevents the economy from returning to equilibrium quickly following the oilprice shock, so measured TFP growth declines.

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The real federal funds rate declines in recessions and rises in expansions, as suggested by the monetary-policy playbook.

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Learning Objectives

I.

Goals of Part 4 A. How macroeconomic policy works and how it can best be used 1. Unemployment and inflation (this chapter) 2. Policy in an open economy—international trade and finance (Ch. 13) 3. Monetary institutions and policy (Ch. 14) 4. Fiscal institutions and policy (Ch. 15)

II. Goals of Chapter 12 A. Describe the Phillips curve relationship between unemployment and inflation (Sec. 12.1) B. Discuss whether the Phillips curve offers a ‘menu’ of inflation-unemployment combinations from which policymakers can choose (Sec. 12.2) C. Identify the costs of unemployment and discuss the natural rate of unemployment (Sec. 12.3) D. Discuss the types and costs of inflation (Sec. 12.4) E. Discuss the challenges and costs of reducing inflation (Sec. 12.5)

III. Notes to Tenth Edition Users A.

In Section 12.3, we added a discussion of the costs of severe recessions

B.

Also in Section 12.3, we simplified the discussion of the natural rate of unemployment

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Teaching Notes

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Unemployment and Inflation: Is There a Trade-off? (Sec. 12.1)

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A. Many people think there is a trade-off between inflation and unemployment 1. The idea originated in 1958 when A.W. Phillips showed a negative relationship between unemployment and nominal wage growth in Britain 2. Since then economists have looked at the relationship between unemployment and inflation 3. In the 1950s and 1960s, many nations seemed to have a negative relationship between the two variables 4. The United States appears to be on one Phillips curve in the 1960s (text Figure 12.1) 5. This suggested that policymakers could choose the combination of unemployment and inflation they most desired 6. But the relationship fell apart in the following three decades (text Figure 12.2) 7. The 1970s were a particularly bad period, with both high inflation and high unemployment, inconsistent with the Phillips curve B. The expectations-augmented Phillips curve 1. Friedman and Phelps: The cyclical unemployment rate (the difference between actual and natural unemployment rates) depends only on unanticipated inflation (the difference between actual and expected inflation) a. This theory was made before the Phillips curve began breaking down in the 1970s b. It suggests that the relationship between inflation and the unemployment rate is not stable 2. How does this work in the extended classical model?

Analytical Problem 3 looks at similar analysis in a Keynesian model. a. First case: anticipated increase in money supply (Figure 12.1; like text Figure 12.3)

Figure 12.1 (1) AD shifts up and SRAS shifts up, with no misperceptions (2) Result: P rises, Y unchanged (3) Inflation rises with no change in unemployment b. Second case: unanticipated increase in money supply (Figure 12.2; like text Figure 12.4)

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Figure 12.2 (1) AD expected to shift up to AD2, old (money supply expected to rise 10%), but unexpectedly money supply rises 15%, so AD shifts further up to AD2, new (2) SRAS shifts up based on expected 10% rise in money supply (3) Result: P rises and Y rises as misperceptions occur (4) So higher inflation occurs with lower unemployment Numerical Problems 1 and 3 and Analytical Problem 2 look at the misperceptions model and how it generates behavior like the Phillips curve.

(5) Long run: P rises further, Y declines to full-employment level c. Expectations-augmented Phillips curve:

p = p e - h(u - u )

(12.1)

(1) When p = p e, u = u (2) When p < p e, u > u Numerical Problem 4 uses the expectations-augmented Phillips curve.

(3) When p > p e, u < u C. The shifting Phillips curve 1. The short-run Phillips curve shows the relationship between unemployment and inflation for a given expected rate of inflation and natural rate of unemployment 2. Changes in the expected rate of inflation (Figure 12.3; like text Figure 12.5)

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Figure 12.3 a. For a given expected rate of inflation, the short-run Phillips curve shows the trade-off between cyclical unemployment and actual inflation b. The short-run Phillips curve is drawn such that p = p e when u = u c. Higher expected inflation implies a higher short-run Phillips curve 3. Changes in the natural rate of unemployment (Figure 12.4; like text Figure 12.6)

Figure 12.4 a. For a given natural rate of unemployment, the short-run Phillips curve shows the trade-off between unemployment and unanticipated inflation Analytical Problem 1 looks at possible ways to change the natural rate of unemployment. b. A higher natural rate of unemployment shifts the short-run Phillips curve to the right 4. Supply shocks and the Phillips curve a. A supply shock increases both expected inflation and the natural rate of unemployment (1) A supply shock in the classical model increases the natural rate of unemployment, because it increases the mismatch between firms and workers

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(2) A supply shock in the Keynesian model reduces the marginal product of labor and thus reduces labor demand at the fixed real wage, so the natural unemployment rate rises b. So an adverse supply shock shifts the short-run Phillips curve up and to the right c. The short-run Phillips curve will be unstable in periods with many supply shocks Numerical Problem 2 looks at the effects of an aggregate demand shock and an aggregate supply shock on the short-run Phillips curve.

5. The shifting short-run Phillips curve in practice a. Why did the original Phillips curve relationship apply to many historical cases?

(1) The original relationship between inflation and unemployment holds up as long as expected inflation and the natural rate of unemployment are approximately constant (2) This was true in the United States in the 1960s, so the Phillips curve appeared to be stable b. Why did the U.S. Phillips curve disappear after 1970?

(1) Both the expected inflation rate and the natural rate of unemployment varied considerably more in the 1970s than they did in the 1960s (2) Especially important were the oil price shocks of 1973–1974 and 1979–1980 (3) Also, the composition of the labor force changed in the 1970s and there were other structural changes in the economy as well, raising the natural rate of unemployment (4) Monetary policy was expansionary in the 1970s, leading to high and volatile inflation (5) Plotting unanticipated inflation against cyclical unemployment shows a fairly stable relationship since 1970 (text Figure 12.7) II. Macroeconomic Policy and the Phillips Curve (Sec. 12.2) A. Can the Phillips curve be exploited by policymakers? Can they choose the optimal combination of unemployment and inflation?

1. Classical model: NO a. The unemployment rate returns to its natural level quickly, as people’s expectations adjust b. So unemployment can change from its natural level only for a very brief time c. Also, people catch on to policy games; they have rational expectations and try to anticipate policy changes, so there is no way to fool people systematically

Policy Application The theory of rational expectations explains why the Phillips curve trade-off appeared to be stable for some time, but failed when policymakers tried to exploit it. In the 1960s people assumed that any rise in inflation would be temporary. But once policymakers began to exploit the trade-off, people caught on quickly. Instead of having adaptive expectations, which were rational in the past, people began to watch what policymakers were doing. Then expected inflation changed quickly with changes in policy.

2. Keynesian model: YES, temporarily a. The expected rate of inflation in the Phillips curve is the forecast of inflation at the time the oldest sticky prices were set b. It takes time for prices and expected prices to adjust, so unemployment may differ from the natural rate for some time

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Theoretical Application The Keynesian models of the early 1970s assumed that people formed adaptive expectations, that is, that expected inflation depended only on past inflation, so p te = f (pt - 1, pt - 2, . . .). According to rational expectations theory, however, people base their inflation expectations on an economic model in which inflation depends on other variables, such as the growth rate of the money supply, the state of the economy, and expectations of future government deficits. Adaptive expectations could be rational, as in the 1950s and 1960s, because an economic model would suggest a simple time-series process for inflation. But once the Fed began using monetary policy for countercyclical policy, or for trying to exploit the Phillips curve, adaptive expectations became irrational. With rational expectations, people began to anticipate changes in monetary policy, and the Phillips curve began to shift with changes in policy.

B. In touch with data and research: The Lucas critique 1. When the rules of the game change, behavior changes 2. For example, if batters in baseball were called out after two strikes instead of three, they would swing more often when they have one strike than they do now 3. Lucas applied this idea to macroeconomics, arguing that historical relationships between variables will not hold up if there has been a major policy change 4. The short-run Phillips curve is a good example—it fell apart as soon as policymakers tried to exploit it 5. Evaluating policy requires an understanding of how behavior will change under the new policy, so both economic theory and empirical analysis are necessary

Theoretical Application Robert Lucas and Tom Sargent spelled out the implications of the Lucas critique for future work on macroeconomics and business cycles in their article, “After Keynesian Macroeconomics.”

Federal Reserve Bank of Minneapolis Quarterly Review, Spring, 1979, pp. 1–16.

C. The long-run Phillips curve 1. Long run: u = u for both Keynesians and classicals 2. The long-run Phillips curve is vertical, since when p = p e, u = u (Figure 12.5; like text Figure 12.8)

Figure 12.5

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3. Changes in the level of money supply have no long-run real effects; changes in the growth rate of money supply have no long-run real effects, either 4. Even though expansionary policy may reduce unemployment only temporarily, policymakers may want to do so if, for example, timing economic booms right before elections helps them (or their political allies) get reelected

Theoretical Application For a well written history of the Phillips curve and its usefulness, see the article by Robert J. Gordon, “The Phillips Curve Now and Then,” National Bureau of Economic Research Working Paper No. 3393, June 1990. Also, see the symposium in the Journal of Money, Credit, and Banking 39 (supplement, Feb. 2007).

III. The Problem of Unemployment (Sec. 12.3) A. The costs of unemployment 1. Loss in output from idle resources a. Workers lose income b. Society pays for unemployment benefits and makes up lost tax revenue c. Using Okun’s Law (each percentage point of cyclical unemployment is associated with a loss equal to 2% of full-employment output), if full-employment output is $17 trillion, each percentage point of unemployment sustained for one year costs $340 billion 2. Personal or psychological cost to workers and their families a. Especially important for those with long spells of unemployment 3. Severe recessions make costs of unemployment worse a. Costs vary inversely with wealth b. Long-term unemployment reduces the probability of finding a job and reduces expected future earnings 4. Costs of unemployment may vary across demographic groups 5. There are some offsetting factors a. Unemployment leads to increased job search and acquiring new skills, which may lead to increased future output b. Unemployed workers have increased leisure time, though most would not feel that the increased leisure compensated them for being unemployed

Data Application Recent research suggests that the costs of unemployment to individual workers may be higher if they become unemployed at the same time as many other people. Research by Stephen J. Davis and Till M. von Wachter, “Recessions and the Cost of Job Loss,” Brookings Papers on Economic Activity, Fall 2011, pp. 1-72, shows that people who are laid off in periods when the overall unemployment rate is 6% or less lose about 1.4 years’ worth of earnings; but those laid off in periods when the overall unemployment rate is above 8% lose twice as much, on average.

B. The long-term behavior of the unemployment rate 1. The changing natural rate a. How do we calculate the natural rate of unemployment? b. CBO’s estimates: about 4.7% in 2017 c. In the 1980s and 1990s, demographic forces reduced the natural rate of unemployment (text Fig. 12.9) (1) The proportion of the labor force aged 16–24 years fell from 25% in 1980 to 16% .

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in 1998 and to 13% in 2018 (2) Research by Shimer showed this is the main reason for the fall in the natural rate of unemployment d. The natural rate of unemployment began declining around 2013, perhaps because of a reduction in labor-force participation rates Data Application A very different picture of the natural rate of unemployment than that of the CBO comes from classical economists, who think the natural rate changes much more than the CBO’s measure does.

One version of this can be found in the article “In Search of the Natural Rate of Unemployment,”

by Thomas B. King and James Morley, Journal of Monetary Economics (2007), pp. 550–564.

2. Measuring the natural rate of unemployment a. Policymakers need a measure of the natural rate of unemployment to use the unemployment rate for setting policy b. Economists disagree about how to measure the natural rate of unemployment and the CBO has often revised its measure c. Staiger, Stock, and Watson found that the natural rate cannot be measured precisely with econometric methods, as the confidence interval is very large d. What should policymakers do in response to uncertainty about the natural rate of unemployment?

(1) They may wish to be less aggressive with policy than they would be if they knew the natural rate more precisely (2) Research (Orphanides-Williams) suggests that the rise of inflation in the 1970s can be blamed on bad estimates of the natural rate Analytical Problem 6 looks at events that change the natural rate of unemployment.

IV. The Problem of Inflation (Sec. 12.4) A. The costs of inflation 1. Perfectly anticipated inflation a. No effects if all prices and wages keep up with inflation b. Even returns on assets may rise exactly with inflation c. Shoe-leather costs: People spend resources to economize on currency holdings; the estimated cost of 10% inflation is 0.3% of GNP d. Menu costs: the costs of changing prices (but technology may mitigate this somewhat) Analytical Problem 4 looks at the costs of anticipated and unanticipated inflation in a cashless society.

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Policy Application Shoe-leather costs are generated by people’s attempt to reduce how much cash they hold.

Implicitly, inflation is like a tax on people’s cash holdings, because the government buys things with newly printed money (just like it could if it collected taxes to pay for them) and people who hold cash lose purchasing power (just as if their money was taxed). Some economists have gone so far as to suggest that using the inflation tax is beneficial to the economy, because much of the burden is borne by people in the underground economy and foreigners who use U.S. dollars. See S. Rao Aiyagari, “Deflating the Case for Zero Inflation,” Federal Reserve Bank of Minneapolis Quarterly Review, Summer 1990.

Policy Application Two other costs of anticipated inflation are increased taxation on capital income and the mortgage-tilt problem.

Because taxes are based on the dollar value of interest that savers receive, the higher the inflation rate is, the larger is the government’s tax revenue as a proportion of a saver’s real return. The increase in the government’s effective real tax rate represents a distortion to the economy—higher anticipated inflation reduces saving and investment.

Another cost of perfectly anticipated inflation is the problem of “tilting” the real value of loan payments over time. To see this, suppose inflation were zero and you borrowed $100,000 to buy a house, repaying the mortgage loan over 30 years. At an interest rate of 5% per year, your monthly mortgage payment would be $540. In real (inflation-adjusted) terms, the payment would be the same over time. But if the inflation rate were 5% per year and the mortgage interest rate were 10% per year, your monthly payment would be $880. In real terms, the value of the monthly payment would be very high initially but decline steadily over time. The real value of your final payment would be just 23% of your initial payment. (The value of a dollar payment made 30 years in the future at an interest rate of 5% is given by the formula 1/1.0530 = $0.23.) A graph of the real payment amount tilts downward, so this phenomenon is often referred to as the mortgage-tilt problem. The tilt is greater, the higher is the inflation rate. Because of the mortgage-tilt problem, homeowners face higher real payments early in the lives of their loans, when they can probably least afford it, and they may face difficulties getting approved for mortgages because the initial payment is a larger fraction of their household income. Thus, anticipated inflation reduces homeownership. (For more discussion of the mortgage-tilt problem and an estimate of the benefits to eliminating the problem by reducing inflation to zero, see Dean Croushore, “What Are the Costs of Disinflation?” Business Review, Federal Reserve Bank of Philadelphia, May/June 1992, pp. 3–16.)

2. Unanticipated inflation (p - p e) a. Realized real returns differ from expected real returns (1) Expected r = i - p e (2) Actual r = i - p (3) Actual r differs from expected r by p e – p (4) Numerical example: i = 6%, p e = 4%, so expected r = 2%; if p = 6%, actual r = 0%; if p = 2%, actual r = 4% b. Similar effect on wages and salaries c. Result: transfer of wealth (1) From lenders to borrowers when p > p e

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(2) From borrowers to lenders when p < p e

Data Application Since the inflation of the mid-1970 was a surprise to people, it led to a large transfer of wealth.

The biggest winners in the 1970s were homeowners who owned land (which appreciated in value with inflation) and had fixed-rate mortgages (whose value fell with inflation). The biggest losers were the wealthy who owned stocks and bonds, as real returns fell dramatically because of inflation. d. So people want to avoid risk of unanticipated inflation (1) They spend resources to forecast inflation

Data Application In my article, “Inflation Forecasts: How Good Are They?” (Federal Reserve Bank of Philadelphia Business Review, May/June 1996), I examine tests of bias in the inflation forecasts of both consumers and professional forecasters. The forecasts looked very bad in the 1970s, probably because of the two big oil price shocks in that period. Since then, the forecasts have been very good, suggesting that the forecasts are formed rationally.

(2) In touch with data and research: Indexed contracts (a) People could use indexed contracts to avoid the risk of transferring wealth because of unanticipated inflation (b) Most U.S. financial contracts are not indexed, with the exception of some long-term contracts like adjustable-rate mortgages and inflation-indexed bonds issued by the U.S. Treasury beginning in 1997 (c) Many U.S. labor contracts are indexed by COLAs (cost-of-living adjustments) (d) Indexed contracts are more prevalent in countries with high inflation

Policy Application It is difficult to figure out how to index wages to inflation, or how low inflation should be, when inflation isn’t measured very well. For an interesting discussion of the issues and implications of mismeasurement of inflation, see the symposium on “Measuring the CPI” in the Journal of Economic Perspectives, Winter 1998. e. Loss of valuable signals provided by prices (1) Confusion over changes in aggregate prices vs. changes in relative prices (2) People expend resources to extract correct signals from prices

Data Application For a review of the empirical evidence on the costs of inflation, see the article by John Driffill, Grayham E. Mizon, and Alistair Ulph, “Costs of Inflation,” in B. M. Friedman and F. H. Hahn, eds., Handbook of Monetary Economics, vol. II, Amsterdam: Elsevier Science Publishers, 1990, pp. 1013–1066.

3. The costs of hyperinflation a. Hyperinflation is a very high, sustained inflation (e.g., 50% or more per month) (1) Hungary in August 1945 had inflation of 19,800% per month .

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(2) In Zimbabwe, the annual rate of inflation was 1017% in 2006, 10,453% in 2007, and soared to 55.6 billion percent in 2008, before dropping to 6.5% in 2009

Data Application There are many wonderful stories one can tell to illustrate the problems that arise in hyperinflations. For example, there is the story about the person who goes to the bank with a wheelbarrow full of money, but cannot get the wheelbarrow through the bank’s door. He goes inside to get help and when he returns, the money is still there but the wheelbarrow has been stolen. There is also the mind-boggling size of the hyperinflation figures. For example, in Hungary between August 1945 and July 1946, the purchasing power of a unit of money fell by a factor of 4 octillion! That’s 4,000,000,000,000,000,000,000,000,000. b. There are large shoe-leather costs, as people minimize cash balances c. People spend many resources getting rid of money as fast as possible d. Tax collections fall, as people pay taxes with money whose value has declined sharply e. Prices become worthless as signals, so markets become inefficient 4. Can Inflation Be Too Low? a. Should central banks be concerned about low inflation rates or even deflation (negative rates of inflation?) b. Low inflation can be harmful 1. Borrowers are hurt by unexpectedly low inflation, as in the 1930s, when deflation led to severe financial distress 2. Anticipated deflation also has costs, such as the increase in real wages if nominal wages are sticky, leading to lower employment 3. Understanding relative prices can also be difficult in a deflationary environment c. Nominal interest rates cannot generally fall below zero, so under deflation, real interest rates cannot be very low 1. So a central bank’s ability to reduce real interest rates to combat a recession is limited 2. For example, if deflation occurs at a rate of 2% (that is, the inflation rate is negative 2%), the lowest real interest rate possible occurs when the nominal interest rate is 0%, in which case the real interest rate is 2% 3. However, if inflation were positive 2%, the central bank could achieve a real interest rate of negative 2% d. What inflation rate should central banks aim for?

1. Many central banks target inflation around 2% 2. An inflation rate around 2% keeps the costs of inflation fairly low 3. But an inflation rate of 2% is high enough that there is only a small risk that the economy will suffer from deflation 4. In addition, inflation measures are biased up, so 2% measured inflation means that true inflation is somewhat lower

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Policy Application Given the costs of inflation and the vertical long-run Phillips curve, what is the optimal rate of inflation? Some economists suggest that the optimal rate of inflation is zero or even negative (so that the nominal rate of interest is zero). See the discussion by Michelle R. Garfinkel, “What Is an ‘Acceptable’ Rate of Inflation? A Review of the Issues,” Federal Reserve Bank of St. Louis Review, July/August 1989. pp. 3–16. The debate over the pursuit of zero inflation reached its peak in 1990 in the United States and Canada. Two conferences reflecting research on zero inflation were held in Canada; see Zero Inflation: The Goal of Price Stability, Richard G. Lipsey, ed., and Taking Aim: The Debate on Zero Inflation, Robert C. York, ed., both published by the C.D. Howe Institute, Ottawa, Ontario, 1990. Canada’s central bank adopted a target of zero inflation in the early 1990s.

V. Fighting Inflation: The Role of Inflationary Expectations (Sec. 12.5) A. If rapid money growth causes inflation, why do central banks allow the money supply to grow rapidly?

1. Developing or war-torn countries may not be able to raise taxes or borrow, so they print money to finance spending 2. Industrialized countries may try to use expansionary monetary policy to fight recessions, then not tighten monetary policy enough later B. Disinflation is a reduction in the rate of inflation 1. But disinflations may lead to recessions 2. An unexpected reduction in inflation leads to a rise in unemployment along the Phillips curve

Data Application There are many problems with price indexes; they are imperfect measures of price changes. What do the indexes do when new goods are introduced? What happens as more efficient stores replace stores that had higher intermediate costs? How do we account for the fact that people substitute cheaper goods for higher-priced goods? Inadequate treatment of these questions means the measures of prices give an overestimate of the inflation rate of 0% to 2%. So a measured inflation rate of 1% might really mean that the true average price level is constant. See David E. Lebow, John M. Roberts, and David J. Stockton, “Understanding the Goal of Price Stability,” Working Paper No. 125, Economic Activity Section, Board of Governors of the Federal Reserve System, April 1992.

C. The costs of disinflation could be reduced if expected inflation fell at the same time actual inflation fell D. Rapid versus gradual disinflation 1. The classical prescription for disinflation is cold turkey—a rapid and decisive reduction in money growth a. Proponents argue that the economy will adjust fairly quickly, with low costs of adjustment, if the policy is announced well in advance b. Keynesians disagree (1) Price stickiness due to menu costs and wage stickiness due to labor contracts make adjustment slow (2) Cold turkey disinflation would cause a major recession

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(3) The strategy might fail to alter inflation expectations, because if the costs of the policy are high (because the economy goes into recession), the government will reverse the policy

Data Application Tom Sargent (“The Ends of Four Big Inflations”) suggests that high rates of inflation may be reduced quickly with little output loss if a country creates an independent central bank and changes its fiscal policy to eliminate government budget deficits. Robert Gordon (“Why Stopping Inflation May Be Costly: Evidence from Fourteen Historical Episodes”) suggests that there have been very few disinflation episodes without substantial output loss; most recent disinflations have been accompanied by substantial recessions. See their articles in Robert E. Hall, ed., Inflation: Causes and Effects, Chicago: University of Chicago Press, 1982.

2. The Keynesian prescription for disinflation is gradualism a. A gradual approach gives prices and wages time to adjust to the disinflation

Policy Application In the late 1980s the Federal Reserve embarked on an attempt at gradualism, at least in their stated ranges for the M2 monetary aggregate. The Fed lowered the growth range for M2 by roughly ½ percentage point each year from 1986 to 1994. b. Such a strategy will be politically sustainable because the costs are low

Data Application In my article “What Are the Costs of Disinflation?” Federal Reserve Bank of Philadelphia Business Review, May/June 1992, pp. 3–16, I examine the costs to the economy of reducing inflation from its existing rate to zero in a variety of models: a Keynesian model, a Monetarist model, a classical (misperceptions) model, and a hybrid model. The costs of disinflation are found to be substantially smaller than the benefits in all but the Keynesian model.

E. In touch with data and research: The sacrifice ratio 1. When unanticipated tight monetary and fiscal policies are used to reduce inflation, they reduce output and employment for a time, a cost that must be weighed against the benefits of lower inflation 2. Economists use the sacrifice ratio as a measure of the costs a. The sacrifice ratio is the number of percentage points of output lost in reducing inflation by one percentage point b. For example, a study of past disinflations by Laurence Ball found that U.S. inflation fell by 8.83 percentage points in the early 1980s, with a loss in output of 16.18 percent of the nation’s potential output (1) The sacrifice ratio was 16.18 divided by 8.83, which equals 1.832 3. Ball studied the sacrifice ratios for many different disinflations around the world in the 1960s, 1970s, and 1980s a. The sacrifice ratios varied substantially across countries, from less than 1 to almost 3 b. One factor affecting the sacrifice ratio is the flexibility of the labor market (1) Countries with slow wage adjustment (e.g., because of heavy government regulation of the labor market) have higher sacrifice ratios

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c.

Ball also found a lower sacrifice ratio from cold turkey disinflation than from gradualism 4. Ball’s results should be interpreted with caution, since it is not easy to calculate the loss of output and because supply shocks can distort the calculation of the sacrifice ratio

Data Application A version of Ball’s article that is accessible to students is “How Costly Is Disinflation? The Historical Evidence,” Federal Reserve Bank of Philadelphia Business Review, November/December 1993, pp. 17–28.

F. Wage and price controls 1. Pro: Controls would hold down inflation, thus lowering expected inflation and reducing the costs of disinflation 2. Con: Controls lead to shortages and inefficiency; once controls are lifted, prices will rise again 3. The outcome of wage and price controls may depend on what happens with fiscal and monetary policy a. If policies remain expansionary, people will expect renewed inflation when the controls are lifted b. If tight policies are pursued, expected inflation may decline Analytical Problem 5 looks at what happens if the government uses wage and price controls, but continues to use expansionary policies.

4. The Nixon wage-price controls from August 1971 to April 1974 led to shortages in many products; the controls reduced inflation when they were in effect, but prices returned to where they would have been soon after the controls were lifted G. Credibility and reputation 1. Key determinant of the costs of disinflation: how quickly expected inflation adjusts 2. This depends on credibility of disinflation policy; if people believe the government and if the government carries through with its policy, expected inflation should drop rapidly 3. Credibility can be enhanced if the government gets a reputation for carrying out its promises 4. Also, having a strong and independent central bank that is committed to low inflation provides credibility H. The U.S. disinflation of the 1980s and 1990s 1. Fed chairmen Volcker and Greenspan gradually reduced the inflation rate in the 1980s and 1990s a. They sought to eliminate inflation as a source of economic instability b. They wanted people to be confident that inflation would never be very high again 2. To judge the Fed’s success, we look at inflation expectations (text Fig. 12.10) a. Inflation expectations were erratic before 1990 b. Inflation expectations fell gradually from 1990 to 1998 and have been stable since then 3. Inflation expectations were slow to decline initially (in the late 1970s and early 1980s) because Volcker and the Fed lacked credibility 4. But as inflation continued to fall, the Fed’s credibility increased, and inflation expectations declined gradually 5. To solidify those expectations, the Fed declared a 2% long-run inflation target in 2012

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Data Application In the severe recession that began in December 2007 and was precipitated by the housing crisis, inflation declined substantially. Some analysts thought that inflation fell mainly because of the decline in housing prices. However, as economists at the Federal Reserve Bank of San Francisco note (see Bart Hobijn, Stefano Eusepi, and Andrea Tambalotti, “The Housing Drag on Core Inflation,” Federal Reserve Bank of San Francisco Economic Letter, 2010–11, April 5, 2010, available online at: www.frbsf.org/publications/economics/letter/2010/el2010-11.pdf), this was not the case; instead, prices of most goods and services stopped growing as rapidly as before. Core inflation including housing prices does not differ much from core inflation excluding housing prices.

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Additional Issues for Classroom Discussion

1.

Additional Costs of Anticipated Inflation

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The interaction of the tax system with inflation. Most countries’ tax systems are not perfectly indexed for inflation. They impose taxes on nominal, not real, returns on investments (bonds and stocks), which distort the prices on those assets. Also, capital gains are taxed in nominal terms, so investors may pay a big tax on assets whose value hasn’t even increased in real terms. Eytan Sheshinski, in “Treatment of Capital Income in Recent Tax Reforms and the Cost of Capital in Industrialized Countries,” in Larry Summers, ed., Tax Policy and the Economy 4, Cambridge, Mass.: MIT Press, 1990, pp. 25–42, found that the implicit tax rate on real investment returns exceeded 100% at times in the 1970s, and was over 50% in the 1980s, all because of taxing nominal returns instead of real returns.

To see this in a simple example (with a simplifying assumption that the real return, not the after-tax real return, is fixed), consider two cases in which there is a 30% tax rate. Case A has inflation of 0% and a nominal interest rate of 2%. An investor loses .6% of the 2% return to taxation, thus netting 1.4% in both nominal and real terms. In case B, inflation is 5% and the nominal interest rate is 7%. Taxation costs 2.1% of the 7% return, leaving a nominal after-tax return of 4.9%. Subtracting the inflation rate gives a real after-tax return of –0.1%. (Though the simplifying assumption generates these results, this seems consistent with the data.) A solution to this problem is to adjust capital values for inflation before taxing them.

The mortgage tilt problem. Mortgage loans are most often made at fixed rates for long terms. When inflation is positive, the constant nominal payment over time is much higher in real terms early in the life of the loan, and lower in real terms later in the life of the loan, because of a higher price level. This means that the burden of paying the loan is higher when households are younger. So if the households are liquidity constrained, they may not be able to afford to buy a home as early as they could if there was no inflation.

Here is a numerical example. Consider a $100,000, 30-year mortgage. In case A inflation is 0% and the nominal interest rate is 5%. The monthly payment is $540, the real value of which is constant over time.

Using the 28% rule used by lenders today (that a person’s mortgage payment should not exceed 28% of income), a person would have to have income of $23,000 to qualify for the mortgage. In case B inflation is 5% and the nominal interest rate is 10%. The monthly payment on the mortgage is $880. But this amount declines steadily over time in real terms because of inflation. The income needed to qualify for the mortgage is $37,000. So in case B with higher inflation, the initial monthly payment is higher and the income needed to qualify for the loan is higher, so inflation discourages homeownership. (Again, the result would not be so dramatic except for some simplifications; the 28% rule might become a higher number if inflation were lower.) There is a potential solution to this problem, which is the introduction of a price-level-adjusted mortgage (PLAM); but PLAMs have not yet been adopted by financial institutions.

2.

Can Unemployment Help Workers and the Economy?

If an unemployed worker always accepted the first job offered, unemployment would decrease in the short run. However, such a practice is likely to reduce output and to lead to more frequent periods of unemployment over several years. Accepting the first opening made available will often put a person into a position that does not match his or her skills, preferences, and abilities. When the job and the individual are not well suited to each other, both the employer and the employee are likely to be dissatisfied and productivity will tend to be lower. Workers are more likely to leave such positions. Taking additional time to find a better fit normally will result in the worker finding a situation that makes good use of his or her skills and abilities. This will often lead to the new employee being very productive and staying with the new company for a long time.

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Should the Fed Aim for Zero Inflation?

Discuss with your students the ultimate goal of the Federal Reserve (or any other country’s central bank).

Should the goal be to drive inflation to zero? Why is zero the best point to be? Is it good enough for inflation to be close to zero, but positive, if it is low and steady?

Here are some things to consider.

First, what is the optimal rate of inflation? Milton Friedman and others have shown theoretically that, in their models, the optimal rate of inflation is negative. Ideally, the marginal private cost of holding money (that is, the opportunity cost, which equals the nominal interest rate) should equal the marginal social cost of holding money, which is zero. For the nominal interest rate to be zero, the inflation rate must equal the negative of the real interest rate. But a different theoretical model, developed by James Tobin and others, suggests that the optimal inflation rate is positive because of downward wage and price rigidity, and (in another model) inflation should be positive to encourage investment. Finally, Martin Feldstein’s research suggests that the optimal rate of inflation is zero, because otherwise inflation interacts with the tax system to distort resource allocation.

Second, if the inflation rate is mismeasured (see the discussion of the bias in the CPI in Chapter 2), that should affect the Fed’s target. If the CPI inflation rate is overstated by 1 to 2 percentage points per year, then a true target of zero inflation corresponds to measured inflation of 1 to 2 percent.

Third, what are the costs and benefits of reducing inflation? Is achieving lower inflation worth the costs?

Calculations of the sacrifice ratio suggest that to permanently reduce inflation by one percentage point costs the economy 2 to 3 percentage points of lost output. That is the cost of the transition to lower inflation.

In addition, there are some permanent costs and benefits of lower inflation. On the cost side, with lower inflation, the government earns less seignorage revenue from printing money, so it will have to increase taxes (which distort economic decisions) to make up for the lost revenue. On the benefit side, lower inflation reduces a number of distortions to the economy. First, a lower inflation rate brings the private cost of holding money closer to the social cost. Second, a lower inflation rate reduces distortions with the tax system. Since the tax system does not adequately account for inflation, it subsidizes housing capital at the expense of other capital, because the returns to housing aren’t taxed.

Finally, how do the costs relate to the benefits? Separate calculations by Martin Feldstein and Andrew Abel (in Christina D. Romer and David H. Romer, eds., Reducing Inflation: Motivation and Strategy, Chicago: University of Chicago Press for NBER, 1997) both show that the benefits of reducing inflation by 2 percentage points outweigh the costs. Many other researchers have found similar results, though some economists have found that the costs exceed the benefits.

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Answers to Textbook Problems

Review Questions 1. The Phillips curve is an empirical negative relationship between inflation and unemployment. The Phillips curve relationship held for U.S. data in the 1960s, but broke down in the 1970s and 1980s.

2. In the original Phillips curve, inflation itself is related to the unemployment rate. In the expectationsaugmented Phillips curve, it is unanticipated inflation (the difference between actual and expected inflation) that is related to cyclical unemployment (the difference between the unemployment rate and the natural rate of unemployment). The short-run Phillips curve appears in the data at times when both expected inflation and the natural rate of unemployment are fixed.

3. In the early 1960s the rate of inflation was fairly low (about 1% to 2%), and it did not vary much from year to year. But supply shocks hit the economy in both the mid- and the late-1970s, causing a rise in expected inflation and an upward shift in the Phillips curve. Expansionary monetary and fiscal policies kept inflation high in the 1970s until the Federal Reserve began pursuing contractionary monetary policy to reduce inflation during 1979–1982. This moved the economy to a lower Phillips curve, which was maintained in the 1980s. The instability of the Phillips curve is largely because of higher expected inflation associated with supply shocks in the 1970s.

4. According to the classical point of view, the economy adjusts quickly to changes in inflation, so there is only a very short period in which unemployment changes because of a change in inflation. Further, any systematic attempt to reduce unemployment by increasing inflation would be fully anticipated, and would have no effect on unemployment.

Keynesians believe, however, that there is a temporary trade-off between unemployment and inflation. If policymakers want to, they can increase inflation to reduce unemployment in the short run. However, the economy must return to the natural rate of unemployment in the long run, so the reduction in unemployment is only temporary.

5. Policymakers want to keep inflation low because inflation imposes costs on the economy. Costs of anticipated inflation include shoe leather costs and menu costs. Costs of unanticipated inflation include unpredictable transfers of wealth between lenders and borrowers, resources used to reduce the risk of such transfers, and reduced efficiency because of the difficulty in observing relative prices.

When there is cyclical unemployment, society as a whole loses because of output that is not produced and the families of the unemployed suffer personal and psychological costs.

6. The natural rate of unemployment is the rate of unemployment that exists when output is at its fullemployment level. This occurs when the only unemployment is frictional and structural, not cyclical.

The natural rate is crucial in understanding the Phillips curve.

The natural rate of unemployment has moved higher over time in the United States and Europe due to a number of factors. First, demographic changes occurred that raised the natural rate. Groups in the labor force that have higher rates of unemployment have increased in size relative to groups that have lower rates of unemployment. Also, there have been structural changes in the economy that may have raised the natural rate in the 1970s. In Europe, hysteresis has kept the unemployment rate from declining much after it hit very high levels in the early 1980s. Hysteresis arises because of government regulation and bureaucratic aspects of firms and labor unions, and due to insiders keeping outsiders from gaining employment.

To reduce the natural rate of unemployment, the government could support job training and worker relocation, reduce regulations to increase labor market flexibility, reform unemployment insurance, or

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create a high-pressure economy.

7. Two costs of anticipated inflation are shoe-leather costs and menu costs. Two costs of unanticipated inflation are transfers of wealth and confusion of price signals.

If the economy experiences hyperinflation, shoe-leather costs become very large as people try to minimize their cash holdings. Also, prices change so frequently they cease to serve as signals. Menu costs do not rise too much, as firms simply quote prices in terms of some other unit of account (a different country’s currency). Transfers of wealth also occur, especially since the government loses tax revenue as people delay paying taxes.

8. The greatest potential cost of disinflation is that it may cause a recession. This occurs because inflation may fall below expected inflation, causing the unemployment rate to rise along the Phillips curve.

However, if the public anticipates the disinflation, expected inflation will adjust quickly and the costs of disinflation will be low.

9. One approach to disinflation is a cold turkey strategy. It has the advantage of reducing inflation quickly, but it may have high costs from increasing unemployment, according to Keynesians.

So, Keynesians suggest a gradualist policy to reduce inflation more slowly but with less rise in unemployment. This also has the advantage of being politically sustainable, since policymakers are less likely to back off from disinflation.

10. The Federal Reserve works hard to establish its credibility so that the costs of reducing inflation will be low. If the Federal Reserve has a great deal of credibility, then people will believe that the inflation rate will not rise in the future, so the expected inflation rate will be low and stable. The sacrifice ratio will also be low, so the costs of disinflation will be reduced.

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Numerical Problems 1.

2.

(a) Equating aggregate demand to short-run aggregate supply gives: 300 + 10(M/P) = 500 + P - Pe, or 300 + (10 ´ 1000/P) = 500 + P - 50, or 10,000/P = 150 + P. Multiplying both sides of the equation by P and rearranging gives P2 + 150P - 10,000 = 0, which can be factored as (P - 50) (P + 200) = 0. This has the nonnegative solution P = 50. Since Pe is also 50, the expected price level equals the actual price level, so output is at its full-employment level of 500 and the unemployment rate is at the natural rate of 6%. These are the long-run equilibrium values of the three variables as well. (b) When the nominal money supply increases unexpectedly to 1260, we again equate aggregate demand to short-run aggregate supply, which gives: 300 + 10(M/P) = 500 + P - Pe, or 300 + (10 ´ 1260/P) = 500 + P - 50, or 12,600/P = 150 + P. Multiplying both sides of the equation by P and rearranging gives P2 + 150P - 12,600 = 0, which can be factored as (P - 60)(P + 210) = 0.

This has the nonnegative solution P = 60. When P = 60, the short-run aggregate supply curve gives Y = 500 + P - Pe = 500 + 60 - 50 = 510. Output of 510 is 2% above full-employment output of 500, because (510 - 500)/500 = 0.02. With a natural unemployment rate of 0.06, Okun’s Law gives 0.02 = - 2(u - 0.06). This can be solved to get u = 0.05.

In the long run, Pe adjusts to equal P, output adjusts to its full-employment level of 500, and unemployment adjusts to the natural rate of 0.06. To find P, use the aggregate demand curve to get 500 = 300 + 10(1260/P), or 200 = 12,600/P, which can be solved to get P = 63.

The results of this exercise are consistent with the existence of an expectations-augmented Phillips curve. Unexpected inflation reduces unemployment in the short run. In the long run, however, inflation is higher and unemployment returns to its natural rate. (a) p = 0.10 - 2(u - 0.06) = 0.22 - 2u. This is shown as the Phillips curve labeled PCa in Figure 12.6.

If the Fed keeps inflation at 0.10, then u = 0.06, the natural rate of unemployment.

Figure 12.6 (b) With expected inflation rising to 12%, the Phillips curve is p = 0.12 – 2(u – 0.06) = 0.24 – 2u.

This is the Phillips curve labeled PC b in the figure. The higher rate of expected inflation has caused the curve to shift up relative to where it was in part (a). With the actual inflation rate at 10%, the Phillips curve equation is 0.10 = 0.12 – 2(u – 0.06), which has the solution u = 0.07.

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So if the Fed tries to maintain the existing rate of inflation after a shock has raised inflation expectations, the unemployment rate increases. However, if the Fed could convince people that the inflation rate really would not rise, so that p e remains at 0.10, then the short-run Phillips curve would remain at PC a, and the unemployment rate would not increase. (c) With the natural rate of unemployment rising to 0.08 at the same time that expected inflation rises to 0.12, the Phillips curve equation is p = 0.12 - 2(u - 0.08) = 0.28 - 2u. This is the Phillips curve labeled PC c in the figure. The new short-run Phillips curve is even higher than those for parts (a) and (b). With the actual inflation rate held to 10%, the equation becomes 0.10 = 0.28 - 2u, which can be solved to get u = 0.09. The unemployment rate rises both because the Fed holds inflation below expected inflation and because the natural rate has increased.

This time, even if the Fed convinced people that inflation would remain just 10%, the unemployment rate would still rise to 8%, since the natural rate has increased to that level.

3.

(a) Beginning in long-run equilibrium, with M = 4000, output must be at its full-employment level of 6000 and the unemployment rate must be equal to the natural rate of .05. Using the values for Y and M in the AD curve, 6000 = 4000 + 2(4000/P), which gives P = 4. This is also the expected price level. Because M has been constant for a long time and is expected to remain constant, p e = 0. (b) With P e = 4, the SRAS curve is Y = 6000 + 100(P - 4). The AD curve is Y = 4000 + 2(4488/P).

The intersection of the two curves occurs when 6000 + 100(P - 4) = 4000 + 2(4488/P).

Simplifying terms gives 100P2 + 1600P - 8976 = 0, which has the solution P = 4.4. Plugging this into the SRAS curve gives Y = 6040. From the Okun’s Law equation we get (6040 - 6000)/6000 = -2 (u - 0.05), so – 0.00333 = u - 0.05, so u = .0467. Cyclical unemployment is u - u = 0.0033. Unanticipated inflation is (P - Pe)/Pe = 0.10 = 10%. (c) The Phillips curve equation is p = p e - h(u - u ), which gives .10 = 0 - h(.0467 - 0.05).

This is solved to get h = 30. So the slope of the Phillips curve is -30.

4.

Since the natural rate of unemployment is 0.06, p = p e - 2(u - 0.06), so u - 0.06 = 0.5(p e - p), or u = 0.06 + 0.5(p e - p). (a) Year 1: u = 0.06 + 0.5(0.08 - 0.04) = 0.06 + 0.02 = 0.08. The unemployment rate is 0.02 higher than the natural rate. The percentage that output falls short of full-employment output is 2 ´ 0.02 = 0.04, or 4%.

Year 2: u = 0.06 + 0.5(0.04 - 0.04) = 0.06. The unemployment rate equals the natural rate, since inflation equals expected inflation. Since unemployment is at its natural rate, output is at its full-employment level.

Since the output loss was 4 percentage points and inflation declined by 8 percentage points, the sacrifice ratio is 4/8 = 0.5. (b) Use equations: u = 0.06 + 0.5(p e – p), output shortfall = 2 (u – 0.06).

Year

p

pe

u

u - 0.06

Output Shortfall

1 2 3 4

0.08 0.04 0.04 0.04

0.10 0.08 0.06 0.04

0.07 0.08 0.07 0.06

0.01 0.02 0.01 0.0

0.02 0.04 0.02 0.0

The total output shortfall is 0.02 + 0.04 + 0.02 + 0.0 = 0.08 = 8-percentage points of output lost.

Inflation fell by 8 percentage points. So the sacrifice ratio is 8/8 = 1. Notice that, compared with

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Analytical Problems 1.

(a) The reduction in structural unemployment would reduce the natural rate of unemployment and thus would shift both the expectations-augmented Phillips curve and the long-run Phillips curve to the left. (b) Despite the expense of the government program to reduce structural unemployment, it would have a permanent effect. Monetary expansion can work only temporarily—in the long run it has no effect.

2. The slope of the short-run aggregate supply curve will be much steeper in economy B, because producers increase their output only a small amount in response to an increase in price. But economy A’s short-run aggregate supply curve will be flatter, as people are likely to perceive price changes as changes in relative price rather than the aggregate price level, and thus will respond more strongly to changes in prices.

The short-run Phillips curve will also be steeper in economy B, since unemployment, like output, won’t respond much to a change in inflation. But in economy A, unemployment and output will respond more strongly to price changes, and the short-run Phillips curve will be flatter.

3.

(a) In Figure 12.7, the SRAS curve shifts up 10% each year, as does the AD curve. Unanticipated inflation is zero, as both actual and expected inflation are 10%. The economy is at full employment, since firms set their prices to exactly match the increase in the general price level.

Figure 12.7 (b) The surprise increase in the money supply at mid-year leads to a rise in output, as shown in Figure 12.8 by the shift of the AD curve from AD1 to AD2. Firms do not adjust their prices, so the SRAS curve remains fixed at SRAS1. When the money supply rises by its regular 10% at the end of the year, the AD curve shifts up to AD3 and firms raise their prices by 15%, shifting the SRAS curve up to SRAS3. Actual inflation is 15%, but expected inflation was only 10%. As a result, there was a temporary increase in output above its full-employment level, and a temporary decline in unemployment below the natural rate. Thus for the year as a whole, cyclical unemployment was negative and unanticipated inflation was positive, just as in the expectationsaugmented Phillips curve.

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Figure 12.8 4.

In the cashless society, there would be no shoe-leather costs, as there would be no cash balances on which to economize. But menu costs would remain for anticipated inflation. The costs of unanticipated inflation would remain as well: both the risk of wealth transfers plus confusion in price signals.

5.

(a) Figure 12.9 shows the effects of increasing the money supply while holding the price level constant. Beginning at point A, the intersection of aggregate demand curve AD1 and short-run aggregate supply curve SRAS1, the increase in the money supply shifts the aggregate demand curve to AD2. Since prices cannot rise, the short-run equilibrium is at point B, with output above its full-employment level.

Figure 12.9 (b) When the price controls are removed, the price level will jump up, with the short-run aggregate supply curve shifting to SRAS2. The new equilibrium is at point C, where there is full employment.

6.

(a) A new law that prohibits people from seeking employment before age eighteen is likely to reduce the natural rate of unemployment because teenagers have a higher-than-average unemployment rate. With no teenagers allowed in the labor force, the average unemployment rate would be lower. (b) A service that makes looking for a job easier is able to match people and jobs more rapidly, which should reduce the natural rate of unemployment.

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(c) If unemployed workers can receive benefits longer, they’ll be in less of a rush to take a job, so the job-matching process will take longer. As a result, the natural rate of unemployment will rise. (d) A structural shift in the types of products people buy is likely to raise the natural rate of unemployment, because it will take time for the economy to shift workers from some types of occupations to others. (e) A recession leads to a rise in cyclical unemployment, but doesn’t affect the natural rate of unemployment.

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Chapter 12

Unemployment and Inflation

Working with Macroeconomic Data 1.

a. Inflation and unemployment show no relationship, or perhaps a positive relationship.

b. Inflation and cyclical unemployment show no apparent relationship.

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c. The change in the inflation rate and cyclical unemployment are strongly negatively correlated.

The results support the expectations-augmented Phillips curve with a changing natural rate of unemployment.

2.

[Note that as of October 2018, the problem cannot be completed because the CBO has not yet produced a potential output series with a 2012 base year. This should be available by February 2019.]

A line through the origin with a slope of 2 is very close to the points on the line, confirming Okun's law.

3.

The fraction of unemployed workers who have been unemployed 15 weeks or more usually rises

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in recessions and continues rising for a time after recessions end. The fraction of unemployed workers who have been unemployed 15 weeks or more is positively related to the unemployment rate but peaks later and is slower to decline than the unemployment rate. Thus, the costs to society of unemployment are higher in a recession than in an expansion because of the elevated nature of long-term unemployment.

4.

Declines in expected inflation of more than 1 percentage point occur near recessions (19801982, 1991, 2001, 2008-2009). Increases of more than 1 percentage point are appear to be mostly unrelated to the business cycle, but are more likely because of oil price shocks, except in 1979.

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Chapter 13 Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy n

Learning Objectives

I.

Goals of Chapter 13 A. Describe real and nominal exchange rates, how they are related, and how they change over time (Sec. 13.1) B. Use and supply-and-demand framework to explain how exchange rates are determined (Sec. 13.2) C. Use the relationship between exchange rates and international trade to develop an openeconomy IS–LM model (Sec. 13.3) D. Discuss the international effects of domestic macroeconomic policies (Sec. 13.4) E. Evaluate the strengths and weaknesses of different types of exchange-rate systems (Sec. 13.5)

II. Notes to Tenth Edition Users A. We modify our discussion of the Big Mac index and PPP to adjust for differences in countries’ GDP per capita B. We add a discussion of Brexit C. We add an analytical problem to analyze tariffs and a trade war

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Teaching Notes

I.

Exchange Rates (Sec. 13.1)

325

A. Nominal exchange rates 1. The nominal exchange rate tells you how much foreign currency you can obtain with one unit of the domestic currency a. For example, if the nominal exchange rate is 120 yen per dollar, one dollar can be exchanged for 120 yen b. Transactions between currencies take place in the foreign exchange market c. Denote the nominal exchange rate (or simply, exchange rate) as enom in units of the foreign currency per unit of domestic currency 2. Under a flexible-exchange-rate system or floating-exchange-rate system, exchange rates are determined by supply and demand and may change every day; this is the current system for major currencies 3. In the past, many currencies operated under a fixed-exchange-rate system, in which governments determined exchange rates a. The exchange rates were fixed because the central banks in those countries offered to buy or sell the currencies at the fixed exchange rate b. Examples include the gold standard, which operated in the late 1800s and early 1900s, and the Bretton Woods system, which was in place from 1944 until the early 1970s c. Even today, though major currencies are in a flexible-exchange-rate system, some smaller countries fix their exchange rates B. In touch with data and research: Exchange rates 1. Trading in currencies occurs around-the-clock, since some market is open in some country any time of day 2. The spot rate is the rate at which one currency can be traded for another immediately 3. The forward rate is the rate at which one currency can be traded for another at a fixed date in the future (e.g., 90 or 180 days from now) 4. A pattern of rising forward rates suggests that people expect the spot rate to be rising in the future C. Real exchange rates 1. The real exchange rate tells you how much of a foreign good you can get in exchange for one unit of a domestic good 2. If the nominal exchange rate is 110 yen per dollar, and it costs 1100 yen to buy a hamburger in Tokyo compared to 2 dollars in New York, the price of a U.S. hamburger relative to a Japanese hamburger is 0.2 Japanese hamburgers per U.S. hamburger 3. The real exchange rate is the price of domestic goods relative to foreign goods, or e = enomP/PFor

(13.1)

4. To simplify matters, we will assume that each country produces a unique good 5. In reality, countries produce many goods, so we must use price indexes to get P and PFor 6. If a country’s real exchange rate is rising, its goods are becoming more expensive relative to the goods of the other country D. Appreciation and depreciation 1. In a flexible-exchange-rate system, when enom falls, the domestic currency has undergone a nominal depreciation (or it has become weaker); when enom rises, the domestic currency has become stronger and has undergone a nominal appreciation

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2. In a fixed-exchange-rate system, a weakening of the currency is called a devaluation, a strengthening is called a revaluation 3. We also use the terms real appreciation and real depreciation to refer to changes in the real exchange rate (Summary 15) Numerical Problem 1 is a simple example of appreciation and depreciation.

E. Purchasing power parity 1. To examine the relationship between the nominal exchange rate and the real exchange rate, think first about a simple case in which all countries produce the same goods, which are freely traded a. If there were no transportation costs, the real exchange rate would have to be e = 1, or else everyone would buy goods where they were cheaper b. Setting e = 1 in Eq. (13.1) gives P = PFor /enom

(13.2)

c. This means that similar goods have the same price in terms of the same currency, a concept known as purchasing power parity, or PPP d. Empirical evidence shows that purchasing power parity holds in the long run but not in the short run because in reality, countries produce different goods, because some goods aren’t traded, and because there are transportation costs and legal barriers to trade 2. When PPP does not hold, using Eq. (13.1), we can decompose changes in the real exchange rate into parts De/e = Denom/enom + DP/P - DPFor /PFor 3. This can be rearranged as Denom/enom = De/e + pFor - p

(13.3)

4. Thus a nominal appreciation is due to a real appreciation or a lower rate of inflation than in the foreign country 5. In the special case in which the real exchange rate does not change, so that De/e = 0, the resulting equation in Eq. (13.3) is called relative purchasing power parity, since nominal exchange rate movements reflect only changes in inflation a. Relative purchasing power parity works well as a description of exchange-rate movements in high-inflation countries, since in those countries, movements in relative inflation rates are much larger than movements in real exchange rates 6. In touch with data and research: McParity a. As a test of the PPP hypothesis, the Economist magazine periodically reports on the prices of Big Mac hamburgers in different countries b. The prices, when translated into dollar terms using the nominal exchange rate, range from $2.29 in Russia to $6.76 in Switzerland (using 2018 data), so PPP definitely doesn’t hold c. The hamburger price data forecasts movements in exchange rates (1) Hamburger prices might be expected to converge, so countries in which Big Macs are expensive may have a depreciation, while countries in which Big Macs are cheap may have an appreciation d. Accounting for differences in GDP per capita improves the accuracy of the PPP hypothesis

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The real exchange rate and net exports 1. The real exchange rate (also called the terms of trade) is important because it represents the rate at which domestic goods and services can be traded for those produced abroad a. An increase in the real exchange rate means people in a country can get more foreign goods for a given amount of domestic goods 2. The real exchange rate also affects a country’s net exports (exports minus imports) a. Changes in net exports have a direct impact on export and import industries in the country b. Changes in net exports affect overall economic activity and are a primary channel through which business cycles and macroeconomic policy changes are transmitted internationally 3. The real exchange rate affects net exports through its effect on the demand for goods a. A high real exchange rate makes foreign goods cheap relative to domestic goods, so there is a high demand for foreign goods (in both countries) b. With demand for foreign goods high, net exports decline c. Thus the higher the real exchange rate, the lower a country’s net exports

Data Application How sensitive are U.S. manufacturing firms to changes in the value of the dollar? Linda Goldberg and Keith Crockett provide an interesting overview of the data in their article “The Dollar and U.S. Manufacturing” in the Federal Reserve Bank of New York’s Current Issues in Economics and Finance, November 1998.

4. The J curve a. The effect of a change in the real exchange rate may be weak in the short run and can even go the “wrong” way b. Although a rise in the real exchange rate will reduce net exports in the long run, in the short run it may be difficult to quickly change imports and exports c. As a result, a country will import and export the same amount of goods for a time, with lower relative prices on the foreign goods, thus increasing net exports d. Similarly, a real depreciation will lead to a decline in net exports in the short run and a rise in the long run e. This pattern of net exports is known as the J curve (Figure 13.1)

Figure 13.1

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5. The analysis in this chapter assumes a time period long enough that the movements along the J curve are complete, so that a real depreciation raises net exports and a real appreciation reduces net exports Numerical Problem 2 gives an example of how a real depreciation can cause net exports to fall.

G. Application: The value of the dollar and U.S. net exports 1. Our theory suggests that the value of the dollar and U.S. net exports should be inversely related 2. Looking at data since the early 1970s, when the world switched to floating exchange rates, confirms the theory, at least in the 1980s (text Figure 13.2) a. From 1980 to 1985 the dollar appreciated and net exports declined sharply b. The dollar began depreciating in 1985, but it was not until late 1987 that net exports began to rise (1) Initially, economists relied on the J curve to explain the continued decline in net exports with the decline of the dollar (2) But two and one-half years is a long time for the J curve to be in effect (3) A possible explanation for this long lag in the J curve is a change in competitiveness (a) The strength of the dollar for such a long period in the first half of the 1980s meant U.S. firms lost many foreign customers (b) Foreign firms made many inroads into the United States (c) This is known as the “beachhead effect,” because it allowed foreign producers to establish beachheads in the U.S. economy (4) The U.S. real exchange rate and net exports moved in opposite directions from 1997 to 2001 (a) The strong dollar reduced net exports (b) But a bigger factor was weak growth in foreign economies (5) From 2002 to 2008, the U.S. real exchange rate declined, though it took until 2006 for net exports to begin rising (6) The dollar appreciated sharply in the financial crisis in 2008, but resumed its longrun decline after the crisis ended, until 2014, when the United States ended its quantitative easing program, while other countries began new quantitative easing programs, and the dollar appreciated II. How Exchange Rates Are Determined: A Supply-and-Demand Analysis (Sec. 13.2) A. What causes changes in the exchange rate?

1. To analyze this, we will use supply-and-demand analysis, assuming a fixed price level 2. Holding prices fixed means that changes in the real exchange rate are matched by changes in the nominal exchange rate 3. The nominal exchange rate is determined in the foreign exchange market by supply and demand for the currency 4. Demand and supply are plotted against the nominal exchange rate, just like demand and supply for any good (Figure 13.2; like text Figure 13.3)

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Figure 13.2 a. Supplying dollars means offering dollars in exchange for the foreign currency b. The supply curve slopes upward, because if people can get more units of foreign currency for a dollar, they will supply more dollars c. Demanding dollars means wanting to buy dollars in exchange for the foreign currency d. The demand curve slopes downward, because if people need to give up a greater amount of foreign currency to obtain one dollar, they will demand fewer dollars 5. Why do people demand or supply dollars? a. People need dollars for two reasons: (1) To be able to buy U.S. goods and services (U.S. exports) (2) To be able to buy U.S. real and financial assets (U.S. financial inflows) b. These transactions are the two main categories in the balance of payments accounts: the current account and the capital and financial account c. People want to sell dollars for two reasons: (1) To be able to buy foreign goods and services (U.S. imports) (2) To be able to buy foreign real and financial assets (U.S. financial outflows) 6. Factors that increase demand for U.S. exports and assets will increase demand for dollars and reduce supply of dollars, shifting the demand curve to the right and the supply curve to the left and increasing the nominal exchange rate a. For example, an increase in the quality of U.S. goods relative to foreign goods will lead to an appreciation of the dollar (Figure 13.3; like text Figure 13.4)

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Figure 13.3 C. Macroeconomic determinants of the exchange rate and net export demand 1. Look at how changes in real output or the real interest rate are linked to the exchange rate and net exports, to develop an open-economy IS–LM model 2. Effects of changes in output (income) a. A rise in domestic output (income) raises demand for goods and services, including imports, so net exports decline

Data Application How do movements in the value of the dollar affect U.S. firms’ ability to compete internationally? Data and analysis of this issue are provided by Thomas Klitgaard and James Orr in their article “Evaluating the Price Competitiveness of U.S. Exports,” Federal Reserve Bank of New York, Current Issues in Economics and Finance, February 1998.

Analytical Problem 4 looks at the effects of a supply shock on net exports. b. To increase purchases of imports, people must sell the domestic currency to buy foreign currency, increasing the supply of foreign currency, which reduces the exchange rate c. The opposite occurs if foreign output (income) rises (1) Domestic net exports rise (2) The exchange rate appreciates 3. Effects of changes in real interest rates a. A rise in the domestic real interest rate (with the foreign real interest rate held constant) causes foreigners to want to buy domestic assets, increasing the demand for domestic currency and raising the exchange rate b. The rise in the exchange rate leads to a decline in net exports c. The opposite occurs if the foreign real interest rate rises (1) Domestic net exports rise (2) The exchange rate depreciates D. Summary Table 16: Determinants of the exchange rate (real or nominal) 1. A rise in domestic output (income) or the foreign real interest rate causes the exchange rate to fall

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2. A rise in foreign output (income), the domestic real interest rate, or the world demand for domestic goods causes the exchange rate to rise E. Summary Table 17: Determinants of net exports 1. A rise in domestic output (income) or the domestic real interest rate causes net exports to fall 2. A rise in foreign output (income), the foreign real interest rate, or the world demand for domestic goods causes net exports to rise III. The IS–LM Model for an Open Economy (Sec. 13.3) A. Only the IS curve is affected by having an open economy instead of a closed economy; the LM curve and FE line are the same 1. Note that we do not use the AD–AS model because we need to know what happens to the real interest rate, which has an important impact on the exchange rate 2. The IS curve is affected because net exports are part of the demand for goods 3. The IS curve remains downward sloping 4. Any factor that shifts the closed-economy IS curve shifts the open-economy IS curve in the same way 5. Factors that change net exports (given domestic output and the domestic real interest rate) shift the IS curve a. Factors that increase net exports shift the IS curve up and to the right b. Factors that decrease net exports shift the IS curve down and to the left B. The open-economy IS curve 1. The goods-market equilibrium condition is S d - I d = NX

(13.4)

a. This means that desired foreign lending must equal foreign borrowing b. Equivalently, Y = C d + I d + G + NX

(13.5)

c. This means the supply of goods equals the demand for goods and is derived using the definition of national saving, S d = Y - C d - G 2. Plotting S d - I d and NX illustrates goods-market equilibrium (Figure 13.4; like text Figure 13.5)

Figure 13.4

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a. Net exports can be positive or negative b. The net export curve slopes downward, because a rise in the real interest rate increases the real exchange rate and thus reduces net exports c. The S - I curve slopes upward, because a rise in the real interest rate increases desired national saving and reduces desired investment d. Equilibrium occurs where the curves intersect 3. To get the open-economy IS curve, we need to see what happens when domestic output changes (Figure 13.5; like text Figure 13.6)

Figure 13.5 a. Higher output increases saving, so the S - I curve shifts to the right b. Higher output reduces net exports, so the NX curve shifts to the left c. The new equilibrium occurs at a lower real interest rate, so the IS curve is downward sloping C. Factors that shift the open-economy IS curve 1. Any factor that raises the real interest rate that clears the goods market at a constant level of output shifts the IS curve up and to the right a. An example is a temporary increase in government purchases (Figure 13.6; like text Figure 13.7)

Figure 13.6

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b. The rise in government purchases reduces desired national saving, shifting the S - I curve to the left, shifting the IS curve up and to the right c. Anything that reduces desired national saving relative to investment shifts the IS curve up and to the right 2. Anything that raises a country’s net exports, given domestic output and the domestic real interest rate, will shift the open-economy IS curve up and to the right (Figure 13.7; like text Figure 13.8)

Figure 13.7 a. The increase in net exports is shown as a shift to the right in the NX curve b. This raises the real interest rate for a fixed level of output, shifting the IS curve up and to the right c. Three things could increase net exports for a given level of output and real interest rate (1) An increase in foreign output, which increases foreigners’ demand for domestic exports (2) An increase in the foreign real interest rate, which makes people want to buy foreign assets, causing the exchange rate to depreciate, which in turn causes net exports to rise (3) A shift in worldwide demand toward the domestic country’s goods, for example, as occurs if the quality of domestic goods improves Analytical Problem 1 looks at the effect of trade barriers that reduce imports.

3. Summary Table 18: International factors that shift the IS curve a. An increase in foreign output, the foreign real interest rate, or the demand for domestic goods relative to foreign goods all shift the IS curve up and to the right D. The international transmission of business cycles 1. The impact of foreign economic conditions on the real exchange rate and net exports is one of the principal ways by which cycles are transmitted internationally 2. What would be the effect on Japan of a recession in the United States? a. The decline in U.S. output would reduce demand for Japanese exports, shifting the Japanese IS curve down and to the left b. In a Keynesian model, or in the classical misperceptions model, this leads to recession in Japan

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c. In a classical (RBC) model, the decline in net exports wouldn’t affect Japanese output 3. A similar effect could occur because of a shift in preferences (or trade restrictions) for Japanese goods

Data Application Some very interesting evidence on the international transmission of business cycles is provided

by Mario Crucini, Ayhan Kose, and Christopher Otrok in their 2011 paper, “What Are the Driving Forces of International Business Cycles?” (Review of Economic Dynamics, v. 14, pp.

156–175).

IV. Macroeconomic Policy in an Open Economy with Flexible Exchange Rates (Sec. 13.4) A. Two key questions 1. How do fiscal and monetary policies affect a country’s real exchange rate and net exports?

2. How do the macroeconomic policies of one country affect the economies of other countries?

B. Three steps in analyzing these questions 1. Use the domestic economy’s IS–LM diagram to see the effects on domestic output and the domestic real interest rate 2. See how changes in the domestic real interest rate and output affect the exchange rate and net exports 3. Use the foreign economy’s IS–LM diagram to see the effects of domestic policy on foreign output and the foreign real interest rate C. A fiscal expansion 1. Look at a temporary increase in domestic government purchases using the classical (RBC) model a. The rise in government purchases shifts the IS curve up and to the right and the FE line to the right (Figure 13.8; like text Figure 13.9)

Figure 13.8 b. The LM curve shifts up and to the left to restore equilibrium as the price level rises c. Both the real interest rate and output rise in the domestic country d. Higher output reduces the exchange rate, while a higher real interest rate increases the exchange rate, so the effect on the exchange rate is ambiguous

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e. Higher output and a higher real interest rate both reduce net exports, supporting the twin deficits idea Numerical Problems 3 and 4 illustrate the effects of an increase in government purchases on the exchange rate and net exports.

2. How do these changes affect a foreign country’s economy? a. The decline in net exports for the domestic economy means a rise in net exports for the foreign country, so the foreign country’s IS curve shifts up and to the right b. In the classical model, the LM curve shifts up and to the left as the price level rises to restore equilibrium, thus raising the foreign real interest rate, but foreign output is unchanged c. In a Keynesian model, the shift of the IS curve would give the foreign country higher output temporarily 3. In either the classical or Keynesian model, a temporary increase in domestic government purchases raises domestic income (temporarily) and the domestic real interest rate, as in a closed economy a. It also reduces domestic net exports, so government spending crowds out both investment and net exports b. The effect on the exchange rate is ambiguous c. The foreign real interest rate and price level rise d. In the Keynesian model, foreign output rises temporarily D. A monetary contraction 1. Look at a reduction in the domestic money supply in a Keynesian model 2. Short-run effects on the domestic and foreign economies (Figure 13.9; like text Figure 13.10)

Figure 13.9 a. The domestic LM curve shifts up and to the left b. In the short run, domestic output is lower and the real interest rate is higher c. The exchange rate appreciates, because lower output reduces demand for imports, thus reducing the supply of the domestic currency to the foreign exchange market, and because a higher real interest rate increases demand for the domestic currency d. How are net exports affected?

(1) The decline in domestic income reduces domestic demand for foreign goods, tending to increase net exports

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(2)

The rise in the real interest rate leads to an appreciation of the domestic currency and tends to reduce net exports (3) Following the J curve analysis, assume the latter effect is weak in the short run, so that net exports increase e. How is the foreign country affected?

(1) Since domestic net exports increase, foreign net exports must decrease, shifting the foreign IS curve down and to the left (2) Output and the real interest rate in the foreign country decline (3) So, a domestic monetary contraction leads to recession abroad 3. Long-run effects on the domestic and foreign economies a. In the long run, wages and prices in the domestic economy decline and the LM curve returns to its original position b. All real variables, including net exports and the real exchange rate, return to their original levels c. As a result, the foreign IS curve returns to its original level as well d. Thus there is no long-run effect on any real variables, either domestically or abroad e. This result holds in the long run in the Keynesian model, but it holds immediately in the classical (RBC) model; monetary contraction affects only the price level even in the short run f. Though a monetary contraction does not affect the real exchange rate, it does affect the nominal exchange rate because of the change in the domestic price level g. Since enom = ePFor/P, the decline in P raises the nominal exchange rate by the same percentage as the decline in the price level and the money supply Analytical Problem 2 uses a classical model to show what happens to capital flows in a classical model with circumstances similar to those of the United States in the 1980s.

V.

Fixed Exchange Rates (Sec. 13.5) A. Fixed-exchange-rate systems are important historically 1. The United States has been on a flexible-exchange-rate system since the early 1970s 2. But fixed exchange rates are still used by many countries 3. There are two key questions we would like to answer a. How does the use of a fixed-exchange-rate system affect an economy and macroeconomic policy? b. Which is the better system, flexible or fixed exchange rates?

B. Fixing the exchange rate 1. The government sets the exchange rate, perhaps in agreement with other countries 2. What happens if the official rate differs from the rate determined by supply and demand? a. Supply and demand determine the fundamental value of the exchange rate (Figure 13.10; like text Figure 13.11)

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Figure 13.10 b. When the official rate is above its fundamental value, the currency is said to be overvalued c. The country could devalue the currency, reducing the official rate to the fundamental value d. The country could restrict international transactions to reduce the supply of its currency to the foreign exchange market, thus raising the fundamental value of the exchange rate (1) If a country prohibits people from trading the currency at all, the currency is said to be inconvertible e. The government can supply or demand the currency to make the fundamental value equal to the official rate (1) If the currency is overvalued, the government can buy its own currency (a) This is done by the nation’s central bank using its official reserve assets to buy the domestic currency in the foreign exchange market (b) Official reserve assets include gold, foreign bank deposits, and special assets created by agencies like the International Monetary Fund (c) The decline in official reserve assets is equal to a country’s balance of payments deficit

Data Application An interesting examination of intervention by the U.S. government in the foreign exchange market is reported by Michael T. Belongia, “Foreign Exchange Intervention by the United States: A Review and Assessment of 1985–89,” Federal Reserve Bank of St. Louis Review, May/June 1992, pp. 32–51. Intervention appears to be more successful (there is a larger change in the exchange rate) when both the Federal Reserve and a foreign central bank intervene on the same day.

(2)

A country cannot maintain an overvalued currency forever, as it will run out of official reserve assets (a) In the gold standard period, countries sometimes ran out of gold and had to devalue their currencies (b) A speculative run (or speculative attack) may end the attempt to support an overvalued currency (text Figure 13.12) (i) If investors think a currency may soon be devalued, they may sell assets denominated in the overvalued currency, increasing the supply of that

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currency on the foreign exchange market (ii) This causes even bigger losses of official reserves from the central bank and speeds up the likelihood of devaluation, as occurred in Mexico in 1994 and Asia in 1997–1998 (3) Thus an overvalued currency cannot be maintained for very long 3. Similarly, in the case of an undervalued currency, the official rate is below the fundamental value (text Figure 13.13) a. In this case, a central bank trying to maintain the official rate will acquire official reserve assets b. If the domestic central bank is gaining official reserve assets, foreign central banks must be losing them, so again the undervalued currency can’t be maintained for long

Policy Application The manner in which a devaluation leads to a recession is explored in the article “Contractionary Effects of Devaluation” by Kenneth Kasa, in the Federal Reserve Bank of San Francisco’s Economic Letter, 98-34, November 1998.

C. Monetary policy and the fixed exchange rate 1. The best way for a country to make the fundamental value of a currency equal the official rate is through the use of monetary policy 2. Rewrite Eq. (13.1) as enom = ePFor /P (13.6) 3. For an overvalued currency, a monetary contraction is desirable a. In a Keynesian model, a monetary contraction causes a real (and nominal) exchange rate appreciation in the short run and a nominal exchange rate appreciation in the long run (with no long-run effect on the real exchange rate) b. Conversely, a monetary expansion causes a nominal exchange rate depreciation in both the short run and the long run c. Plotting the relationship between the money supply and the nominal exchange rate shows the level of the money supply for which the fundamental value of the exchange rate equals the official rate (Figure 13.11; like text Figure 13.14

Figure 13.11 .

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339

A higher money supply yields an overvalued currency A lower money supply yields an undervalued currency

Numerical Problem 5 is an exercise in finding the level of the nominal money supply that fixes the exchange rate at a sustainable level.

4. This implies that countries cannot both maintain the exchange rate and use monetary policy to affect output a. Using expansionary monetary policy to fight a recession would lead to an overvalued currency b. So, under fixed exchange rates, monetary policy cannot be used for macroeconomic stabilization Analytical Problem 3 looks at the effects of different macroeconomic policies when exchange rates are fixed.

5. However, a group of countries may be able to coordinate their use of monetary policy a. If two countries increase their money supplies together to fight joint recessions, there need not be an overvaluation b. One country increasing its money supply by itself would lead to a depreciation c. But when the other country increases its money supply, it provides an offsetting effect d. If the money supplies expand in each country, they offset each other, so the exchange rate need not change (text Figure 13.15) 6. Overall, fixed exchange rates can work well if countries in the system have similar macroeconomic goals and can coordinate changes in monetary policy a. But the failure to cooperate can lead to severe problems D. Fixed versus flexible exchange rates 1. Flexible-exchange-rate systems also have problems, because the volatility of exchange rates introduces uncertainty into international transactions

Data Application A very detailed and comprehensive review of the world’s experience under flexible exchange rates is given by Maurice Obstfeld, “Floating Exchange Rates: Experience and Prospects,” Brookings Papers on Economic Activity, 2:1985, pp. 369–450. He suggests that while the problem of volatility in the exchange rate is important, floating exchange rates allow more rapid adjustment to disturbances than fixed exchange rates. In many cases it is macroeconomic policies, not the floating-exchange-rate system, that are to blame for exchange-rate volatility.

2. There are two major benefits of fixed exchange rates a. Stable exchange rates make international trades easier and less costly b. Fixed exchange rates help discipline monetary policy, making it impossible for a country to engage in expansionary policy; the result may be lower inflation in the long run

Policy Application Some prominent economists have called for a return to fixed exchange rates. Ronald I. McKinnon puts forth his suggestion that the major industrial countries return to a system of fixed exchange rates in his article “Monetary and Exchange Rate Policies for International Financial Stability: A Proposal,” Journal of Economic Perspectives, Winter 1988, pp. 83–103. .

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Arthur J. Rolnick and Warren E. Weber, from the Federal Reserve Bank of Minneapolis, present their views in “A Case for Fixing Exchange Rates,” Federal Reserve Bank of Minneapolis 1989 Annual Report.

3. But there are some disadvantages to fixed exchange rates a. They take away a country’s ability to use expansionary monetary policy to combat recessions b. Disagreement among countries about the conduct of monetary policy may lead to the breakdown of the system

Policy Application Michael T. Belongia and K. Alec Chrystal point out that maintaining fixed exchange rates is difficult because of changes in underlying real economic conditions, in their article “The Pitfalls of Exchange Rate Targeting: A Case Study from the United Kingdom,” Federal Reserve Bank of St. Louis Review, September/October 1990, pp. 15–24. Structural changes in one country may cause unnecessary changes in inflation if the real exchange rate does not adjust.

4. Which system is better may thus depend on the circumstances a. If large benefits can be gained from increased trade and integration, and when countries can coordinate their monetary policies closely, then fixed exchange rates may be desirable b. Countries that value having independent monetary policies, either because they face different macroeconomic shocks or hold different views about the costs of unemployment and inflation than other countries, should have a floating exchange rate

Policy Application A detailed discussion of the pros and cons of having flexible exchange rates is provided by Joseph A. Whitt, Jr., “Flexible Exchange Rates: An Idea Whose Time Has Passed?” Federal Reserve Bank of Atlanta Economic Review, September/October 1990, pp. 2–15. He suggests that moving back toward a system with fixed exchange rates is appealing, but requires that governments give up independence of economic policies.

E. Currency unions 1. Under a currency union, countries agree to share a common currency a. They often cooperate economically and politically as well, as was the case with the 13 original U.S. colonies 2. To work effectively, a currency union must have just one central bank a. Since countries do not usually want to give up control over monetary policy by not having their own central banks, currency unions are very rare b. But a currency union has advantages over fixed exchange rates because having a single currency reduces the costs of trading goods and assets across countries and because speculative attacks on a national currency can no longer occur 3. But the major disadvantage of a currency union is that all countries share a common monetary policy, a problem that also arises with fixed exchange rates a. Thus if one country is in recession while another is concerned about inflation, monetary policy can’t help both, whereas with flexible exchange rates, the countries could have monetary policies that help their particular situation 4. A currency union makes sense if a region is an optimum currency area

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a. Four criteria (1) Extensive trade (2) Similar business cycle patterns (3) Capital and labor mobility (4) Fiscal transfers for stabilization policy because countries give up their ability to engage in monetary policy 5. Application: Is either the United States or Europe an optimum currency area? a. The United States meets all four criteria b. In Europe, labor mobility is limited because of language and cultural barriers and countries control their own fiscal policies c. The future of the euro remains an open question d. The 2016 Brexit vote, in which voters in the UK decided to withdraw from the European Union, raises more concerns about the euro’s future viability 6.

Application: European monetary unification a. In 1991, countries in the European Community adopted the Maastricht treaty, which provides for a common currency (1) The currency, called the euro, came into being on January 1, 1999 (2) The motivation was to increase economic growth and to help end nationalism (3) Eleven countries took part in the union, initially b. Monetary policy is determined by the Governing Council of the European Central Bank (ECB) c. The ECB differs from the Federal Reserve in two ways (1) In Europe, each individual country monitors its own banks (until recently), whereas in the United States, the Fed can set rules for all banks (2) In Europe, each country sets its own fiscal policy, whereas in the United States a central government determines fiscal policy d. The United States and Europe differed in their handling of the financial crisis in 2008 (1) U.S. banks could raise capital more easily but European banks could not because each country regulated banks differently (2) Weakness at European banks cause the financial crisis to have a more prolonged effect on the European economy than the U.S. economy e. European countries had violated the requirement to keep their government budget deficits low prior to the crisis (1) In the crisis, the countries lent to their banks, which increased the government budget deficit, which caused interest rates to rise, which caused banks to weaken further (2) So, the government budget crisis in Europe is related to the financial crisis f. Because of the euro, exchange rates between countries in good financial condition, such as Germany, and countries in weaker financial condition, such as Greece, could not adjust to restore equilibrium

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Additional Issues for Classroom Discussion

1.

What Other Relationships Are There Between Currencies?

In financial markets, there are many relationships between the returns on different assets. In international financial markets, these relationships depend a lot on the exchange rate. Ask your students how they would determine how much money to invest in foreign countries. What are the returns to such investment, translated into U.S. dollars? What risks are there? What happens to the value of your investment when the exchange rate changes?

To help organize the discussion, you might wish to introduce another parity notion—interest rate parity.

For example, suppose you could invest in a U.S. one-year government bond, earning 5% interest over the next year. Alternatively, you could invest in German government bond, earning 4% over the next year. If exchange rates do not change, then you’re obviously better off investing in the U.S. bond, which has a higher interest rate.

But suppose circumstances are such that investors in the market expect the euro to appreciate against the dollar. Then, if you take your dollars today, trade them for euros, invest in the German bond, then take the euros you get in one year and convert them back into dollars, the rate of return in dollars will be (approximately) equal to the interest rate on the German bond plus the percentage by which the euro has appreciated.

An investment like the one described above is risky because no one knows for sure what the future exchange rate will be. Suppose, for example, that you bought the German bond because you thought the euro would appreciate 2% against the dollar, making your total return 6% (4% euro return plus 2% appreciation). But if in fact the euro fell in value against the dollar by 2%, instead of appreciating, then your return would be only 2% (4% euro return minus 2% depreciation). The process described here is known as uncovered interest-rate parity. It’s uncovered because it’s risky. Another process, covered interest parity, involves trades using forward or futures contracts to make a riskless profit.

2.

How Predictable Are Exchange Rates?

Economists’ theories of exchange rates are very well developed, especially after hundreds of years of experience. How precisely do you think financial market participants, such as currency traders, can forecast exchange rates?

It turns out that despite all our economic theories and extensive empirical work, forecasts of exchange rates are notoriously bad over short horizons. For long time periods, like two years or more, exchangerate forecasts aren’t too bad when based on economic theories like purchasing power parity. But for forecasts of one year or less, the exchange rate often moves in exactly the opposite direction than economic theory predicts.

For example, suppose you look in the financial section of the newspaper and see that one-year Canadian government bonds are paying an interest rate that’s one percent higher than the interest rate on a comparable U.S. bond. A theory known as interest rate parity might suggest to you that the reason the interest rates are different is largely attributable to the fact that investors expect the U.S. dollar to appreciate one percent against the Canadian dollar over the next year. But, surprisingly, in such situations, forecasts based on interest-rate parity are generally wrong, and in fact, on average, the U.S. dollar depreciates one percent against the Canadian dollar.

Evidence like this suggests that economists need to do a lot more work to be able to predict exchange rates effectively. Recently, computers are allowing economists to use some very fancy models, in which the riskiness of exchange rates changes over time, to make better exchange-rate forecasts. But, so far at least, short-term exchange rate forecasting is far more an art than a science.

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Answers to Textbook Problems

Review Questions 1. The nominal exchange rate is the rate at which two currencies can be exchanged for each other in the market. The real exchange rate is the price of domestic goods relative to foreign goods. Changes in the real exchange rate are related to changes in the nominal exchange rate depending on the inflation rates of the two countries: De/e = Denom/enom + p - p For. 2. The two major types of exchange-rate systems are fixed exchange rates and flexible exchange rates.

In a fixed-exchange-rate system, exchange rates are set at officially determined levels. In a flexibleexchange-rate system, exchange rates are determined by conditions of demand and supply in the foreign exchange market. Currently, the major currencies of the world are on a flexible-exchangerate system.

3. Purchasing power parity, PPP, is the idea that similar foreign and domestic goods, or baskets of goods, should have the same price when priced in terms of the same currency. Purchasing power parity does seem to explain exchange rates in the long run, but over shorter periods it doesn’t work well because countries produce very different sets of goods, because some goods aren’t traded internationally, and because there are transportation costs and legal barriers.

4. The J curve shows the response of net exports to a real depreciation. At first the real depreciation reduces net exports, as the decline in the real exchange rate means that a country pays more for its imports and receives less for its exports. But as time passes, the higher price of imports reduces the demand for imports, while the lower price of the country’s exports increases their demand abroad.

So, eventually net exports begin to increase.

5. An increase in domestic income leads people to buy more goods, including imported goods, so net exports decline. An increase in foreign income leads foreigners to buy more goods, including goods exported from the domestic country, so net exports increase. An increase in the domestic real interest rate makes domestic assets more attractive and foreign assets less attractive to both domestic and foreign investors. This causes a reduction in the supply of the domestic currency on the foreign exchange market and an increase in demand for the domestic currency on the foreign exchange market. The result is an appreciation of the domestic currency, which leads to a decline in net exports.

6. Foreigners demand dollars in the foreign exchange market to be able to buy U.S. goods and services (U.S. exports) and U.S. real and financial assets (U.S. capital inflows). Americans supply dollars to the foreign exchange market to be able to buy foreign goods and services (U.S. imports) and real and financial assets in foreign countries (U.S. capital outflows). The demand for dollars increases if the demand for U.S. goods increases, the domestic real interest rate increases, foreign income increases, or the foreign real interest rate decreases. The supply of dollars increases if the demand for foreign goods increases, the domestic real interest rate decreases, domestic income increases, or the foreign real interest rate increases.

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7. The IS–LM model for the open economy differs from the closed-economy IS–LM model in that international influences may shift the IS curve. Factors that raise a country’s net exports, given domestic output and the domestic real interest rate, shift the IS curve upward, while factors that reduce a country’s net exports shift the IS curve downward. A recession could be transmitted from one country to another because a recession in one country reduces the net exports of other countries, shifting their IS curves down. In the Keynesian model in the short run, this would lead to a reduction in output in the other countries.

8. Expansionary fiscal policy increases output and the real interest rate in the short run (using a Keynesian model), both of which lead to a reduction of net exports. Expansionary monetary policy increases output in the short run, which tends to reduce net exports, but reduces the real interest rate, which tends to increase net exports (by reducing the exchange rate). The overall effect is potentially ambiguous, but the effects of changes in the real exchange rate on net exports may be weak in the short run, so it is likely that net exports will decline.

9. In the short run, expansionary monetary policy increases output (using a Keynesian model), which decreases net exports, leading to an increased supply of the domestic currency in the foreign exchange market, causing it to depreciate. Expansionary monetary policy also reduces the real interest rate, causing reduced demand for domestic assets, again causing the currency to depreciate.

With the price level fixed, there is both a real and nominal depreciation. In the long run, expansionary monetary policy causes a depreciation in the nominal exchange rate alone. In the long run, no real variables are affected by the expansionary policy; only nominal variables are affected.

So, the price level is higher, but real exchange rates are not affected. Using Eq. (13.6), enom = ePFOR /P, since the real exchange rate, e, and the foreign price level PFOR are unaffected, the nominal exchange rate declines.

10. The fundamental value of a currency is the value of the exchange rate that would be determined by free-market forces of demand and supply without government intervention. When the official exchange rate is higher than its fundamental value, it is said to be overvalued. This is a problem, because to maintain the official exchange rate, the central bank will have to buy the currency with official reserve assets. To prevent having an overvalued currency, the country can change the official exchange rate, restrict international transactions, or use contractionary monetary policy.

11. A country is limited in changing its money supply under a fixed-exchange-rate system, because only one level of the money supply is consistent with the official exchange rate being equal to its fundamental value. As a result, a country isn’t free to use expansionary monetary policy to combat recession. The only exception occurs when different countries coordinate their use of monetary policy. If countries use expansionary monetary policy at the same time, then the currencies won’t become overvalued or undervalued relative to each other. But coordination is likely only if countries face the same economic circumstances and share common macroeconomic goals.

12. Flexible exchange rates have the advantage of allowing a country to use expansionary monetary policy to combat recessions, but currency values fluctuate substantially, introducing uncertainty into international transactions. Fixed exchange rates avoid this problem, but a country may have to give up the independent use of monetary policy. This latter factor is a disadvantage when it comes to combating recessions, but might be an advantage in helping keep inflation low. As long as countries can coordinate on overall monetary policy, the fixed exchange rate system can be maintained. A currency union is very similar to a system of fixed exchange rates, but has further advantages. Costs of trading goods and assets across countries are even lower than under fixed exchange rates and speculative attacks on the currency cannot occur. But a currency union requires even greater coordination of political and financial institutions than a fixed-exchange-rate system does.

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Numerical Problems 1. The price level in the West is PW = 5 guilders per ordinary soap bar. The price level in the East is PE = 100 florins per deluxe soap bar. The real exchange rate is 2 ordinary soap bars per deluxe soap bar. (a) Use Eq. (13.6) to get enom = ePFOR /P = 2 ordinary soap bars per deluxe soap bar ´ 5 guilders per ordinary soap bar/100 florins per deluxe soap bar = 0.10 guilders per florin, or 10 florins per guilder. (b) Inflation in the West is pW = 10%. Inflation in the East is p E = 20%. The real exchange rate is constant. Use Eq. (13.3) to get Denom/enom = (De/e) + pFOR - p = 0 + 10% - 20% = -10%. So, the nominal exchange rate (guilders per florin) depreciates at a 10% rate. The East Bubble florin depreciates, the West Bubble guilder appreciates.

2.

(a) Japan imports 64 barrels of oil, worth 16 cameras at 4 barrels of oil per camera. It exports 40 cameras, so the real value of its net exports is 24 cameras. (b) Japan now imports 60 barrels of oil, worth 20 cameras at 3 barrels of oil per camera. It exports 42 cameras, so the real value of its net exports declines to 22 cameras. (c) In the long run, Japan imports 54 barrels of oil, worth 18 cameras at 3 barrels of oil per camera.

It exports 45 cameras, so the real value of its net exports rises to 27 cameras. (d) This illustrates the J curve, as a real depreciation leads to an initial decline in net exports followed by a later rise in net exports.

3. Begin by writing the equation for the IS curve, which is S d - I d = NX. S d = Y - C d - G = Y - (300 + 0.5Y - 200r) - G. NX = 150 - 0.1Y - 0.5e = 150 - 0.1Y - 0.5(20 + 600r) = 140 - 0.1Y - 300r.

Using these in the IS curve equation gives: (0.5Y - 300 + 200r - G) - (200 - 300r) = 140 - 0.1Y - 300r.

Rearranging terms and simplifying gives the IS curve: 800r = 640 - 0.6Y + G. (a) With G = 100 and Y = 900, the IS curve gives 800r = 640 - 540 + 100 = 200, so r = 0.25.

Then e = 20 + 600r = 170, NX = 150 - 90 - 85 = -25, C = 300 + 450 - 50 = 700, and I = 200 - 75 = 125. (b) With Y = 940, the IS curve gives 800r = 640 - 564 + 100 = 176, so r = .22.

Then e = 20 + 600r = 152, NX = 150 - 94 - 76 = -20, C = 300 + 470 - 44 = 726, and I = 200 - 66 = 134. The rise in domestic output reduces the real interest rate and real exchange rate, and increases net exports, consumption, and investment. (c) With G = 132, the IS curve gives 800r = 640 - 564 + 132 = 208, so r = .26.

Then e = 20 + 600r = 176, NX = 150 - 94 - 88 = -32, C = 300 + 470 - 52 = 718, and I = 200 - 78 = 122. The rise in government spending increases the real interest rate and the real exchange rate, and decreases net exports, consumption, and investment.

4.

(a) Begin by writing the equation for the IS curve, which is S d - I d = NX. NX = 150 - 0.08Y - 500r.

S = Y - C - G = Y - {200 + 0.6[Y - (20 + 0.2Y)] - 200r} - G = 0.52Y - (188 + G) + 200r. d

d

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Using these in the IS curve equation gives: 0.52Y - (188 + G) + 200r - (300 - 300r) = 150 - 0.08Y - 500r.

Rearranging terms and simplifying gives the IS curve: 1000r = (638 + G) - 0.6Y. The LM curve comes from the expression M/P = L, which is 924/P = 0.5Y - 200r. In the long run we’ll use this equation to find the price level, so we’ll write this as P = 924/(0.5Y - 200r).

In the short run we’ll combine the LM curve with the IS curve to find equilibrium, so we’ll write it as 200r = 0.5Y - 924/P. With G = 152 and Y = Y = 1000, the IS curve gives 1000r = 790 - 600 = 190, so r = 0.19.

From the LM curve, P = 924/(500 - 38) = 2. Then NX = 150 - 80 - 95 = -25, C = 200 + 0.6(1000 - 220) - 38 = 630, and I = 300 - 57 = 243. (b) In the short run with G = 214 and P = 2, the IS curve now gives 1000r = (638 + 214) - 0.6Y, and the LM curve is 200r = 0.5Y - 462. Take five times the LM equation and subtract it from the IS equation to get (852 + 2310) - 3.1Y = 0, or Y = 1020. Plug this in the LM equation to get r = 0.24.

Then NX = 150 - 81.6 - 120 = -51.6, C = 200 + 0.6(1020 - 224) - 48 = 629.6, and I = 300 72 = 228.

In the long run, using Y = 1000 in the IS curve gives 1000r = (638 + 214) - (0.6 ´ 1000) = 252, so r = 0.252. From the LM curve, P = 924/(500 - 50.4) = 2.055. Then NX = 150 - 80 - 126 = -56, C = 200 + 468 - 50.4 = 617.6, and I = 300 - 75.6 = 224.4. (c) With G = 152 and an increase in net exports of 62, the IS curve is the same as in part (b). The only difference in the results is the amount of G and NX. In the short run, NX is 62 higher, or 10.4, while G is 62 lower, or 152. In the long run, NX is 62 higher than before (NX = 6), while G is 62 lower at 152.

5.

(a) AD intersects AS at 1000 = 400 + 50M/P, which means M/P = 12. With M = 48 francs, P = 4 francs/bottle. Use the formula enom = ePFor /P = 5 wedges/bottle ´ 20 crowns/wedge/4 francs/ bottle = 25 crowns/franc. (b) At 50 crowns/franc, the franc is overvalued as the official rate exceeds the fundamental value.

The domestic central bank will lose reserve assets over time if it tries to maintain the official rate. (c) To get enom = 50 crowns/franc for the fundamental value, use the formula enom = ePFor/P to find the necessary price level. This is 50 crowns/franc = 5 wedges/bottle ´ 20 crowns/wedge/P francs/bottle, so P = 2 francs/bottle. Since M/P = 12, you need M = 24 francs to get P = 2 francs/bottle.

6.

(a) c0 = 200, cY = 0.6, t0 = 20, t = 0.2, cr = 200 i0 = 300, ir= 300 x0 =150, xY = 0.08, xYF = 0, xr = 500, xrF = 0 r = a IS¢ - b IS¢ Y

a IS¢ = (c0 + i0 + G - cYt0 + x0 + xYFYFor + xrFrFor)/(cr + ir + xr) = (200 + 300 + 152 - (0.6 ´ 20) + 150 + 0 + 0)/(200 + 300 + 500) = 790/1000 = 0.79 b IS¢ = [1 - (1 - t)cY + xY]/(cr + ir + xr) = [1 - (1 - 0.2)0.6 + 0.08]/1000 = 0.0006

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347

r = aLM - (1/ r ) M/P + bLMY

aLM = ( 0 / r ) - p e, bLM = 0

= 0,

r

= 200,

Y

Y

/ r

= 0.5, p e = 0

aLM = 0 bLM = 0.5/200 = 0.0025 (c) In general equilibrium, Y = 1000, so IS: r = 0.79 - (0.0006 ´ 1000) = 0.19 LM: r = 0 - (1/200)924/P + (0.0025 ´ 1000), so 4.62/P = 2.31, so P = 2. (d) AD: Combine IS and LM in terms of P and Y: LM: r = - 0.005M/P + 0.0025Y IS: r = 0.79 - 0.0006Y -0.005M/P + 0.0025Y = 0.79 - 0.0006Y, so 0.0031Y = 0.79 + 0.005M/P = 0.79 + (0.005 ´ 924/P), so Y = 254.84 + 1490.3/P. If NX rises by 62, x0 rises, which changes a IS¢ by 62/1000, or 0.062, increasing the constant term in the equation for a IS¢ from 0.79 to 0.852. So, the AD curve becomes: 0.0031Y = 0.852 + 0.005M/P = 0.852 + (0.005 ´ 924/P), so Y = 274.84 + 1490.3/P. (e) With P = 2, Y = 274.84 + 1490.3/2, so Y = 1020.

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Analytical Problems 1.

(a) The temporary import restriction increases net exports. Since it raises the demand for domestic goods relative to foreign goods, the real exchange rate increases. The rise in the exchange rate mitigates somewhat the increase in net exports caused by the restriction, but the latter dominates, so net exports rise.

Suppose the economy is initially in a recession at the intersection of the IS1 and LM curves in Figure 13.12. The increase in net exports due to the restriction shifts the IS curve from IS1 to IS2, and (if done in the right amount) returns the economy to full employment. The real interest rate increases, as does output. Since output rises, employment rises. The price level does not change.

Figure 13.12 (b) Since the restriction increases the home country’s net exports, it must decrease foreign countries’ net exports. This is shown by the shift to the left of the IS curve from IS1 to IS2 in Figure 13.13. Thus output and the real interest rate decline in the foreign country. The fall in output leads to a decline in employment. The price level is unchanged in the short run. The foreign currency depreciates, since the domestic currency appreciates.

Figure 13.13

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Although the results of this exercise indicate that import restrictions can be used to fight recessions in the short run, this is a poor method for doing so. The main objection to this method is simply that foreign countries may retaliate by imposing similar restrictions. The reduction in worldwide trade makes everyone worse off, because the gains to specialization are lost. Indeed, many economists believe that in the 1930s import restrictions contributed to the decline in output during the Great Depression. It makes more sense to fight a recession by other means, such as expansionary fiscal and monetary policies. (c) In the classical model, import restrictions can’t affect output, just the composition of output.

Import restrictions shift the IS curve up, but the price level rises to restore equilibrium as the LM curve shifts up. The real interest rate is higher, so the real exchange rate will be higher, but there will be no effect on output or employment. Net exports are higher at the expense of consumption and investment.

2.

The fall in the MPK f abroad and the rise in the MPK f in the United States increases U.S. investment for any given real interest rate, shifting the IS curve up and to the right. This is shown in Figure 13.14 as a shift from IS1 to IS2. To restore equilibrium, prices must rise so that the LM curve shifts up from LM1 to LM2. At the new equilibrium the real interest rate is higher. So, the result is an increase in the price level, an increase in the real interest rate, and no change in output. (Note: The reduction in MPKf abroad reduces investment abroad, leading to a decline in domestic net exports. If this effect is large enough, the domestic IS curve would shift down instead of up.)

Figure 13.14 The rise in the U.S. real interest rate increases the real exchange rate. This leads eventually to a decline in U.S. net exports. Capital is flowing into the United States because of the higher return relative to the return in other countries.

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(a) West Bubble’s contractionary monetary policy shifts its LM curve up and to the left, from LM 1 to LM 2 in part (a) of Figure 13.15. The intersection of the IS and LM curves is one in which output is below full-employment output and the real interest rate is higher than before.

Figure 13.15 The decrease in West Bubble’s output increases its net exports. The higher real interest rate causes the currency to appreciate, which decreases its net exports. It is likely that the reduction in income increases net exports by more. So, West Bubble’s net exports rise.

Since West Bubble’s net exports increase, East Bubble’s must decrease, thus East Bubble’s IS curve shifts down from IS1 to IS2. As part (b) of the figure shows, for East Bubble both the real interest rate and output decrease. Since West Bubble’s currency appreciates, East Bubble’s currency must depreciate.

In the long run, of course, the price level in West Bubble adjusts to return the economy to its initial equilibrium, so there are no permanent effects on real variables, including the real exchange rate.

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(b) In the short run East Bubble’s real exchange rate decreases, and since the price level does not change in the short run, East Bubble’s nominal exchange rate must also decrease [since enom = ePFor /P]. In the long run the price level declines in West Bubble, but there is no effect on the price level in East Bubble. The decline in the price level in West Bubble occurs as the LM curve shifts from LM2 back to LM1 to restore equilibrium. With equilibrium restored in West Bubble, income and the real interest rate return to their original levels, so net exports return to their original levels in both countries. In East Bubble the IS curve shifts back to IS1. So, the only difference between the new equilibrium and the old is that West Bubble has a lower price level.

Using the expression enom = ePFor/P for East Bubble, the only term that has changed on the righthand side is the decline in PFor, so enom must decrease. (c) If East Bubble wants to offset West Bubble’s contractionary policy to keep it from affecting the exchange rate, it must also use contractionary policy. When West Bubble uses contractionary policy, East Bubble’s IS curve shifts down, because its net exports decline. To prevent the nominal exchange rate from declining, East Bubble must itself use contractionary monetary policy to shift the LM curve to the left. The contractionary policy causes East Bubble’s output to decline. Since the nominal exchange rate is unchanged and the price levels of the two countries do not change in the short run, the real exchange rate is unchanged. The effect on net exports is ambiguous. Both East Bubble and West Bubble have declines in income, so the effect on net exports depends on the sensitivity in each country of net exports to changes in income.

Comparing the case in which East Bubble does not respond to the change in the exchange rate in part (a) to the case in which East Bubble fixes its exchange rate in part (c) gives the following table:

No response Fix exchange rate

Output

Real Exchange Rate

Net Exports

falls falls

falls no change

fall uncertain

(d) If East Bubble doesn’t change its macroeconomic policies, its currency will become overvalued.

Then it must devalue the currency, impose restrictions on international transactions, or support the currency by buying it in the foreign exchange market, losing official reserve assets.

4.

(a) If people don’t want to spend more at a given real interest rate, they must increase desired saving, so the S - I curve shifts to the right. Since people aren’t spending more on imports, the NX curve doesn’t shift. The new equilibrium is one with a lower real interest rate and higher net exports. (b) If people spend the full amount of the additional income, there will be no change in saving, so the S - I curve won’t shift. But some of the additional spending is on imports, so net exports fall, and the NX curve shifts to the left. (c) A temporary increase in income is more likely to be saved, as in part (a), so net exports are likely to be higher. This confirms the prediction of the model in Chapter 5, Section 5.3, which showed that a temporary adverse supply shock would reduce the current account balance; so a beneficial supply shock would increase the current account and hence increase net exports.

5. Since the benefits of comparative advantage are lost, the FE line shifts to the left, as less can be produced without international trade. With imports and exports affected equally, the IS curve does not shift. In a classical model with no effect on labor supply, the shift to the left in the FE line leads the LM curve to shift up and to the left to restore general equilibrium. This occurs as the price level rises.

As a consequence, output declines and the real interest rate rises.

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In a Keynesian model, with reduced investment by firms in exporting industries and consumption lower, the IS curve would also shift to the left in the short run. This would lead to a decline in output and a decline in the real interest rate in the short run.

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Working with Macroeconomic Data 1.

a. Real exchange-rate fluctuations arise primarily from nominal exchange-rate fluctuations.

b. In the data, the relationship between the real interest rate and the exchange rate is not clear.

There are some times when a rise in real interest rates is associated with an appreciation of the dollar but the relationship is not consistent.

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2.

Generally, the real exchange rate rose when net exports declined in the 1980s and 1990s.

The scatter plot shows a slight negative relationship, as expected.

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3.

The Hong Kong dollar was generally depreciating relative to the U.S. dollar between 1981 and late 1983. The Hong Kong dollar was neither appreciating nor depreciating relative to the U.S. dollar after 1983. In late 1983, Hong Kong adopted a currency board, pegging the value of the Hong Kong dollar to the U.S. dollar.

4.

The euro generally moves in the same direction as other currencies do against the dollar; in part because trade with Europe makes up a large part of U.S. trade. However, starting in 2015, the exchange rates diverge a lot, as the dollar strengthened against other currencies more than it did against the euro.

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The IEB-IRP Model

The real exchange rate, the quantity of foreign goods that can be acquired in exchange for one unit of the domestic good, is an important determinant of a country’s net exports and therefore of domestic production and employment. But what determines a country’s real exchange rate? We will see that the real exchange rate is determined by two equilibrium conditions, each of which is economically significant in its own right. One of these conditions applies to the international market for goods and one applies to the international market for assets. We study these conditions in turn below.

The International Flow of Goods: Intertemporal External Balance As discussed in Chapter 5, a country with positive net exports produces more goods than are purchased by its consumers, firms, and governments. The country’s excess of output over spending equals its lending to other countries. In the future the country will be paid back what it has lent with interest, which will allow it to spend more than it produces and have negative net exports.

Similarly, a country with negative net exports produces less output than is bought by domestic consumers, firms, and governments and therefore must borrow from abroad an amount equal to the excess of its spending over its output. Ultimately, the country must repay with interest the funds that it borrows from other countries. In order to repay foreign loans, countries with negative net exports today must at some point in the future achieve positive net exports.

The requirement that countries that have positive net exports and lend today have negative net exports in the future—and similarly, that countries that have negative net exports and borrow today have positive net exports in the future—is known as intertemporal external balance. (External refers to the flows of goods across international borders, and intertemporal emphasizes that the flow of goods between countries need not balance in every period but must balance over time.) Put simply, intertemporal external balance—or external balance, for short—says that no country can borrow abroad indefinitely without repaying, and that no country would want to lend abroad indefinitely without being repaid.

To illustrate the concept of external balance, consider a numerical example with only two periods, the current period and the future period. Suppose that a country’s current net exports NX are negative, equal to -100 home goods. To pay for this deficit, the country borrows in the international capital market at a real interest rate r of 8% per period. In the future period the country must repay its international borrowing with interest, for a total repayment of 108 goods. Where will the country get the 108 goods it needs to repay its foreign debt? To obtain the 108 goods it needs, in the future period the country must spend 108 goods less than it produces, so that its future net exports NX f equal 108 goods.

In general, for a country to achieve external balance, its future net exports NX f must equal -(1 + r)NX, where NX is current net exports and r is the real interest rate. (For simplicity, we continue to assume two periods.) In our example NX = -100 and r = 0.08, so NX f = 108, as we found. Alternatively, suppose that the country’s current net exports were positive and equal to 100 home goods. With net exports of 100 goods, the country lends 100 goods abroad today. If the real interest rate is 0.08, the country will be repaid 108 goods in the future, which means that it will be able to have future net exports of -108 goods.

This result is once again as implied by the formula NX f = -(1 + r)NX. Formally, we write the intertemporal external balance (IEB) condition as NX(e, . . .) + NX f(e f, . . .)/(1 + r) = 0,

(13.6)

which is a rearrangement of the condition that NX f = -(1 + r)NX. In Eq. (13.6) e is the real exchange rate in the current period and e f is the real exchange rate in the future period. The notations NX(e, . . .) and NX f(e f, . . .) emphasize that the country’s net exports in each period depend on the real exchange rate in that period, as well as on other factors. [Those readers who covered Chapter 8 will recognize that

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Eq. (13.6) requires the present value of net exports to equal zero.]

The Intertemporal External Balance Curve The intertemporal external balance curve IEB in Figure 13.16 shows the combinations of the current real exchange rate e and the future real exchange rate e f that satisfy the external balance condition, Eq. (13.6).

To understand why this relation slopes downward, suppose the economy starts with the combination of current and future real exchange rates represented by point A in Figure 13.16. The exchange rates at point A, eA and e fA, lie on the IEB curve and thus satisfy the external balance condition. Now suppose that the current real exchange rate increases to eB, a real appreciation. The real appreciation reduces the country’s net exports in the current period. So that external balance is maintained and the country can repay foreign borrowings, lower net exports today must be offset by higher net exports in the future. This increase in future net exports can be achieved by real depreciation in the second period, or a decrease in the future real exchange rate to e fB. The new equilibrium combination of exchange rates, eB and e fB, is represented by point B in Figure 13.16. Since points A and B both satisfy external balance, the IEB curve slopes downward.

Figure 13.16 In general, external balance requires that an increase in the current real exchange rate be offset by a decline in the expected future real exchange rate. Intuitively, a high real exchange rate today causes negative net exports today, so a low real exchange rate in the future is needed to allow net exports to be positive in the future. Thus the IEB curve slopes downward, as shown in Figure 13.16.

Factors That Shift the IEB Curve The IEB curve shows the combinations of current and future real exchange rates that lead to external balance. Factors other than real exchange rates that affect current net exports or future net exports will shift the IEB curve. We discuss three important IEB curve shifters: a change in domestic income, a change in foreign income, and shifts in demand. Table 13.1 gives a summary of these shifters.

Domestic Income Suppose that a country’s current and future real exchange rates are represented by point E on the curve IEB1 in Figure 13.17, so that the country is initially in external balance. Now imagine that current income (output) increases. At the initial values of e and ef the increase in income makes domestic consumers wealthier, leading them to spend more on all goods, including imported foreign goods, in both the current and future periods. The increase in imports reduces net exports in both periods, so that the country is no longer in external balance. For external balance to be restored, real exchange rates must fall. For example, a depreciation of the current real exchange rate, with the future real exchange rate held constant—represented by the movement to point F in Figure 13.17—would increase current net exports and restore external balance. Alternatively, future net exports could be increased by a depreciation .

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of the future real exchange rate, with the current real exchange rate held constant—represented by the movement to point H. Thus the increase in domestic income causes the IEB curve to shift downward to IEB2, which passes through points F and H.

Figure 13.17 Foreign Income The effect of an increase in foreign income on the IEB curve is just the opposite of the effect of an increase in domestic income. Suppose that before the increase in foreign income the current and future real exchange rates are represented by point E on IEB1 in Figure 13.18. Because foreign consumers are made wealthier by the increase in income, they will buy more of the goods produced by the home country in the current period and in the future, which increases net exports by the home country in both periods. An appreciation of the current real exchange rate, represented by the movement to point F, will reduce the net exports of the home country and restore external balance. Alternatively, an appreciation of the future real exchange rate, represented by the movement to point H, would restore external balance. Therefore the new IEB curve, IEB2, which passes through points F and H, lies above the original IEB curve, IEB1.

Figure 13.18 Shifts in Demand A shift in demand away from foreign goods toward goods produced by the home country shifts the IEB curve upward, just as an increase in foreign income does. The reason is that, like an increase in foreign income, a shift in demand toward domestic goods increases both current and future net .

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exports by the home country. For external balance to be restored, the current real exchange rate or the future real exchange rate must appreciate; so the IEB curve shifts upward.

The International Asset Market: Interest Rate Parity Besides affecting the international flow of goods, the real exchange rate also plays a key role in international asset markets. We will see in this section that there is a close link between the expected behavior of the exchange rate and the interest rates that are paid on assets in different countries.

Returns on Domestic and Foreign Assets To illustrate the role of the real exchange rate in international asset markets, we again use a numerical example. Imagine that you want to invest $10,000 in a financial asset for one year, and suppose that you have limited your choice to either U.S. government bonds or German government bonds. U.S. government bonds are denominated in dollars and pay a nominal interest rate of 8% for one year (i.e., i = 0.08).

German government bonds, which are denominated in euros, pay a nominal interest rate of 6% for one year (iFor = 0.06). The two financial investments have comparable risk and liquidity. If you want to maximize your financial return, which bonds should you buy?

Table 13.1

Summary: Factors That Shift the IEB Curve

An Increase in

Shifts the IEB Curve

Reason

Domestic income (output) Y

Down

Foreign income (output) YFor

Up

Demand for domestic goods relative to foreign goods

Up

Higher domestic income raises import demand and reduces net exports, so real exchange rates must fall to restore external balance Higher foreign income raises demand for domestic exports and increases net exports, so real exchange rates must rise to restore external balance Net exports increase, so exchange rates must rise to restore external balance

At first glance, the answer seems obvious: Buy the U.S. government bonds, because they offer a higher interest rate. But this answer may not be right. The correct answer depends on what you think is going to happen to the exchange rate between the U.S. dollar and the euro over the next year.

We can compare the financial returns on the two assets by calculating the value in dollars one year from now of $10,000 invested in each asset. For the U.S. government bond the answer is easy. At a nominal interest rate of 8% per year, the bond will earn $800 in interest and will be worth $10,800 in one year. For the German bond, however, we must take into account that the $10,000 must first be converted into euros in order to buy the bond; then when the German bond matures in one year, the principal and interest (which will be in euros) must be converted back into dollars.

Table 13.2 illustrates the calculation of the future dollar value of the German bond, assuming that (1) the current nominal exchange rate enom is 2.00 euros per dollar and that (2) the exchange rate is expected to f depreciate by 3% over the coming year, so that the expected future nominal exchange rate enom equals 1.94 euros per dollar (1.94 is 97% of 2.00). Converting $10,000 to euros at an exchange rate of 2 euros per dollar yields 20,000 euros (step 1 in Table 13.2), which are used to buy a German bond. At a 6% nominal interest rate the German bond earns 1200 euros interest and is worth 21,200 euros at the end of one year (step 2). Finally, converting 21,200 euros to dollars at 1.94 euros per dollar yields $10,928 .

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(step 3)—which is higher than the $10,800 that would be obtained from investing in a U.S. bond! Thus the German bonds have a higher expected rate of return in this case, even though they pay a lower nominal interest rate.

The German bonds have a higher rate of return in this example because, relative to the dollar asset, the German bonds have two sources of return. The first source is the nominal interest paid on the bonds (iFor = 0.06). The second source of return is the appreciation of the euro relative to the dollar. At the end of the year, when you convert your investment back into dollars, the value of a euro in terms of dollars is 3% higher than at the beginning of the year, when you converted your dollars into euros.

The gross nominal rate of return on an investment is the value at the end of the year (in terms of dollars) of one dollar invested at the beginning of the year. The gross nominal rate of return from investing in U.S. government bonds is 1 + i, which is 1.08 in this example because each dollar invested in these bonds is worth $1.08 at the end of the year. The bottom section of Table 13.2 calculates the gross nominal rate of return on the German bond. One dollar will buy enom euros (step 1), which can be invested in a German bond at a nominal interest rate of iFor to yield (1 + iFor)enom euros at the end of a year (step 2). Converting f the (1 + iFor)enom euros to dollars yields (1 + iFor) enom /enom dollars at the end of the year (step 3). Thus the gross nominal rate of return from investing in the German government bond is f gross nominal rate of return on foreign bond = (1 + iFor) enom /enom

= (1.06) (2 euros per dollar)/1.94 euros per dollar = 1.0928.

(13.7)

With a gross nominal rate of return equal to 1.0928, a $10,000 investment grows to a value of $10,928 at the end of one year, just as we calculated previously.

Equation (13.7) is an exact expression for the gross nominal rate of return. A simple approximation (») to the gross nominal rate of return is gross nominal rate of return on foreign bond » 1 + iFor - Denom/enom

(13.8)

In our example of the German government bond with iFor = 0.06 and Denom/enom = -0.03, Eq. (13.8) indicates that the gross nominal rate of return from investing in the German government bond is approximately 1.09, which is very close to the exact value of 1.0928. The approximation in Eq. (13.8) permits easy calculation of the gross nominal return, generally without using pencil and paper (or a calculator). The other virtue of this approximation is that it makes clear the two sources of return from holding the German government bond: the interest on the bond iFor, and the nominal appreciation of the euro relative to the dollar over the course of the year, -Denom/enom.

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Table 13.2

Calculating the Gross Nominal Rate of Return for a Foreign Asset Example Today: enom = 2 euros/dollar iFor = 0.06 Future: e f

= 1.94 euros/dollar Step 3 nom

Step 1 Convert home currency to foreign currency $10,000 ® 20,000 euros General Case Today Step 1 Convert home currency to foreign currency 1 unit of ® enom units of home currency foreign currency

Step 2 Earn interest on foreign bond ® 21,200 euros

Step 2 Earn interest on foreign bond ® (1 + iFor)enom units of foreign currency

Convert foreign currency to home currency ® $10,928 Future Step 3 Convert foreign currency to home currency f ® [(1 + iFor)enom]/ enom units of home currency

Interest Rate Parity In our example the gross nominal rate of return expected on the German government bond exceeded the gross nominal rate of return on the U.S. government bond. However, if both types of government bonds have the same risk and liquidity, this difference in rates of return would not persist for long. If savers are free to choose between German bonds and U.S. bonds, they will choose the German bonds as long as they offer a higher gross nominal rate of return than U.S. bonds. But if investors choose German bonds in preference to U.S. bonds, the rate of return on German bonds will fall and the rate of return on U.S. bonds will increase until the two rates of return are equal.

In general, when the international asset market is in equilibrium, the gross nominal rates of return to domestic and foreign assets of comparable risk and liquidity must be the same. This equilibrium condition can be written as f (enom /enom ) (1 + iFor) = 1 + i,

(13.9)

where the left side is the gross nominal rate of return on the foreign bond (Eq. 13.7) and the right side is the gross nominal rate of return on the domestic bond. The equilibrium condition in Eq. (13.9) is the nominal interest rate parity condition, which says that the nominal returns on foreign and domestic financial investments with equal risk and liquidity, when measured in a common currency, must be the same. [With the approximation in Eq. (13.8) the nominal interest rate parity condition can also be expressed more simply as iFor - Denom/enom » i. According to this approximate formula for interest rate parity, the difference between nominal interest rates in two countries equals the rate at which the currency of the country with the higher nominal interest rate is expected to depreciate.]

Interest rate parity can also be expressed in terms of real interest rates and real exchange rates as the real interest rate parity condition: (e/ef )(1 + rFor) = 1 + r,

(13.10)

where rFor is the foreign real interest rate, r is the domestic real interest rate, and e and ef are the current and future real exchange rates. The real interest rate parity condition, Eq. (13.10), is identical to the nominal interest parity condition, Eq. (13.9), except that the nominal interest and exchange rates in

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Eq. (13.9) are replaced by real interest and exchange rates in Eq. (13.10).

Notice that real interest rate parity does not require that the domestic real interest rate r and the foreign real interest rate rFor be equal. The two real interest rates are not directly comparable, since r is measured in terms of the domestic good and rFor is measured in terms of the foreign good. Instead, real interest rate parity requires that the real returns on domestic and foreign assets be equal when real returns are measured in terms of the same good. [If there is only one good, as we assumed in Chapter 5, then e = e f = 1, and Eq. (13.10) reduces to rFor = r.]

The Interest Rate Parity Line Like the intertemporal external balance condition in the international goods market, the real interest rate parity condition in the international asset market can be shown graphically as a relationship between the current and future real exchange rates, e and ef. To write the real interest rate parity condition in a form that is easily graphed, we multiply both sides of Eq. (13.10) by ef and then divide both sides by 1 + r, to obtain e f = [(1 + rFor)/(1 + r)]e.

(13.11)

Equation (13.11) shows that the future real exchange rate ef is proportional to the current real exchange rate e if the domestic and foreign real interest rates are held constant. Equation (13.11) also shows that if the foreign real interest rate is greater than the domestic real interest rate, then the future real exchange rate must exceed the current real exchange rate. The reason is that no financial investor will hold domestic assets paying a lower real return than is available on foreign assets unless a real appreciation of the domestic exchange rate is expected. Similarly, if the real return on foreign assets is lower than the real return on domestic assets, a real depreciation must be expected. An expected real depreciation implies that the future real exchange rate is lower than the current real exchange rate.

Figure 13.19 graphs the real interest rate parity (IRP) condition in Eq. (13.11). Given values of r and rFor, the IRP line relates the expected future real exchange rate ef to the current real exchange rate e. Because the future real exchange rate ef is proportional to the current real exchange rate e, the IRP line is a straight line through the origin.

Figure 13.19

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Factors That Shift the IRP Line The position of the IRP line depends on only two factors: the domestic real interest rate r and the foreign real interest rate rFor. As you can see in Eq. (13.11), the slope of the IRP line is (1 + rFor)/(1 + r). So, if we are given the values of r and rFor, the IRP line is completely determined.

A fall in the foreign real interest rate rFor or a rise in the domestic real interest rate r reduces the slope of the IRP line, (1 + rFor)/(1 + r), thus causing the IRP line to pivot clockwise (see Figure 13.20). A decline in the real rate of return on the foreign asset relative to the domestic asset is possible only if financial investors expect the domestic real exchange rate to depreciate. Thus for any given current real exchange rate e, the future real exchange rate ef must fall, which causes the IRP line to pivot clockwise. Similarly, a rise in the real return on foreign assets relative to the real return on domestic assets would increase the slope of the IRP line and cause it to pivot counterclockwise.

Figure 13.20 Table 13.3 summarizes the effects of domestic and foreign real interest rates on the IRP line.

Table 13.3 Summary: Factors That Shift the IRP Line An Increase in Shifts the IRP Line Domestic real interest rate r

Down (clockwise)

Foreign real interest rate rFor

Up (counterclockwise)

.

Reason Increase in the domestic real interest rate requires an expected real depreciation, or a fall in the future real exchange rate for any given current real exchange rate Increase in the foreign real interest rate requires an expected real appreciation, or a rise in the future real exchange rate for any given current real exchange rate

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The Determination of the Real Exchange Rate In the previous two sections we focused on the role of real exchange rates in the international markets for goods and assets. We derived and discussed two equilibrium conditions, the intertemporal external balance (IEB) condition in the goods market and the real interest rate parity (IRP) condition in the asset market. In this section we put these two conditions together to discuss the determinants of real exchange rates.

The determination of the current and future real exchange rates is shown in Figure 13.21, which graphs both the intertemporal external balance (IEB) curve and the interest rate parity (IRP) line. As you can see in the figure, the only combination of e and ef that simultaneously satisfies both the intertemporal external balance condition and the real interest rate parity condition is represented by point E, the intersection of the IEB curve and the IRP line. The values of the current and future real exchange rates that correspond to point E are the values that will occur in equilibrium.

Figure 13.21 Using the diagram in Figure 13.21, we can examine the factors that influence real exchange rates. As an aid to intuition, it is helpful to keep in mind that the real value of a currency, say the dollar, depends on supplies and demands in the foreign exchange market. When foreigners want to buy American goods or assets, they must trade their own currency for dollars (they demand dollars in the foreign exchange market); and when Americans want to buy foreign goods or assets, they must trade dollars for foreign currencies (they supply dollars to the foreign exchange market). Thus factors that make American goods or assets more attractive to foreigners raise the demand for dollars and increase the real value of the dollar (the real exchange rate). Likewise, factors that make foreign goods or assets more attractive to Americans increase the supply of dollars and thus reduce the real value of the dollar.

Factors That Change the Real Exchange Rate Any factor that shifts the IEB curve or the IRP line will change the equilibrium combination of current and future real exchange rates. Table 13.4 summarizes the effects of several factors on the real exchange rate, which we discuss below.

Table 13.4

Summary: The Determination of Real Exchange Rates Current Real An Increase in Shifts Exchange Rate

Domestic income (output) Y Foreign income

Future Real Exchange Rate

IEB down

Falls

Falls

IEB up

Rises

Rises

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Chapter 13 Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy

(output) YFor Demand for domestic gods relative to foreign goods Domestic real interest rate r Foreign real interest rate rFor

IEB up

Rises

Rises

IRP clockwise

Rises

Falls

IRP counterclockwise

Falls

Rises

365

Domestic Income (Output) An increase in domestic income raises the home country’s demand for foreign goods. To buy foreign goods, domestic residents supply their own currency to the foreign exchange market, which—by the intuitive argument suggested a few moments ago—lowers the real exchange rate. In terms of the IEB-IRP diagram (Figure 13.22), if we start from an initial equilibrium at point E, an increase in domestic income raises imports by the home country and causes the IEB curve to shift downward, from IEB1 to IEB2 (see Table 13.1). The interest rate parity line is unaffected by the change in domestic income. At the new equilibrium, point F, both the current and the future real exchange rates have fallen. The fall in the current and future real exchange rates restores external balance while maintaining interest rate parity.

Figure 13.22 Foreign Income (Output) An increase in foreign income has exactly the opposite effect of an increase in domestic income. Intuitively, higher foreign income increases the demand for home country exports, raises the demand for the home country’s currency, and thus causes the real exchange rate to rise. In terms of Figure 13.23, an increase in foreign income shifts the IEB curve upward, from IEB1 to IEB2 (see Table 13.1).

The IRP line is not affected by the change in foreign income. At point F, the new equilibrium, the values of the current and future real exchange rates both increase. The higher real exchange rates restore external balance in a way that is consistent with interest rate parity. Again, notice that the effects of the increase in foreign income are just the opposite of the effects of an increase in the home country’s income.

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Figure 13.23 Shifts in Demand A shift in demand toward the goods produced by the home country increases the demand for the home country’s currency and thus raises the real exchange rate. In terms of the IEB-IRP diagram, a shift in demand toward the home country’s exports causes the IEB curve to move upward (see Table 13.1). The IRP line is not affected by the shift in the demand for goods. Figure 13.23, which was introduced to illustrate the effects of an increase in foreign income, applies to the shift in demand toward home goods as well. As a result of the shift in demand toward the goods produced by the home country, both the current and future equilibrium values of the real exchange rate increase.

The Domestic Real Interest Rate An increase in the domestic real interest rate makes domestic assets more attractive, which increases the demand for the home country’s currency and thus causes the current real exchange rate to appreciate. Diagrammatically, an increase in the domestic real interest rate reduces the slope of the IRP line and causes it to pivot clockwise, from IRP1 to IRP2 in Figure 13.24 (see Table 13.3).

The IEB curve is unaffected by the change in the domestic real interest rate. [To say that the domestic real interest rate does not affect the IEB curve is not quite accurate, since the real interest rate r does appear in the external balance condition, Eq. (13.6). A change in r has no effect on the IEB curve at the point at which exports equal imports in both periods (NX = NX f = 0), and the effect is small at points at which exports and imports in each period are close to being in balance. Since allowing for an effect of the domestic real interest on the IEB curve does not significantly affect our results, for simplicity we ignore this effect.] Therefore, the equilibrium moves from point E to point F, where IEB intersects IRP2. The result of an increase in the domestic real interest rate is a rise in the current real exchange rate and a fall in the future real exchange rate, or a larger expected rate of exchange rate depreciation. Since the domestic real interest rate has increased, the larger expected depreciation is needed to make financial investors willing to hold foreign assets.

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Figure 13.24 The Foreign Real Interest Rate An increase in the foreign real interest rate has the opposite effects of an increase in the domestic real interest rate. As you can verify, an increase in the foreign real interest rate (by rotating the IRP line counterclockwise and leaving the IEB curve unaffected) depreciates the current real exchange rate and appreciates the future real exchange rate. Intuitively, the fall in the current real exchange rate occurs because the rise in the foreign real interest rate makes foreign assets more attractive.

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Chapter 14 Monetary Policy and the Federal Reserve System n

Learning Objectives

I.

Goals of Chapter 14 A. Explain how the nation’s money supply is determined (Sec. 14.1) B. Describe the policy tools used by the Federal Reserve to control the money supply (Sec. 14.2) C. Explain the Fed’s setting of monetary policy targets (Sec. 14.3) D. Discuss the difficulties of making monetary policy (Sec. 14.4) E. Discuss whether monetary policy should be conducted by rules or discretion (Sec. 14.5)

II.

Notes to Ninth Edition Users A. We added material on the Dodd-Frank Act, capital requirements, bank stress tests, and the Financial Stability Oversight Council B. We deleted some of the material on central bank independence and inflation

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Teaching Notes

I.

Principles of Money Supply Determination (Sec. 14.1)

369

A. Three groups affect the money supply 1. The central bank is responsible for monetary policy 2. Depository institutions (banks) accept deposits and make loans 3. The public (people and firms) holds money as currency and coin or as bank deposits B. The central bank (the Federal Reserve Bank in the United States) has a balance sheet showing its assets (what it owns or is owed) and liabilities (what it owes to others) 1. The sum of reserve deposits and currency (held by the nonbank public and by banks) is the monetary base or high-powered money.

2. Banks hold liquid assets called bank reserves a. When bank reserves are equal to deposits, the system is called 100% reserve banking b. But banks lend out some of their deposits, as only a fraction of reserves are needed to meet the need for outflows c. If the bank needs to keep only 25% of the amount of its deposits on reserve to meet the demand for funds, it can lend the other 75% d. The reserve–deposit ratio would be 25% e. When the reserve–deposit ratio is less than 100%, the system is called fractional reserve banking Numerical Problem 1 gives students practice dealing with bank balance sheets.

C. Open-market operations 1. The most direct and frequently used way of changing the money supply is by raising or lowering the monetary base through open-market operations 2. To increase the monetary base, the central bank prints money and uses it to buy assets in the market; this is an open-market purchase a. Banks then find that their reserve–deposit ratio is higher than desired; this leads to a multiple expansion of loans and deposits b. Banks then increase their loans until the reserve–deposit ratio returns to the desired level.

3. If the central bank wants to decrease the monetary base, it uses an open-market sale

Policy Application Most of the use of open-market operations turns out not to be related to changes in monetary policy at all, but rather to changes in money demand. There is a seasonal component to money demand, which the Fed offsets by changing money supply so that interest rates don’t change over the seasons. There are also other factors that affect the money supply, such as the U.S. Treasury Department’s use of funds. The Fed offsets these factors as well. Doing so is called defensive open-market operations. When open-market operations are used to affect the economy, they are said to be dynamic.

D. The money multiplier 1. The relationship between the monetary base and the money supply can be shown algebraically

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2. Let M = money supply, BASE = monetary base, DEP = bank deposits, RES = bank reserves, CU = currency held by nonbank public, res = banks’ desired reserve–deposit ratio (RES/DEP), cu = public’s desired currency–deposit ratio (CU/DEP) 3. The money supply consists of currency held by the nonbank public and deposits, so M = CU + DEP

(14.1)

4. The monetary base is held as currency by the nonbank public and as reserves by banks, so BASE = CU + RES

(14.2)

5. Taking the ratio of these two equations gives M/BASE = (CU + DEP)/(CU + RES)

(14.3)

6. This can be written as M/BASE = [(CU/DEP) + 1]/[(CU/DEP) + (RES/DEP)]

(14.4)

7. The currency–deposit ratio (CU/DEP, or cu) is determined by the public 8. The reserve–deposit ratio (RES/DEP, or res) is determined by banks 9. Rewrite Eq. (14.4) as M = [(cu + 1)/(cu + res)]BASE

(14.5)

10. The term (cu + 1)/(cu + res) is the money multiplier a. The money multiplier is greater than 1 for res less than 1 (that is, with fractional reserve banking) b. If cu = 0, the multiplier is 1/res, as when all money is held as deposits c. The multiplier decreases when either cu or res rises d. Look at U.S. data to illustrate the multiplier (text Table 14.1) Numerical Problems 2 and 3 deal with the money multiplier.

11. The monetary base is called high-powered money because each unit of the base that is issued leads to the creation of more money E. Bank runs 1. If people think a bank will not be able to give them their money, they may panic and rush to withdraw their money, causing a bank run 2. To prevent bank runs, the FDIC insures bank deposits, so that depositors know their funds are safe, and there will be no need to withdraw their money F.

Application: The money multiplier during severe financial crises 1. The money multiplier during the Great Depression a. The money multiplier is usually fairly stable, but it fell sharply in the Great Depression b. The decline in the multiplier was due to bank panics, which affected the multiplier in two ways (1) People became mistrustful of banks and increased the currency–deposit ratio (text Figure 14.1) (2) Banks held more reserves, in anticipation of bank runs, which raised the reserve– deposit ratio c. Even though the monetary base grew 20% from March 1930 to March 1933, the money supply fell 35% (text Figure 14.2)

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d. As a result, the price level fell sharply (nearly one-third) and there was a decline in output (though attributing the drop in output to the decline in the money supply is controversial) 2. The money multiplier during the financial crisis of 2008 a. The worldwide financial panic in fall 2008 caused the money multiplier to decline sharply, especially because of a sharp rise in the reserve–deposit ratio (text Figure 14.3) b. Banks wanted to hold more reserves because the Fed increased the monetary base significantly and banks had few good lending opportunities c. Despite the sharp decline in the money multiplier, the money supply rose modestly because the Fed significantly increased the monetary base by more than the decline in the money multiplier (text Figure 14.4) d. The money supply did not increase too rapidly, so inflation remained low II. Monetary Control in the United States (Sec. 14.2) A. The Federal Reserve System 1. The Fed began operation in 1914 for the purpose of eliminating severe financial crises 2. There are twelve regional Federal Reserve Banks (Boston, New York, Philadelphia, Cleveland, Richmond, Atlanta, Chicago, St. Louis, Minneapolis, Kansas City, Dallas, and San Francisco), which are owned by private banks within each district (text Figure 14.5)

Policy Application What do the twelve Federal Reserve Bank do? First, they clear checks between banks and supply currency to banks. They also supervise and regulate banks. They collect the raw data that goes into the monetary aggregates M1 and M2. They have staffs of economists who provide advice to policymakers, do research on economics, and publish articles that are readable by the general public, some of which I have cited in this manual. The Reserve Banks differ in their macroeconomic philosophies; for example. Minneapolis and Richmond have many classical economists, St. Louis is the leader in monetarism, while New York and Boston tend toward Keynesian views.

3. The leadership of the Fed is provided by the Board of Governors of the Federal Reserve System in Washington, D.C. a. There are seven governors, who are appointed by the president of the United States, and have fourteen-year terms b. The chairman of the Board of Governors has considerable power, and has a term of four years

Policy Application There are a number of features of the setup of the Fed designed to prevent undue political influence on monetary policy. The governors are appointed to long (fourteen-year) terms, each of which expires every two years. The chairman of the Board of Governors serves a four-year term, which expires more than halfway through the term of a U.S. president. The Fed is completely self-financed, through its holdings of U.S. Treasury securities, so Congress cannot pressure the Fed by threatening to withhold funding.

4. Monetary policy decisions are made by the Federal Open Market Committee (FOMC), which consists of the seven governors plus five presidents of the Federal Reserve Banks on a rotating basis (with the New York president always on the committee)

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a. The FOMC meets eight times a year b. It may meet more frequently if economic developments warrant

Policy Application The policymakers on the FOMC are briefed by economists before each meeting. A typical briefing will cover a number of topics, including the state of the regional economy, national economic data, a review of financial markets, forecasts for the next several years, and a discussion of policy options to be considered.

B. The Federal Reserve’s balance sheet and open-market operations 1. Balance sheet of Fed (text Table 14.2) a. Largest asset is holdings of Treasury securities b. Also owns mortgage-backed securities, federal agency debt, and gold, makes loans to banks, and holds other assets including foreign exchange c. One major liability of the Fed is currency outstanding (1) Some is held in bank vaults and is called vault cash (2) The rest is held by the public d. Another major liability is deposits by banks and other depository institutions e. Vault cash plus banks’ deposits at the Fed are banks’ total reserves (RES) Analytical Problem 1 looks at various effects on the money supply, some through changes in the Fed’s balance sheet.

2. The monetary base equals banks’ reserves plus currency held by the nonbank public (text Figure 14.6) 3. The primary method for changing the monetary base is open-market operations a. When the Fed does open-market operations, it affects the market for reserves b. The interest rate when banks borrow reserves from each other is the federal funds rate or fed funds rate c. Generally, the fed funds rate moves in line with other short-term interest rates (text Fig. 14.7)

Policy Application The FOMC generally votes on three options concerning immediate changes in policy: option A to ease policy, option B to maintain the current policy stance, or option C to tighten policy. In recent years prior to the Great Recession, this was usually interpreted as option A lowers the fed funds rate by ½ percentage point, option B maintains the current fed funds rate, and option C raises the fed funds rate by ½ percentage point. Often the committee chooses only a ¼ percentage point change, however. During and after the Great Recession, the policy decision was often the amount of quantitative easing to engage in, until December 2015 when the Fed went back to focusing on the fed funds rate.

C. Reserve requirements 1. The Fed forces banks to hold reserves of about 10% of the value of their transactions deposits (less for small banks) 2. The Fed could change the money supply by changing reserve requirements but seldom does so because reserve requirements have a large impact on both the money supply and bank

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profits

Policy Application Changes in reserve requirements are such a powerful tool that they aren’t used much. A small change in reserve requirements can make a big difference in the reserves a bank holds. So movements of reserve requirements aren’t used for day-to-day monetary policy, only when a major change is under way or there’s been some structural change in the banking system.

D. Discount window lending 1. Discount window lending is lending reserves to banks so they can meet depositors’ demands or reserve requirements 2. The interest rate on such borrowing is called the discount rate

Policy Application The formal mechanism by which the discount rate is changed is rather complicated. The board of directors of each Federal Reserve Bank must vote every two weeks on the discount rate. They send their recommendation to the Board of Governors in Washington, who must approve any changes in the rate. The Board of Governors then decides when to act to change the rate, so all the Reserve Banks change their rates about the same time.

3. The Fed was set up to halt financial panics by acting as a lender of last resort through the discount window 4. A discount loan increases the monetary base

Policy Application The Fed has three different categories for lending at the discount window: (1) adjustment credit, which is a short-term loan to help banks meet temporary liquidity needs; (2) seasonal credit, which is a longer-term loan to help banks meet the seasonal demand for credit (this is especially useful in agricultural regions); and (3) extended credit, which is a longer-term loan for banks that may be in some difficulty and have serious liquidity needs.

Also, there are two different discount rates for adjustment credit. The primary credit discount rate is available to banks in good condition. Banks that are not in good condition must pay the higher secondary credit discount rate and will be placed under close supervision by the Fed. E. Application: The lender of last resort 1. Central bankers can reduce the damage to the economy from a financial crisis by acting as a lender of last resort 2. Bagehot’s dictum is that the central bank should lend freely against good collateral at a penalty rate 3. If the central bank does not act as a lender of last resort, depositors and creditors of banks will all seek cash at once, making the crisis worse 4. Acting as a lender of last resort, the Bank of England thwarted many crises in the 19th century, leading the United States to give the Fed that power in 1913 F. Interest rate on reserves 1. In the financial crisis that began in 2008, the Fed began paying interest to banks on their reserves held on deposit at the Fed

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2. The payment of interest on reserves gives banks the incentive not to spend resources avoiding holding reserves 3. The interest rate paid on reserves is now a tool that the Fed can use to affect the amount of reserves that banks hold and the money supply G. Summary 19: Factors affecting the monetary base, the money multiplier, and the money supply 1. An increase in res, cu, reserve requirements, or the interest rate on reserves has no effect on the monetary base, decreases the money multiplier, and decreases the money supply 2. An open-market purchase, an increase in discount window borrowing, or a decrease in the discount rate increase the monetary base, have no effect on the money multiplier, and increase the money supply

Policy Application The Fed has two other instruments, though they are seldom used. The Fed can set margin requirements on stock purchases. Currently, the margin requirements is 50%, which means an investor who wants to buy stock can borrow a maximum of 50% of the value of the stock and must have cash to pay for the remaining 50% or more. Also, the Fed can impose credit controls on the economy to regulate credit cards and consumer loans. When this was done in 1980 the controls had a powerful effect, reducing consumption spending, leading to an immediate recession.

III. Setting Monetary Policy Targets (Sec. 14.3) A. Targeting the federal funds rate 1. The Fed uses intermediate targets to guide policy as a step between its tools or instruments (such as open-market purchases) and its goals or ultimate targets of price stability and stable economic growth 2. Intermediate targets are variables the Fed cannot directly control but can influence predictably, and they are related to the Fed’s goals 3. Most frequently used are monetary aggregates such as M1 and M2, and short-term interest rates, such as the fed funds rate 4. The Fed cannot target both the money supply and the fed funds rate simultaneously a. Suppose both the money supply and the fed funds rate were above target, so the Fed needs to lower them b. Since a decrease in the money supply shifts the LM curve up, it will increase the fed funds rate 5. In recent years the Fed has been targeting the fed funds rate (Figure 14.1; like text Figure 14.8)

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Figure 14.1 a. This strategy works well if the main shocks to the economy are to the LM curve (shocks to money supply or money demand) b. The strategy stabilizes output, the real interest rate, and the price level, as it offsets the shocks to the LM curve completely c. But if other shocks to the economy (such as IS shocks) are more important than nominal shocks, the policy may be destabilizing, unless the Fed changes the target for the fed funds rate d. Suppose a shock shifts the IS curve to the right from IS1 to IS2 (Figure 14.2; text Figure 14.9) (1) If the Fed were to maintain the real interest rate, it would increase the money supply, shifting the LM curve from LM1 to LM2, thus making output rise even more, which would be destabilizing (2) Instead, the Fed needs to raise the real interest rate to stabilize output, shifting the LM curve to LM3, and increasing the real interest rate to r3 (3) Research suggests that the optimal fed funds rate varies substantially over time. But there is substantial uncertainty about what the level of the optimal fed funds rate is on any given date

Figure 14.2

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6. The LR curve a. If the Fed is targeting a real interest rate, then a modification of the LM curve will simplify our analysis (1) We can replace the LM curve with a horizontal line drawn at the target real interest rate, rT (Figure 14.3; text Figure 14.10). The horizontal line is labeled LR (2) The Fed uses open-market operations to hit its target for the real interest rate; it allows the money supply to be whatever is necessary to hit that target

Figure 14.3 b. The key to good policymaking now becomes shifting the target for the real interest rate in response to shocks to the IS curve, as Figure 14.2 (text Fig. 14.9) showed c. The advantage to targeting a real interest rate is that shocks to money demand or money supply are offset automatically Analytical Problem 3 examines how various shocks shift the LR curve and how the economy responds.

Policy Application Monetary policymakers sometimes distinguish intermediate targets from what are called operating targets. In this context an operating target is a variable that is closely affected by the Fed’s open-market operations, while intermediate targets are affected more slowly and less directly. With this distinction, the fed funds rate and the monetary base would be considered operating targets, while the monetary aggregates M1 and M2, as well as long-term interest rates, would be considered intermediate targets.

IV. Making Monetary Policy in Practice (Sec. 14.4) A. The IS–LM model makes monetary policy look easy—just change the money supply to move the economy to the best point possible 1. In fact, it is not so easy because of lags in the effect of policy (impact lag) and uncertainty about the state of the economy (recognition lag), economic models, and expectations B. Lags in the effects of monetary policy 1. It takes a fairly long time for changes in monetary policy to have an impact on the economy 2. Interest rates change quickly, but output and inflation barely respond in the first four months after the change in money growth (text Figure 14.11) 3. Tighter monetary policy causes real GDP to decline sharply after about four months, with the full effect being felt about 16 to 20 months after the change in policy .

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4. Inflation responds even more slowly, remaining essentially unchanged for the first year, then declining somewhat 5. These long lags make it very difficult to use monetary policy to control the economy very precisely 6. Because of the lags, policy must be made based on forecasts of the future, but forecasts are often inaccurate 7. The Fed has made preemptive strikes against inflation based on forecasts of higher future inflation

Policy Application Alan Blinder, an economist from Princeton University who served several years in the Federal Reserve System as vice-chairman, offers advice to policymakers and academic economists in his article “Distinguished Lecture on Economics in Government: What Central Bankers Could Learn from Academics—and Vice Versa” in the Journal of Economic Perspectives, Spring 1997, pp. 3–19.

C. Conducting Monetary Policy Under Uncertainty 1. Uncertainty about state of economy a. Conflicting signals from data b. Data revisions and inaccurate initial releases of data c. Need to combine information from many variables (CFNAI or ADS) 2. Incomplete models of the economy a. No one knows the best model that describes the economy (classical vs. Keynesian, slopes and locations of curves, levels of full-employment output and natural rate of unemployment) b. Some research suggests policymakers should respond less because model is not known c. Recent research suggests stronger action is needed to prevent a bad outcome d. Uncertainty about predominant source of shocks suggests using a rule, such as the Taylor rule 3. Uncertainty about how expectations of public will be affected by shocks and policy actions a. Central bank may need to anchor inflation expectations and inform people of its plans b. The Fed under Chairman Bernanke has increased the information it provides D. Monetary Policy in the Great Recession 1. The housing crisis, which began in 2007, led to losses at financial institutions, but no one thought it would lead to a major financial crisis 2. In the Great Recession, the economy deteriorated rapidly in late 2008 and early 2009; the recession rivaled those of 1973–1975 and 1981–1982, and the recovery from the recession was weak 3. The Zero Lower Bound a. The Fed cut interest rates to near zero by the end of 2008, hitting the zero lower bound b. In such a liquidity trap, increases in the money supply are held by banks or the public, and have no effect on spending c. Application: Is there really a zero lower bound?

(1) In a few cases, nominal interest rates have become negative (2) But one could just hold cash and earn a zero nominal interest rate; danger of loss of cash allows it (3) Japan in 1990s had the first negative nominal interest rate (4) US had negative nominal interest rates for a short time in financial crisis

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(5) European countries had numerous cases of negative nominal interest rates in and following financial crisis (6) When we refer to zero lower bound, we really mean not far below zero d. To escape the problems caused by the zero lower bound, the Fed took unusual policy measures from 2009 to 2014 (1) It affected interest-rate expectations by using forward guidance (a) The Fed signaled how long it expected interest rates to remain low (b) It hoped to reduce long-term interest rates to stimulate spending (c) The Fed implemented forward guidance first in 2009 and for many years following (2) The Fed expanded the amount of assets it held, engaging in quantitative easing (a) Increasing the amount of assets on its balance sheet increases the monetary base (b) Quantitative easing also reduces long-term interest rates (c) The Fed bought long-term Treasury securities and debt and mortgagebacked securities issued by Fannie Mae and Freddie Mac (d) Buying long-term Treasury securities was designed to reduce long-term interest rates (e) Buying securities from Fannie Mae and Freddie Mac was designed to support the housing market (f) In 2011, the Fed engaged in Operation Twist (Maturity Extension Program), selling short-term Treasury securities and buying long-term Treasury securities to reduce long-term interest rates to stimulate spending e.

The Fed began quantitative easing in 2008, did more in 2010, and still more from 2012 to 2014 (text Fig. 14.12) f.

Doing so increased the inflation rate, preventing deflation from occurring (text Fig. 14.13) E. Application: The financial crisis of 2008 1. Financial institution troubles that began in 2007 represented a shock, shifting the IS curve down and to the left as housing investment declined 2. Banks began to reduce credit availability because of worries that some financial institutions were no longer viable because of losses on mortgage-backed securities; in response, the Fed made credit available through special lending facilities 3. The recession that began in December 2007 seemed mild through September 2008, but then failures at Fannie Mae, Freddie Mac, Lehman Brothers, and AIG led to panic by investors worldwide 4. The panic led to a sharp decline in investment, shifting the IS curve further down and to the left, so the Fed cut its interest rate target sharply, trying to shift the LM curve down and to the right and the LR curve down. The Federal government introduced the TARP program to inject capital into banks and the FDIC raised its insurance coverage to prevent bank runs 5. Dodd-Frank Act increased bank capital requirements to increase safety of banks (1) Fed also introduced stress tests to examine bank safety (2) Financial Stability Oversight Council created to oversee systemic risk in financial system V.

The Conduct of Monetary Policy: Rules Versus Discretion (Sec. 14.5) A. Monetarists and classical macroeconomists advocate the use of rules

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1. Rules make monetary policy automatic, as they require the central bank to set policy based on a set of simple, prespecified, and publicly announced rules 2. Examples of rules a. Increase the monetary base by 1% each quarter b. Maintain the price of gold at a fixed level 3. The rule should be simple; there should not be much leeway for exceptions 4. The rule should specify something under the Fed’s control, like growth of the monetary base, not something like fixing the unemployment rate at 4%, over which the Fed has little control 5. The rule may also permit the Fed to respond to the state of the economy B. Most Keynesian economists support discretion 1. Discretion means the central bank looks at all the information about the economy and uses its judgment as to the best course of policy 2. Discretion gives the central bank the freedom to stimulate or contract the economy when needed; it is thus called activist 3. Since discretion gives the central bank leeway to act, while rules constrain its behavior, why would anyone suggest that the central bank follow rules?

C. The monetarist case for rules 1. Monetarism is an economic theory emphasizing the importance of monetary factors in the economy 2. The leading monetarist is Milton Friedman, who has argued for many years (since 1959) that the central bank should follow rules for setting policy 3. Friedman’s argument for rules comes from four main propositions a. Proposition 1: Monetary policy has powerful short-run effects on the real economy. In the longer run, however, changes in the money supply have their primary effect on the price level (1) This proposition comes from Friedman’s research with Anna Schwartz on monetary history (2) Friedman and other monetarists think monetary policy is a main source of business cycles b. Proposition 2: Despite the powerful short-run effect of money on the economy, there is little scope for using monetary policy actively to try to smooth business cycles (1) First, the information lag makes it difficult to know the current state of the economy (2) Second, monetary policy works with a long and variable lag, so it is not clear how to set policy quantitatively (3) Third, wage and price adjustment is fast enough that by the time a change in policy begins to affect the economy, it may be moving the economy in the wrong direction, thus destabilizing the economy c. Proposition 3: Even if there is some scope for using monetary policy to smooth business cycles, the Fed cannot be relied on to do so effectively (1) Friedman believes the Fed responds to political pressure and tends to stimulate the economy in election years (2) Historically, monetary policy has tended to destabilize, rather than stabilize, the economy; so eliminating monetary policy as a source of instability would improve macroeconomic performance d. Proposition 4: The Fed should choose a specific monetary aggregate (such as M1 or M2) and commit itself to making that aggregate grow at a fixed percentage rate every year (1) The Fed needs to give up activist, or discretionary, policy completely and follow a simple rule (2) Friedman prefers a constant money growth rule, since the money supply is

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controllable by the Fed and the Fed would not follow destabilizing monetary policies (3) To reduce inflation to zero, the money growth target should be gradually lowered over time D. Rules and central bank credibility 1. New arguments for rules suggest that rules are valuable even if the central bank has a lot of information and forms policy wisely a. The new arguments suggest that rules improve the credibility of the central bank b. The credibility of the central bank influences how well monetary policy works 2. Rules, commitment, and credibility a. How does a central bank gain credibility? b. One way to get credibility is by building a reputation for following through on its promises, even if it is costly in the short run c. Another, less costly, way is to follow a rule that is enforced by some outside agency Analytical Problem 4 looks at rules and commitment applied to a noneconomic situation. d. Keynesians argue that there may be a trade-off between credibility and flexibility (1) To be credible, a rule must be nearly impossible to change (2) But if a rule cannot be changed, what happens in a crisis situation?

(3) For example, if a rule is based on economic relationships that change suddenly, then the lack of flexibility may be very costly (4) So a rule may create unacceptable risks

Policy Application For a good description of the rules versus discretion issue applied to monetary policy, see the article by Herb Taylor, “Time Inconsistency: A Potential Problem for Policymakers,” Federal Reserve Bank of Philadelphia Business Review, March/April 1985, pp. 3–12.

E. The Taylor rule 1. John Taylor of Stanford University introduced a rule that allows the Fed to take economic conditions into account 2. The rule is i = p + 0.02 + 0.5y + 0.5 (p - 0.02), (14.6) where i is the nominal fed funds rate, p is the inflation rate over the last 4 quarters, y = (Y - Y )/Y = the percentage deviation of output from full-employment output 3. The rule works by having the real fed funds rate (i - p) respond to: a. y, the difference between output and full-employment output b. p - 0.02, the difference between inflation and its target of 2 percent 4. If either y or p increase, the real fed funds rate is increased, causing monetary policy to tighten (and vice versa) 5. Taylor showed that the rule is similar to what the Fed does in practice 6. The data show that in the 1960s and 1970s when the Fed set the federal funds rate below the rule’s suggestion, inflation rose; when the Fed set the federal funds rate fairly close to the rule’s suggestion in the 1990s, inflation was stable (text Fig. 14.14) 7. In the 2000s, the Fed kept the federal funds rate below the level suggested by the rule because of concerns about deflation 8. Economists are experimenting with variations on the original rule, using forecasts rather than past data and looking at different coefficients in the rule .

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9. Uncertainty about the output term in the Taylor rule is large because of data revisions and uncertainty about potential output in real time Analytical Problem 2 examines the ability of the Taylor rule to stabilize the economy, while Numerical Problem 4 provides practice for students in calculating the rule and how the target for the fed funds rate changes in response to a shock.

Policy Application Many economists within the Fed use the Taylor rule for analyzing policy. Following the financial crisis in 2008, the Fed began to consider its exit strategy from the extraordinary measures it took to ease monetary policy in the crisis. For an analysis of the Fed’s exit strategy based on the Taylor rule, as of mid-2010, see the article by Glenn D. Rudebusch, “The Fed’s Exit Strategy for Monetary Policy,” Federal Reserve Bank of San Francisco FRBSF Economic Letter, 2010-18, June 14, 2010.

F.

Other ways to achieve central bank credibility besides targeting money growth or inflation 1. Increasing the central bank’s reputation as an inflation fighter a. The central bank could improve its reputation by establishing inflation goals and meeting them b. Appointing someone who has a well-known reputation for being tough in fighting inflation may help establish credibility for the central bank (1) For example, in 1979 the appointment of Paul Volcker to be chairman of the Fed was designed to convince people that President Carter was serious about stopping inflation (2) Even in Volcker’s case, however, disinflation proved to be costly 2. If the executive and legislative branches of government cannot interfere with the central bank, people are more likely to believe that the central bank is committed to keeping inflation low and will not cause a political business cycle

G. Application: Inflation targeting 1. Since 1989, some countries have adopted a system of inflation targeting 2. New Zealand was the pioneer, announcing explicit inflation targets that had to be met a. Canada, the UK, Sweden, Australia, Spain, and others followed with some version of inflation targeting b. The European Central Bank uses a modified inflation targeting approach c. Under inflation targeting, the central bank announces targets for inflation over the next 1 to 4 years d. The major disadvantage of inflation targeting is that inflation responds to policy actions with a long lag, so it is hard to judge what policy actions are needed to hit the inflation target and hard for the public to tell if the central bank is doing the right thing, so central banks may miss their targets badly, losing credibility e. The Fed discussed inflation targeting while Bernanke was chairman but decided not to adopt it because of the dual mandate to keep inflation low and to keep employment high (1) But the Fed uses several strategies associated with inflation targeting, including providing forecasts to the public (2) The Fed announced in 2012 a long-run inflation objective of 2%, which may be viewed as an inflation target, even if the Fed has other objectives besides inflation

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Additional Issues for Classroom Discussion

1.

Should the Federal Reserve Be More Responsive to the Public?

Central banks in different countries vary dramatically in both their degree of independence from political pressure and the degree of accountability for their actions. Is the U.S. Federal Reserve sufficiently independent and accountable for optimal policymaking?

In discussing this topic, you should note that most power in the Fed resides with the Chairman and the Board of Governors, who are appointed by the U.S. President and confirmed by the Senate. But the presidents of the regional Federal Reserve banks also have significant influence on the decisions of the Federal Open Market Committee (FOMC), which makes the major monetary-policy decisions. Those presidents are not subject to any political controls at all, as the private citizens who serve on the Reserve Banks’ boards of directors appoint them. Should the presidents, who are not accountable to the public at all, have so much power? How do you evaluate the tradeoff between independence and accountability?

Should you judge the desirability of this setup on its principles or its outcomes?

2.

Should the Fed Deliberately Reduce Inflation, or Wait for a Recession?

When the Fed wanted to reduce the inflation rate in the 1980s, some members of the Federal Open Market Committee discussed how actively the Fed should reduce the inflation rate in moving to its long-run goal of zero inflation. Should the Fed actively tighten monetary policy, or wait for the right circumstances to reduce inflation, since inflation generally falls in a recession?

In discussing this issue, you should note that waiting for a recession (a strategy known as “opportunistic disinflation”) has some advantages and some disadvantages compared to taking deliberate action to reduce inflation. Supporters of an opportunistic strategy argue that the long and variable lags in the effects of monetary policy make it difficult to know how tight monetary policy should be to reduce inflation by a particular amount. If the Fed does not know exactly how tight monetary policy should be, then trying a deliberate strategy of reducing inflation might lead to overly tight policy that could cause a recession.

Instead, supporters of opportunistic disinflation suggest keeping policy roughly neutral during an economic expansion, keeping inflation from rising but not forcing it to decline. Then, if an unavoidable recession hits, the recession itself would cause inflation to decline, even as the Fed eases monetary policy to reduce the recession’s severity.

Supporters of a deliberate strategy to reduce inflation claim that the lags and uncertainty associated with monetary policy are not that severe. Some suggest that always keeping policy a bit on the tight side would gradually bring down the rate of inflation with little danger of recession. Further, many recessions are caused by supply shocks (like dramatic increases in oil prices) that cause inflation to rise, not to fall.

So the strategy of waiting for a recession to hit may cause inflation to rise over time, not to fall.

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Answers to Textbook Problems

Review Questions 1. The monetary base, or high-powered money, consists of the sum of currency held by the non-bank public and banks’ reserves. In an all-currency economy, the money supply equals the monetary base; more generally, the money supply equals the money supply times the money multiplier.

2. The money multiplier is the number of dollars of the money supply that can be created from each dollar of monetary base. Changes in the desire by the public for holding currency affect the currency– deposit ratio, thus changing the money multiplier. Similarly, changes in banks’ desire to hold reserves affect the reserve–deposit ratio, thus changing the money multiplier. Increases in either the currency– deposit ratio or the reserve–deposit ratio reduce the money multiplier. But these effects do not mean that the central bank cannot control the money supply, because changes in the money multiplier can be offset by changes in the monetary base to leave the money supply unchanged.

3. An open-market purchase increases the monetary base. The increase in the monetary base leads to an increase in the money supply through the multiple expansions of loans and deposits.

4. Monetary policy in the United States is determined by the Federal Reserve System. The President appoints the seven members of the Board of Governors of the Federal Reserve System, including the chairman, but otherwise has no direct influence on monetary policy.

5. Means of controlling the money supply other than open-market operations include: (1) Reserve requirements. An increase in reserve requirements forces banks to hold more reserves, increasing the reserve–deposit ratio, thus reducing the money multiplier. With a lower money multiplier, the money supply is reduced for a given size of the monetary base.

(2) Discount window lending. A reduction in discount window lending, which may be caused by the Fed increasing the discount rate or by the Fed refusing to lend, causes a reduction in banks’ reserves, decreasing the monetary base. Also, a higher discount rate may lead banks to choose a higher reserve–deposit ratio, so the money multiplier declines. Both effects reduce the money supply.

(3) Interest rate on reserves. The Fed can increase reserve holdings by banks by increasing the interest rate on reserves, thus reducing the money multiplier and the money supply.

6. Intermediate targets are macroeconomic variables that the Fed cannot directly control, but can influence fairly predictably, and that are related to the ultimate goals of monetary policy. The ultimate goals of monetary policy are achieving price stability and promoting stable growth of aggregate economic activity. Since the Fed can’t control its ultimate goals directly, it influences its intermediate targets as a method for achieving those goals.

If the Fed targets the fed funds rate, then it engages in monetary policy to peg a particular real interest rate, thus allowing the LM curve to shift to whatever location is necessary to hit its target for the real interest rate. Implicitly, then, the target for the real interest rate becomes a horizontal LR curve, replacing the LM curve.

7. The three main sources of uncertainty that affect monetary policymakers are (1) uncertainty about the current state of the economy; (2) incompleteness of their models of the economy; and (3) uncertainty about how the expectations of the public will be affected by economic shocks and policy actions.

Examples of uncertainty about the current state of the economy include the fact that different economic variables often give conflicting signals about the current strength of the economy and the fact that data are often revised, and the initial releases of the data are much less accurate than later

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releases of the data. Examples of incompleteness of models of the economy include the fact that no one is certain whether a classical model or the Keynesian model is the best description of the economy, our lack of knowledge about the slopes and locations of each of the curves in each model, and uncertainty about the levels of full-employment output and the natural rate of unemployment. In addition, there is uncertainty about the predominant source of shocks to the economy. Examples of uncertainty about expectations include the idea that the public is not sure of the central bank’s motives, which might affect their expectations.

8. The main tools the Fed used in the Great Recession to avoid problems caused by the zero lower bound include forward guidance and quantitative easing. Using forward guidance, the Fed tried to convince people about the path of future short-term interest rates, to affect long-term interest rates and spending decisions. Using quantitative easing, the Fed bought many assets to increase the amount of assets on its balance sheet, leading to higher inflation expectations, preventing deflation. The Fed also bought mortgage-market-related assets to help the housing market and used Operation Twist to reduce long-term interest rates.

9. The monetarist response to the argument that discretion is more flexible than following a rule is to argue that (1) because of information lags, it is difficult for the central bank to tell what the appropriate policy is at a particular time; (2) there are long and variable lags between monetary policy actions and their economic results; and (3) the lags mean that by the time a policy change has an effect, it may be destabilizing—moving the economy in the wrong direction. Further, discretion allows political manipulation of the economy.

The more recent argument is that the central bank’s credibility can be enhanced by tying itself to rules rather than relying on discretion. If people believe that the central bank is committed to a rule, they will know that the Fed will not take advantage of them by using unexpected inflation to increase output temporarily. As a result, inflation will be lower.

10. The Taylor rule sets the fed funds rate target depending on recent inflation, the deviation of output from the level of full-employment output, and the deviation of recent inflation from its target of 2%.

The rule has explained the movements of inflation fairly well in the past; when the Fed has set interest rates below those called for by the Taylor rule, inflation has often increased and when the Fed has followed the Taylor rule, inflation has been stable.

11. Inflation targeting may improve a central bank’s credibility because the public can easily observe whether the central bank has achieved its goals. The main disadvantage is the long lag between changes in monetary policy and changes in inflation, so that the Fed may not know exactly how to change policy to hit its goals and the public may not know at any time if the Fed is engaging in the best policy.

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Numerical Problems 1.

Initial balance sheet of banks (all amounts in dollars): Assets Reserves

Liabilities

500,000

Deposits

500,000

Banks want to hold reserves equal to only 20% of deposits. This is 0.20 ´ 500,000 = 100,000. So they have 400,000 they’d like to lend. If they lend 400,000, the public will hold half of it (200,000) in deposits and the other 200,000 in currency. Since the public holds 200,000 of additional currency, banks’ reserves are 500,000 - 200,000 = 300,000. The first-round balance sheet of banks is: Assets Reserves Loans

Liabilities

300,000 400,000

Deposits 700,000

Banks still want reserves to equal just 20% of deposits, or 0.20 ´ 700,000 = 140,000. Since they are still holding reserves of 300,000, they can lend another 160,000. Of this amount, 80,000 comes back to the bank in the form of new deposits, and the other 80,000 is held by the public in the form of currency. Banks have reduced their reserves by 80,000 from 300,000, so reserves are 220,000.

The second-round balance sheet of banks is: Assets Reserves Loans

Liabilities

220,000 560,000

Deposits

780,000

The process continues until banks reach their desired reserve–deposit ratio. Since the public wants to hold its money in equal amounts of currency and deposits, the currency–deposit ratio is 1. The money multiplier in this case is (cu + 1)/(cu + res) = (1 + 1)/(1 + 0.20) = 2/1.2 = 1 2/3. Since the monetary base is 1 million dollars, the money supply is 1 2/3 million dollars. Since half of the money supply is in currency and half is in deposits, these are each equal to 833 1/3 thousand dollars. With a reserve–deposit ratio of 0.2, total reserves held by banks are 0.2 ´ 833 1/3 = 166 2/3 thousand dollars. The final balance sheets are: Central Bank Assets Securities

1,000,000

Liabilities Currency

1,000,000

Banks Assets Reserves 166,666 2/3 Loans 666,666 2/3

Liabilities Deposits 833,333 1/3 Public

Assets Currency 833,333 1/3 Deposits 833,333 1/3

Liabilities Loans 666,666 2/3 Net Worth 1,000,000

©2020 Pearson Education, Inc.

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Dollar amounts are in millions of dollars. (a) DEP = M - CU = 6 - 2 = 4. RES = res ´ DEP = 0.25 ´ 4 = 1.

BASE = CU + RES = 2 + 1 = 3. Multiplier = M/BASE = 6/3 = 2. (b) RES = vault cash + reserves at central bank = 1 + 4 = 5.

CU = BASE - RES = 10 - 5 = 5. M = CU + DEP = 5 + 20 = 25.

Multiplier = M/BASE = 25/10 = 2.5.

3.

(a) res = 0.4 - 2(0.10) = 0.2.

Multiplier = (cu + 1)/(cu + res) = (0.4 + 1)/(0.4 + 0.2) = 2 1/3.

M = multiplier ´ BASE = 2 1/3 ´ 60 = 140.

Setting M/P = L gives 140/1 = 0.5Y - 10(0.10), or 140 + 1 = 0.5Y, which has the solution Y = 282. (b) res = 0.4 - 2(0.05) = 0.3.

Multiplier = (cu + 1)/(cu + res) = (0.4 + 1)/(0.4 + 0.3) = 2.

M = multiplier ´ BASE = 2 ´ 60 = 120.

Setting M/P = L gives 120/1 = 0.5Y - 10(0.05), or 120 + 0.5 = 0.5Y, which has the solution Y = 241. (c) In this case the multiplier is unchanged from part (a) at 2 1/3, so the money supply is unchanged at 140. Setting M/P = L gives 140/1 = 0.5Y - (10 ´ 0.05), or 140 + 0.5 = 0.5Y, which has the solution Y = 281. (d) If the reserve–deposit ratio is unaffected by the real interest rate, the LM curve is steeper than when it is affected by the real interest rate. To see why, consider the effect of a decline in the real interest rate. If the reserve–deposit ratio is affected by the real interest rate, the fall in the real interest rate causes banks to hold more reserves, since they are cheaper (they have a lower opportunity cost). The increase in reserves reduces the money multiplier, reducing the nominal money supply. At the same time, the fall in the real interest rate increases the real demand for money. Since the price level is fixed in the short run, the decline in the nominal money supply means that the real money supply has declined as well. Since the real money supply declines while real money demand increases, something must adjust to restore equilibrium. Along an LM curve, given a particular real interest rate, output adjusts to restore equilibrium. A decline in output is necessary to reduce real money demand and restore equilibrium in the asset market.

If the reserve–deposit ratio is not affected by the fall in the real interest rate, then there is no effect on money supply, just an increase in money demand. So, it takes a smaller decline in output to restore the asset market to equilibrium. Since output need not change as much, this means that the LM curve is steeper.

4.

(a) The Taylor rule is i = p + 0.02 + 0.5y + 0.5 (p - 0.02). The inflation rate over the past year is [(149.2 - 147.3)/147.3] = 0.013. The percentage deviation of output from potential output is (12,892.5 - 13,534.2)/13,534.2 = -0.047. So the Taylor rule suggests a target fed funds rate equal to: i = p + 0.02 + 0.5y + 0.5 (p - 0.02) = 0.013 + 0.02 + [0.5 ´ (-0.047)] + 0.5[0.013 - 0.02] = 0.006 = 0.6%. (b) Now the inflation rate over the past year is –0.004 and the percentage deviation of output from potential output is its old deviation – 0.043 (because potential output increased .03 and actual output declined .013, for a net decline of 0.043), or y = –0.047 – 0.043 = –0.09. The Taylor rule is i = p + 0.02 + 0.5y + 0.5 (p – 0.02) = –0.004 + 0.02 + [0.5× (–0.09)] + 0.5[–0.004 – 0.02] = – 0.041 = –4.1%. The Fed would like to set the fed funds rate at a negative level, but nominal interest rates cannot be negative.

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Analytical Problems 1.

(a) The increase in banks’ reserve–deposit ratio reduces the money multiplier, causing the money supply to decline. (b) The increased holding of cash raises the currency–deposit ratio, reducing the money multiplier and causing the money supply to decline. (c) The sale of gold to the public has the same effect as an open-market sale of government securities—it reduces the monetary base, thus causing the money supply to decline. (d) If the Fed pays a lower interest rate on reserves, banks are likely to decrease their reserve–deposit ratio, thus increasing the money multiplier, causing the money supply to increase. (e) As people sell their stocks and increase their deposits, the currency–deposit ratio will decline.

This causes the money multiplier to increase, which causes the money supply to increase. (f ) When the Fed monetizes the government debt, the monetary base increases, so the money supply increases. (g) When the Fed sells securities in exchange for yen, there is no change in the U.S. monetary base or in the U.S. money supply. The Fed has simply changed the composition of its assets.

2.

To examine the Taylor rule, we will use the classical model with misperceptions. (a) An increase in money demand causes the aggregate demand curve to shift down and to the left, reducing the price level and inflation and decreasing output, if the money supply is unchanged.

In response to these changes in output and inflation, the Taylor rule decreases the nominal fed funds rate, which means the money supply is increased. This shifts the aggregate demand curve up and to the right and helps stabilize the economy. (b) A temporary increase in government purchases causes the aggregate demand curve to shift up and to the right, increasing the price level and inflation and increasing output, if the money supply is unchanged. In response to these changes, the Taylor rule increases the nominal fed funds rate, which means the money supply is decreased. The decrease in the money supply shifts the aggregate demand curve down and to the left and helps stabilize the economy. (c) An adverse supply shock causes the aggregate supply curve to shift up and to the left, increasing the price level and inflation and decreasing output, if the money supply is unchanged. In response to these changes, the Taylor rule is ambiguous about which way to move the nominal fed funds rate, since higher inflation increases the funds rate but lower output decreases the funds rate. (d) A decline in consumer confidence causes the aggregate demand curve to shift down and to the left, reducing the price level and inflation and decreasing output, if the money supply is unchanged. In response to these changes in output and inflation, the Taylor rule decreases the nominal fed funds rate, which means the money supply is increased. The increase in the money supply shifts the aggregate demand curve up and to the right and helps stabilize the economy. (e) An increase in export demand causes the aggregate demand curve to shift up and to the right, increasing the price level and inflation and increasing output, if the money supply is unchanged.

In response to these changes in output and inflation, the Taylor rule increases the nominal fed funds rate, which means the money supply is decreased. The decrease in the money supply shifts the aggregate demand curve down and to the left and helps stabilize the economy.

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(a) The investment tax credit causes desired investment to rise, shifting the IS curve up and to the right (Figure 14.4). The short-run equilibrium occurs at point B, with a higher level of output and an unchanged real interest rate. In the long run (Figure 14.5), the equilibrium must occur at the intersection of the FE line and the IS curve, so the existing real interest rate is not tenable; the price level will increase, causing the LM curve to shift up and to the left, leading the LR curve to shift up. Compared with the initial situation, output is unchanged, the price level is higher, and the real interest rate is higher.

Figure 14.4

Figure 14.5

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(b) If the Fed raises its target for the real interest rate to keep output stable in response to the shift in the IS curve, it shifts the LR curve up to LR2 (Figure 14.6) The short-run and long-run equilibria both occur at the same point B, at which the real interest rate is higher but output and the price level are unchanged.

Figure 14.6 (c) The increase in the expected inflation rate causes the real interest rate to decline, if the Fed keeps the nominal interest rate unchanged, causing the LR curve to shift down (Figure 14.7). The shortrun equilibrium occurs at point B, with a higher level of output and lower real interest rate. In the long run (Figure 14.8), the equilibrium must occur at the intersection of the FE line and the IS curve, so the existing real interest rate is not tenable; the price level will increase, causing the LM curve to shift up and to the left, leading the LR curve to shift up, with the equilibrium again occurring at point A. Compared with the initial situation, output is unchanged, the price level is higher, and the real interest rate is unchanged.

Figure 14.7

Figure 14.8

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(d) If the Fed raises its target for the nominal interest rate to keep the real interest rate unchanged in response to the increase in the expected inflation rate, then there is no shift in the LR curve (Figure 14.9). The short-run and long-run equilibria both occur at the same point as the initial equilibrium A, with no change in output, the real interest rate, or the price level.

Figure 14.9 4.

Governments have policies against negotiating with hostage-taking terrorists, because if they negotiate with some terrorists, more terrorists will take hostages in the future. Then they cannot credibly say they will not negotiate with the next set of terrorists. If the government commits to never negotiate with terrorists, then there is no gain to the terrorists for taking hostages, so there will be less terrorism.

This example is like that of monetary rules. If you want to stop hostage taking, you must have a credible commitment not to negotiate. Similarly, a central bank that wants to stop inflation must have a credible commitment not to increase money-supply growth once inflation expectations have been set. If governments have negotiated with terrorists in the past, they cannot say they will not negotiate with the next set of terrorists, or the outcome is likely to be many dead hostages. Similarly, if a central bank has used unexpected inflation to expand the economy in the past, it cannot credibly say that it will not do so in the future. Consequently, an attempt to reduce money-supply growth won’t be believed, and the output costs of disinflation will be high.

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Working with Macroeconomic Data 1.

The money multiplier was fairly stable from 1995 to 2005, but it declined sharply in the Great Recession. The currency–deposit ratio generally trended down from 1959 to 1987 but trended up from 1988 to 1999. The reserve–deposit ratio trended down from 1959 to 1985, then trended up from 1986 to 1993, then trended down from 1993 to 2008. The reserve–deposit ratio rose very sharply in the Great Recession. It seems that financial innovations and reduced use of currency and reserves are behind these trends prior to the Great Recession.

2.

Quarterly Change in Interest Rates 5 4

TB3MS

3

GS10

Percent per year

2 1 0 -1 -2 -3 -4 -5 1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

The volatility of the short-term interest rate increased substantially between 1979 and 1982. After 1982, the volatility of the short-term interest rate declined relative to the 1979-to-1982 period. The .

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volatility of the long-term interest rate increased around 1979 and remained high after 1982.

3.

The short-term interest rate should be negatively related to the unemployment rate, if the Fed reduces interest rates to engage in expansionary monetary policy in recessions, when the unemployment rate rises. In the data, the short-term interest rate is negatively related to the unemployment rate, as theory suggests.

4.

Prior to the financial crisis, the monetary base is growing steadily but excess bank reserves remain close to zero. However, in the financial crisis, the Fed begins paying interest on reserves, encouraging banks to hold excess reserves. As a result, as the Fed engages in quantitative easing, much of the added monetary base is held as excess reserves at banks. .

Chapter 15 Government Spending and Its Financing n

Learning Objectives

I.

Goals of Chapter 15 A. Use the measures of government outlays and taxes to measure government surpluses and deficits (Sec. 15.1) B. Describe how government spending and taxing decisions affect the macroeconomy (Sec. 15.2) C. Discuss the economic effects of government deficits and debt (Sec. 15.3) D. Explain the link between deficits and inflation (Sec. 15.4)

II.

Notes to Ninth Edition Users A. We added material on the Tax Act of 2017, including its potential to raise the US debt-GDP ratio to 100 percent by 2028

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n

Teaching Notes

I.

The Government Budget: Some Facts and Figures (Sec. 15.1) A. Government outlays 1. Three categories of government expenditures a. Government purchases (G) (1) Government investment, which is about 1/6 of total government purchases, consists of purchases of capital goods (2) Government consumption expenditures are about 5/6 of total government purchases b. Transfer payments (TR) (1) Transfers are expenditures for which the government receives no current goods or services in return (2) Examples: social security benefits, pensions for government retirees, welfare payments c. Net interest payments (INT) (1) Interest paid to holders of government bonds less interest received by the government (2) Government makes loans to students, farmers, small businesses d. Subsidies less surpluses of government enterprises; relatively small, so we ignore it 2. Total (Federal, state, and local) government outlays are about 39% of GDP (text Figure 15.1) a. Government purchases increased enormously in World War II (1) Government purchases rose in other wars as well (2) Since the late 1960s, government purchases have drifted downward from about 23% of GDP to about 17% of GDP in late 1990s (3) They rose sharply in the financial crisis of 2008 but since have declined to about 18% of GDP b. Transfer payments have been rising steadily (1) They averaged about 12% of GDP in the 2000s before the financial crisis and 15% of GDP since then (2) Many social programs, including Social Security, Medicare, and Medicaid, have expanded over time c. Net interest payments have also changed over time (1) They doubled between 1941 and 1946 because of the higher debt to finance World War II (2) They increased significantly in the 1980s, as both the government debt and interest rates increased sharply (3) They declined in the 1990s and 2000s because of lower interest rates 3. Comparing U.S. government spending to that of other countries shows that the United States spends less as a percentage of GDP than almost any other OECD country (text Table 15.1) B. Taxes 1. Total tax collections increased from about 16% of GDP in 1940 to about 28% in 2000, then declined to about 23.5% in 2011, and has been about 26% to 27% from 2013 to 2017 (text Fig. 15.2) 2. Four principal categories a. Personal taxes (1) Personal income taxes (2) Property taxes (3) Personal taxes have risen steadily over time, except for the Kennedy-Johnson tax cut of 1964, the Reagan tax cut of 1981, and the Bush tax cuts in the early 2000s

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b. Contributions for social insurance have increased steadily as a percentage of GDP since World War II c. Taxes on production and imports are mostly sales taxes and have been steady relative to GDP since World War II d. Corporate taxes declined gradually over time relative to GDP from the mid-1950s to the mid-1980s, and now average about 2% to 3% of GDP 3. The composition of outlays and taxes: the Federal government versus state and local governments a. To see the overall picture of government spending, we usually combine Federal, state, and local government spending b. But the composition of the Federal government budget is quite different from state and local government budgets (text Table 15.2) (1) Consumption expenditures (a) About 2/3 of state and local current expenditures are purchases of goods and services (b) By contrast, less than 25% of Federal current expenditures are for purchases, and of those, about 3/5 is for national defense (c) Of all government purchases of nondefense goods and services, over 80% is done by state and local governments (2) Transfer payments (a) The Federal government budget is more heavily weighted to transfers than state and local budgets (3) Grants-in-aid are payments from the Federal government to state and local governments Analytical Problem 1 looks at the reasons for grants-in-aid.

(4) Net interest paid (a) Net interest is significant and positive for the Federal government (b) It is small and sometimes negative for state and local governments (5) Composition of taxes (a) Personal taxes and contributions for social insurance account for over 80% of Federal receipts, but only about 20% of state and local government receipts (b) Taxes on production and imports provide about half of state and local government receipts, but less than 5% of Federal receipts See the symposium in the Journal of Economic Perspectives, Winter 2007, on U.S. tax policy in international perspective; to compare the U.S. system with the tax systems in other countries.

C. Deficits and Surpluses 1. When outlays exceed revenues, there is a deficit; when revenues exceed outlays, there is a surplus 2. Formally, deficit = outlays - tax revenues = government purchases + transfers + net interest - tax revenues = G + TR + INT - T (15.1)

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3. Another useful deficit definition is the primary government budget deficit, which excludes net interest payments: primary deficit = outlays - net interest - tax revenues = government purchases + transfers - tax revenues = G + TR - T

(15.2)

a. The total deficit tells the amount the government must borrow to cover all its expenditures b. The primary deficit tells if the government’s receipts are enough to cover its current purchases and transfers c. The primary deficit ignores interest payments, because those are payments for past government spending (text Figure 15.3) Numerical Problems 1, 2, 6, and 7, and Analytical Problem 3, deal with various aspects of the deficit and primary deficit.

4. The separation of government purchases into government investment and government consumption expenditures introduces another set of deficit concepts a. The current deficit equals the deficit minus government investment b. The primary current deficit equals the primary deficit minus government investment, which equals the current deficit minus interest payments

Data Application You might think that the current deficit would be smaller than the deficit, since the current deficit is the deficit minus government investment. But the concept of government investment used here is government net investment, which equals gross investment (spending on new capital goods) minus depreciation. In 2014, for example, the federal government’s gross investment was less than depreciation, so its net investment was negative. Thus the current deficit in 2014 exceeded the deficit.

5. The current deficit and primary current deficit usually move together over time (text Figure 15.4) a. Large current deficits occurred in World War II, the mid-1970s, and the early 1980s b. The primary current deficit became a primary surplus in some years in the 1980s and 1990s c. Large interest payments kept the overall deficit large until the late 1990s d. Deficit became larger in the 2000s, then grew dramatically because of increased government spending during the Great Recession e. From 2013-2017, overall deficit has been 4% to 5% of GDP, and primary current deficit has been 1% to 2% of GDP II.

Government Spending, Taxes, and the Macroeconomy (Sec. 15.2) A. Fiscal policy and aggregate demand 1. An increase in government purchases increases aggregate demand by shifting the IS curve up 2. The effect of tax changes depends on the economic model a. Classical economists accept the Ricardian equivalence proposition that lump-sum tax changes have no effect on national saving or on aggregate demand b. Keynesians think a tax cut is likely to increase consumption and decrease saving, thus .

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increasing aggregate demand 3. Classicals and Keynesians disagree about using fiscal policy to stabilize the economy a. Classicals oppose activist policy while Keynesians favor it b. But even Keynesians admit that fiscal policy is difficult to use (1) There is a lack of flexibility, because much of government spending is committed years in advance (2) There are long time lags, because the political process takes time to make changes 4. Automatic stabilizers and the full-employment deficit a. Automatic stabilizers cause fiscal policy to be countercyclical by changing government spending or taxes automatically b. One example is unemployment insurance, which causes transfers to rise in recessions c. The most important automatic stabilizer is the income tax system, since people pay less tax when their incomes are low in recessions, and they pay more tax when their incomes are high in booms d. Because of automatic stabilizers, the government budget deficit rises in recessions and falls in booms (1) The full-employment deficit is a measure of what the government budget deficit would be if the economy were at full employment (2) So the full-employment deficit does not change with the business cycle, only with changes in government policy regarding spending and taxation (3) The actual budget deficit is much larger than the full-employment budget deficit in recessions (text Figure 15.5) Numerical Problem 3 looks at how automatic stabilizers affect the budget deficit over the business cycle.

B. Government capital formation 1. Fiscal policy affects the economy through the formation of government capital—long-lived physical assets owned by the government, such as roads, schools, and sewer systems 2. Also, fiscal policy affects human capital formation through expenditures on health, nutrition, and education 3. Data on government investment include only physical capital, not human capital a. In 2017, 55% of federal government investment was on national defense and 45% on nondefense capital b. Most federal government investment is in intellectual property products, such as research and development, but most state and local government investment is for structures C. Incentive effects of fiscal policy 1. Average versus marginal tax rates a. Average tax rate = total taxes/pretax income b. Marginal tax rate = taxes due from an additional dollar of income c. Example: Suppose taxes are imposed at a rate of 25% on income over $10,000 (text Table 15.3) (1) For someone earning less than $10,000, the marginal tax rate and average tax rate are both zero (2) Anyone earning over $10,000 would have a marginal tax rate of 25% (3) Someone earning $18,000 would pay ($18,000 - $10,000) ´ .25 = $2,000 in taxes, so he or she would have an average tax rate of 11.1% (4) Someone earning $50,000 would pay ($50,000 - $10,000) ´ .25 = $10,000 in taxes,

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so he or she would have an average tax rate of 20% (5) Someone earning $100,000 would pay ($100,000 - $10,000) ´ .25 = $22,500 in taxes, so he or she would have an average tax rate of 22.5% d. The distinction between average and marginal tax rates affects people’s decisions about how much labor to supply (1) If the average tax rate increases, with the marginal tax rate held constant, a person will increase labor supply (a) The higher average tax rate causes an income effect (b) With lower income, a person consumes less and wants less leisure, so he or she works more (c) The labor supply curve shifts right (2) If the marginal tax rate increases, with the average tax rate held constant, a person will decrease labor supply (a) The higher marginal tax rate causes a substitution effect (b) With a lower after-tax reward for working, a person wants to work less (c) The labor supply curve shifts left (3) Tax Act of 2017 reduced marginal tax rates for most taxpayers (a) Designed to encourage economic activity (b) Might increase GDP growth by 0.9 percentage points in 2019 (c) Also reduced business taxation, which could boost future capital stock Numerical Problem 4 and Analytical Problem 2 look at the effects of tax rates on labor supply.

3. Application: Supply-side economics a. Congress reduced tax rates twice in the 1980s (1) At the beginning of the decade the highest marginal tax rate on labor income was 50% (2) The 1981 tax act (ERTA) reduced tax rates in three stages, phased in until 1984 (3) The tax reform of 1986 further reduced personal tax rates, dropping the top marginal tax rate to 28% b. Supply-side economists promoted the tax rate reductions, arguing that labor supply, saving, and investment would all increase substantially c. If tax cuts caused labor supply to increase enough, tax revenues might rise, rather than declining (1) The Laffer curve (text Figure 15.6) shows that as tax rates rise beyond level, tax revenues will decline (2) If the current tax rate is beyond the peak of the Laffer curve, then a cut in tax rates will cause tax revenue to increase, rather than to decline (3) The data suggest that although labor supply is affected by tax rates, the response is not large (4) Overall, it appears that the U.S. economy was on the left side of the Laffer curve (5) As a result, tax cuts cause tax revenue to decline, and tax increases cause tax revenue to rise

Policy Application Four articles evaluating the results of the Tax Reform Act of 1986 are presented in a symposium in the Winter 1992 issue of the Journal of Economic Perspectives.

4. Tax-induced distortions and tax rate smoothing

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a. In the absence of taxes, the free market works efficiently (1) Taxes change economic behavior, reducing welfare (2) Thus tax-induced deviations from free-market outcomes are called distortions b. The difference between the number of hours a worker would work without taxes and the number of hours he or she actually works when there is a tax reflects the tax distortion c. The higher the tax rate, the greater the distortion d. Fiscal policymakers would like to raise the needed amount of government revenue while minimizing distortions

Policy Application Joel Slemrod thinks we need to focus more research on tax collection, understanding that collecting taxes is costly. Collection costs affect the choice of tax instruments as well as the degree of tax evasion. See Slemrod’s article “Optimal Taxation and Optimal Tax Systems,” Journal of Economic Perspectives, Winter 1990, pp. 157–178. e. It is better to keep the tax rate constant over time than to raise it and lower it, because the higher tax rate has a higher distortion (1) For example, keeping the tax rate at a steady 15% is better than having it at 10% one year and 20% the next, since the distortions in the second year are much higher (2) Keeping a constant tax rate over time is called tax rate smoothing

Theoretical Application Robert Barro introduced the idea of tax smoothing in relation to the government debt in his article “On the Determination of Public Debt,” Journal of Political Economy, October 1979, pp. 940–971.

(3) Empirical studies suggest that the Federal government has not always smoothed tax rates as much as it could to minimize distortions (4) But borrowing to finance wars, thus avoiding the need to raise taxes a lot in war years, is consistent with the idea of tax rate smoothing Numerical Problem 5 and Analytical Problem 4 look at tax smoothing and labor supply.

III. Government Deficits and Debt (Sec. 15.3) A. The growth of the government debt 1. The deficit is the difference between expenditures and revenues in any fiscal year 2. The debt is the total value of outstanding government bonds on a given date 3. The deficit is the change in the debt in a year a. DB = nominal government budget deficit (15.3) b. B = nominal value of government bonds outstanding 4. A useful measure of government’s indebtedness that accounts for the ability to pay off the debt is the debt–GDP ratio a. The U.S. debt–GDP ratio (text Figure 15.7) fell from over 1 after World War II to a low point in the mid-1970s b. From 1979 to 1995, the debt–GDP ratio rose significantly, but it fell from 1995 to 2001, then began to rise in 2002 and grew dramatically in the Great Recession

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Data Application In my article “How Big Is Your Share of Government Debt?” Federal Reserve Bank of Philadelphia Economic Review, November/December 1990, I look at how government’s debt and assets have changed over time in the United States. Since the government’s assets exceed its debts, U.S. citizens have positive net wealth from the government. But the amount of net wealth declined substantially in the 1980s as the government took on more debt and acquired few assets.

5. Change in debt–GDP ratio = deficit/nominal GDP - [(total debt/nominal GDP) ´ growth rate of nominal GDP] (15.4) a. So two things cause the debt–GDP ratio to rise (1) A high deficit relative to GDP (2) A slow rate of GDP growth b. During World War II, large deficits raised the debt–GDP ratio c. For the next 35 years, deficits were small or negative, and GDP growth was rapid, so the debt–GDP ratio fell d. During the 1980s and early 1990s, the debt–GDP ratio rose because of high deficits e. Large surpluses reduced the debt-GDP ratio in the late 1990s, but large deficits raised it beginning in 2002 and increased it more sharply during the Great Recession f. Tax cut of 2017 might propel the debt-GDP ratio to the highest levels since WWII

Theoretical Application Andy Abel asks the question, “Can the Government Roll Over Its Debt Forever?” in the November/December 1992 issue of the Federal Reserve Bank of Philadelphia Business Review.

The answer to the question depends on whether there is too much capital in the economy, on the relation between the interest rate and growth rate, and on the presence of uncertainty. Economic research has provided no definitive answer to the question, however.

Data Application Robert Eisner argues that government debt is not all that big once you adjust for inflation and take account of government’s assets. See his book How Is the Federal Deficit? New York: The Free Press, 1986.

B. Application: Social Security: How can it be fixed?

1. The Social Security system may not be able to pay future promised benefits 2. The system is mostly pay as you go, so that most taxes collected today go to paying benefits to current retirees—there is only a small trust fund 3. The pay-as-you-go system worked as long as the number of workers greatly exceeded the number of retirees, but demographic changes will soon decrease the ratio of workers to retirees 4. The result will be payouts in excess of tax revenue (text Figure 15.8) 5. Fixing the social security system a. Increase tax revenue by raising taxes, but this distorts labor supply decisions b. Increase the rate of return by investing in the stock market, but this is risky c. Reduce benefits by increasing retirement age

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C. The burden of the government debt on future generations 1. People worry that their children will have to pay back the debt that past generations have accumulated 2. To the extent that U.S. citizens own government bonds, future generations will just be paying themselves; but now more than half of U.S. debt is owned by foreigners, so this argument is no longer valid 3. However, there could be a burden, because if tax rates have to be raised in the future to pay off the debt, the higher tax rates could be distortionary 4. Also, since bondholders are richer on average than nonbondholders, when the debt was repaid there would be a large transfer from the poor to the rich 5. Finally, government deficits reduce national saving according to many economists a. If so, with lower saving there will be lower investment b. Lower investment means a smaller capital stock c. A smaller capital stock means less output in the future d. So the future standard of living will be lower e. However, this assumes that government deficits reduce national saving; that is a key and unsettled question

Policy Application Many points of view about the government budget deficit are presented in a symposium in the Journal of Economic Perspectives, Spring 1989. There are articles by Edward M. Gramlich, who finds that the budget deficits of the 1980s clearly reduced national saving; Robert J. Barro, who supports the Ricardian equivalence proposition and cites empirical evidence in support of it; B. Douglas Bernheim, who dismisses Ricardian equivalence in favor of a neoclassical paradigm that suggests deficits have real effects; and Robert Eisner, who focuses on the market value of the government debt relative of GDP and finds it declining in the late 1980s.

D. Budget deficits and national saving: Ricardian equivalence revisited 1. When will a government deficit reduce national saving? a. It almost certainly does when government spending rises b. But it may not for a cut in taxes or increase in transfers 2. Ricardian equivalence: an example a. Suppose the government cuts taxes by $100 per person b. Since S = Y - C - G, (15.5) national saving declines only if consumption rises (assuming Y is fixed at its full-employment level) c. Consumption might not rise if people realize that a tax cut today must be financed by higher taxes in the future (1) A tax cut of $100 per person could be financed by a tax increase of (1 + r) ∙ $100 next year (2) Then taxpayers’ ability to consume is the same with or without the tax cut (3) People will simply save the tax cut so they can pay off the future taxes d. As a result, national saving should be unaffected 3. Ricardian equivalence across generations a. What if the higher future taxes are to be paid by future generations? b. Then people might consume more today, because they would not have to pay the higher future taxes c. But as Barro pointed out, if people care about their children, they will increase their bequests to their children so their children can pay the higher future taxes

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(1) After all, if people wanted to consume at their children’s expense, they could have lowered their planned bequests (2) So why should the fact that the government gives people a tax cut cause them to consume at their children’s expense?

Theoretical Application The classic article on bequests and Ricardian equivalence is Robert J. Barro, “Are Government Bonds Net Wealth?” Journal of Political Economy, 1974, pp. 1095–1117. Barro suggests that even if there are departures from Ricardian equivalence, examining the economy assuming Ricardian equivalence provides a useful baseline case.

E. Departures from Ricardian equivalence 1. The data show that Ricardian equivalence holds sometimes, but not always a. It certainly did not hold in the United States in the 1980s, when high government deficits were accompanied by low savings b. It did seem to hold in Canada and Israel sometimes c. But overall, there seems to be little relationship between government budget deficits and national saving 2. What are the main reasons Ricardian equivalence may fail? a. Borrowing constraints (1) If people cannot borrow as much as they would like, a tax cut financed by higher future taxes essentially lets them borrow from the government b. Shortsightedness (1) If people do not foresee the higher future taxes, or spend based on rules of thumb about their current after-tax income, they may increase consumption in response to a tax cut c. Failure to leave bequests (1) People may not leave bequests because they do not care about their children, or because they think their children will be richer than they are, so they will increase consumption spending in response to a tax cut d. Non–lump-sum taxes (1) When taxes are not lump sum, changes in tax rates affect economic decisions (2) However, a tax cut will not necessarily lead to an increase in consumption in this case F.

In touch with data and research: Measuring the impact of government purchases on the economy 1. The stimulus package of 2009 increased federal government spending by about $500 billion and reduced taxes by almost $300 billion, leading economists to debate its impact 2. Temporary increases in government purchases lead to higher output in both Keynesian and classical models 3. Research reviewed by Ramey suggests that the multiplier (the short-run change in output from a one unit change in government purchases) is between 0.8 and 1.5 4. Auerbach and Gorodnichenko find that the multiplier is between 0 and 0.5 in expansions but much higher, between 1 and 1.5, in recessions 5. Eggertsson’s research shows that the government purchases multiplier is even higher if monetary policy is constrained by the zero lower bound, as has been the case in the years following the Great Recession in the United States

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Policy Application If the government has a large debt, and if Ricardian equivalence does not hold, then the manner in which the government handles the debt is important. For example, should it borrow long (by issuing mostly 30-year bonds) or short (by issuing 3-month bills)? For a handle on this and related issues, see the article, “Managing the Public Debt” by D. Keith Sill, Federal Reserve Bank of Philadelphia Business Review, July/August 1994.

IV. Deficits and Inflation (Sec. 15.4) A. The deficit and the money supply 1. Inflation results when aggregate demand rises more quickly than aggregate supply 2. Budget deficits could be related to inflation, but we usually think of expansionary fiscal policy as leading to a one-time jump in the price level, not a sustained inflation 3. The only way for a sustained inflation to occur is for there to be sustained growth in the money supply 4. Can government deficits lead to ongoing increases in the money supply? a. Yes, if spending is financed by printing money b. The revenue that a government raises by printing money is called seignorage c. Usually, governments do not just buy things directly with newly printed money, they do so indirectly (1) The Treasury borrows by issuing government bonds (2) The central bank buys the bonds with newly printed money (3) The relationship between the deficit and the increase in the monetary base is deficit = DB = DBp + DBcb = DBp + DBASE

(15.6)

(4) DB is the increase in government debt, which is divided into government debt held by the public Bp and government debt held by the central bank Bcb (5) Changes in Bcb equal changes in the monetary base BASE (6) In an all-currency economy, the change in the monetary base is equal to the change in the money supply: deficit = DB = DBp + DBcb = DBp + DM

(15.7)

5. Why would governments use money creation to finance deficits, knowing that it causes inflation? a. Developed countries rarely use seignorage, because it does not raise much revenue b. But war-torn or developed countries are unable to raise sufficient tax revenue to cover government spending and may not be able to borrow from the public

Policy Application If the government runs persistent budget deficits, can monetary policymakers keep inflation low?

No, according to Thomas J. Sargent and Neil Wallace in their article “Some Unpleasant Monetarist Arithmetic,” Federal Reserve Bank of Minneapolis Quarterly Review, Fall 1981, pp. 1–17. Monetary policymakers lose control over inflation if government debt grows faster than the economy does, for then some of the government deficit will eventually be financed by seignorage.

B. Real seignorage collection and inflation 1. The real revenue the government gets from seignorage is closely related to the inflation rate

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2. Consider an all-currency economy with a fixed level of real output and a fixed real interest rate, plus constant rates of money growth and inflation a. The real quantity of money demanded is constant, so real money supply must be constant b. Thus p = DM/M (15.8) c. Real seignorage revenue R is DM/P, but since p = DM/M, then so

DM = p M,

(15.9)

R = DM/P = p M/P.

(15.10)

3. Seignorage is called the inflation tax, because the government’s seignorage revenue equals the inflation rate times real money balances a. So seignorage is like a tax (at the rate of inflation) on real money balances b. The government collects its revenue from the inflation tax when it buys goods with newly printed money c. The inflation tax is paid by everyone who holds money 4. Will a rise in money growth increase seignorage revenue? a. As the money growth rate rises, inflation rises, but people may hold less real balances b. Whether seignorage rises or falls depends on whether inflation rises more or less than the decline in real money holdings (Fig. 15.1; like text Fig. 15.9)

Figure 15.1 .

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c. Real seignorage revenue is shown by the shaded rectangles in the figures, which represent p M/P d. At low inflation rates, seignorage is low e. As the inflation rate rises, seignorage rises Numerical Problems 8 and 9 look at seignorage. f. But at some inflation rate, seignorage begins to decline because of the decline in real money demand g. Plotting inflation against real seignorage revenue illustrates this result (Figure 15.2; like text Figure 15.10)

Figure 15.2 5. If governments raise money supply too rapidly, they may cause hyperinflation, but get less seignorage revenue than they would get with less money growth a. In Germany after World War I, inflation reached 322% per month b. Cagan estimated the inflation rate that maximizes seignorage at only 20% per month C. Application: Quantitative easing and inflation 1. Quantitative easing increases the monetary base and finances the government budget deficit, but will it lead to inflation?

2. Quantitative easing occurred in the United States, United Kingdom, Europe, and Japan a. All were at or near the zero lower bound b. As a result, banks held the increased monetary base as reserves, so the money supply did not rise very much c. The challenge is that inflation is too low, not too high, in these countries 3. Will future inflation rise as the economies return to normal and raise interest rates above zero? a. All the central banks plan to raise interest rates to keep inflation from rising too much b. The Fed plans to raise the interest rate on reserves to avoid a large increase in the money supply 4. Financial markets seem to believe that inflation will remain low a. Long-term interest rates remain low b. Long-term inflation expectations are near 2%

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n

Additional Issues for Classroom Discussion

1.

Should the Tax System Be Reformed?

People spend a huge amount of resources both paying taxes and preparing tax returns. Should the U.S. tax system be fundamentally reformed? If so, how?

To organize the discussion of this issue, you may want to ask your students to think about the following issues: (1) Should we move toward a consumption tax and away from an income tax to encourage saving and investment?

(2) Should we continue with efforts begun in the Reagan and Bush administrations to “broaden the base and flatten the rates”? Proposals include eliminating many deductions, such as the one for mortgage interest, and keeping the number of different tax brackets small. One proposal would tax everyone at the same marginal tax rate. Note that this is the opposite direction of that taken under Presidents Clinton and Obama, in which marginal tax rates on those with high incomes were increased, not decreased.

(3) Should we integrate the corporate and personal tax systems to eliminate the double taxation of dividend income?

(4) Should we eliminate the tax on capital gains to avoid the “lock-in effect” that arises because people do not want to sell assets that have appreciated in value?

(5) Should the entire tax system be indexed for inflation, so taxes would be based on real returns instead of nominal returns?

2.

Should the Social Security System Invest in the Stock Market?

One solution to the coming crisis in the Social Security system is to allow the trust fund to invest in the stock market, which has a higher return, on average, than the government bonds that the fund currently buys. Should we allow the fund to invest in stocks?

The advantage of investing in the stock market is that the returns have been substantially larger to stocks than to bonds—so much so that we could solve the problem completely. One way to do this would be to allow every person to control their own Social Security account, making his or her own investment decisions. But there are two major objections to this approach: (1) it would be risky, and (2) it would be costly.

The risk occurs because the stock market is a riskier place to put your money than the bond market. The costs come because if individuals make their own investments, transactions costs will be large. In fact, this proposal is strongly supported by investment firms on Wall Street, who see themselves getting rich on the transactions fees they will charge people.

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Answers to Textbook Problems

Review Questions 1. The major sources of government outlays are government purchases, transfer payments, and net interest payments. The major sources of government revenues are personal taxes, contributions for social insurance, indirect business taxes, and corporate taxes. The federal government’s outlays and revenues differ from those of state and local governments in that: (1) most spending on nondefense goods and services is done by state and local governments; (2) the federal government spends far more on transfers than on nonmilitary goods and services; (3) the federal government makes grants in aid to state and local governments; (4) the federal government is a large payer of net interest, while state and local governments are net recipients of interest payments; and (5) most of the federal government’s revenues come from personal taxes and contributions for social insurance, while state and local governments rely more heavily on indirect business taxes (sales taxes).

2. The overall budget deficit equals the primary budget deficit plus net interest payments. Both concepts are useful. The overall deficit tells how much the government must borrow currently to pay for its outlays. The primary deficit tells whether current revenues are sufficient to pay for current programs.

Net interest payments are ignored in the primary deficit because they are due to the borrowing for expenditures in the past.

The concept of the current deficit is the same as that of the overall deficit, but counting government expenditures instead of outlays; that is, not counting government investment as a current expenditure.

The idea is that government investment provides capital goods for the future, so should not be counted as current spending in calculating the deficit.

So, the overall deficit, the primary deficit, and the current deficit all measure very different things conceptually. Which one should be used depends on the purpose for which an analyst is using the measure.

3. The government deficit is the change in the government debt. A large change in the debt-GDP ratio can be caused by: (1) a high deficit relative to GDP, and (2) a slow growth rate of nominal GDP. 4. Fiscal policy affects the macroeconomy in three ways: (1) aggregate demand effects, (2) government capital formation, and (3) incentive effects.

The aggregate demand channel affects the macroeconomy because expansionary fiscal policy shifts the IS curve up and to the right, causing the AD curve to shift up and to the right as well.

Both classicals and Keynesians agree that an increase in government spending shifts the IS and AD curves. There is disagreement about the effects of tax changes, however. Classicals generally believe in the Ricardian equivalence proposition, so that the IS and AD curves do not shift. Keynesians reject the Ricardian equivalence proposition and believe that the IS and AD curves do shift in response to tax changes.

The formation of government capital affects the macroeconomy. The quantity and quality of public infrastructure, such as roads, schools, sewer and water systems, and hospitals, are important determinants of the growth rate of the economy. In addition, human capital formation, especially through education programs, affects the productivity of the labor force in the future.

Fiscal policy also has incentive effects that influence the macroeconomy. Tax policies influence economic behavior. Capital income taxes affect people’s decisions to save and invest, while labor income taxes affect people’s labor-supply decisions.

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5. An automatic stabilizer is a provision in the budget that causes government spending to rise or taxes to fall automatically (without legislative action) when GDP falls. An example is unemployment insurance. The advantage of automatic stabilizers over legislated changes in spending and taxes is that they occur quickly, while legislation takes a long time to put in place.

6. An example would be no tax on income below $15,000, then a tax at 20% on income above $15,000.

Someone with income of $30,000 would pay taxes of .20($30,000 - $15,000) = $3000. The average tax rate is 10%, while the marginal tax rate is 20%. The average tax rate most directly affects how wealthy a person feels, while the marginal tax rate affects the reward for working an extra hour.

7. Increasing the tax rate increases distortions by more than reducing the tax rate (by the same amount) reduces distortions. Varying between a high and low tax rate leads to a greater average distortion than keeping the tax rate constant at a medium level.

8. Government debt is a potential burden on future generations in two ways. First, if tax rates must be raised in the future to pay off the debt, then the economy will operate less efficiently in the future because of the increased distortions from the higher tax rates. Second, government deficits may reduce national saving, so the economy accumulates less capital and future output will be lower.

Or if the government borrows from abroad, future citizens will face the burden of making interest payments to foreigners. In either case, the future standard of living will be lower.

However, government deficits caused by (lump-sum) tax cuts do not reduce national saving if the Ricardian equivalence proposition is valid. This occurs because the tax cut does not cause consumption to rise, so there is no change in national saving.

9. Ricardian equivalence might not hold if people face borrowing constraints, if they are shortsighted, if they fail to leave bequests, or if taxes aren’t lump sum.

10. The inflation tax, or seignorage, arises when the government raises revenue by printing money.

The inflation tax is equal to the inflation rate times the real money supply in an all-currency economy in which the money multiplier equals 1. (More generally, the inflation tax collected by the government equals the inflation rate multiplied by the monetary base.) The government collects the inflation tax by printing money to purchase goods and services. The tax is paid by anyone who holds money, because the purchasing power of his or her money is eroded by inflation. The government cannot always increase its real revenues from the inflation tax by increasing money growth and inflation, because a high enough inflation rate causes the real money supply to fall enough that seignorage revenue begins to fall when inflation increases.

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Numerical Problems 1.

The following table shows the categories of the budget: Central Government

Provincial Governments

Combined Governments

200

150

350

100 100 90 490

50 0 -30 170

150 100 60 660

Taxes Grants in aid Total receipts

450 0 450

100 100 200

550 100 650

Deficit Primary deficit

40 -50

-30 0

10 -50

Outlays Purchases of goods and services Transfer payments Grants in aid Net interest paid Total Outlays Receipts

To calculate net interest paid in this table: The central government has debt of 1000 and the nominal interest rate is 10%, so it pays 1000 ´ 0.10 = 100 in interest on its debt. Of this amount, since provincial governments hold debt of 200, they get 200 ´ 0.10 = 20 in interest, while the private sector gets the other 80 in interest payments.

The central government receives 10 in interest, so its net interest payments are 100 - 10 = 90.

Provincial governments receive 20 in interest from the central government and 10 in interest from the private sector, so their net interest payments are -30.

The deficit is total outlays minus total receipts. The primary deficit is the deficit minus net interest payments.

2.

In the year in which the transfer is made, both the deficit and the primary deficit increase by $1 billion.

In the next year, the deficit increases by the amount of the increased interest payments, which total $1 billion times the nominal interest rate, or $1 billion ´ 0.10 = $100 million. The primary deficit is unchanged.

In the following year, the government debt has increased by $1100 million ($1 billion due to the initial debt, plus $100 million of interest from the past year). So the deficit is higher by the amount $1100 million ´ 0.10 = $110 million. Again the primary deficit is unchanged.

3. Deficit = G + TR + INT - T = 1800 + (800 - 0.05Y) + 100 - (1000 + 0.1Y) = 1700 - 0.15Y. The full-employment budget deficit is the deficit that would occur if the economy were at full employment. Full-employment output is 10,000, so the full-employment deficit is 1700 - (0.15 ´ 10,000) = 200. (a) When Y = 12,000, the deficit is 1700 - (0.15 ´ 12,000) = -100. This is smaller than the fullemployment deficit of 200. (b) When Y = 10,000, the deficit is 200 (as calculated above), which is equal to the full-employment deficit, since output is at its full-employment level.

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(c) When Y = 8000, the deficit is 1700 - (0.15 ´ 8000) = 500. This is larger than the fullemployment deficit of 200.

In general, the full-employment deficit is unaffected by the state of the economy, while the actual deficit rises relative to the full-employment deficit in recessions and falls relative to the fullemployment deficit in expansions.

4.

(a) In this situation, someone earning income Y between $8000 and $20,000 pays a total tax of T = 0.25 (Y - $8000), while someone earning between $20,000 and $30,000 pays tax of T = $3000 + 0.30 (Y - $20,000).

Someone with income of $16,000 then pays tax of 0.25($16,000 - $8000) = $2000. This gives an average tax rate of $2000/$16,000 = 12.5%, while the marginal tax rate is 25%.

Someone with income of $30,000 then pays tax of $3000 + 0.30($30,000 - $20,000) = $6000.

This gives an average tax rate of $6000/$30,000 = 20%, while the marginal tax rate is 30%. (b) In this situation, someone earning income Y between $6000 and $20,000 pays a total tax of T = 0.20 (Y - $6000), while someone earning between $20,000 and $30,000 pays tax of T = $2800 + 0.30 (Y - $20,000).

Someone with income of $16,000 then pays tax of .20($16,000 - $6000) = $2000. This gives an average tax rate of $2000/$16,000 = 12.5%, while the marginal tax rate is 20%.

Someone with income of $30,000 then pays tax of $2800 + .30($30,000 - $20,000) = $5800.

This gives an average tax rate of $5800/$30,000 = 19.33%, while the marginal tax rate is 30%. (c) The person making $16,000 has the same average tax rate, but a lower marginal tax rate, so there’s no income effect, just a substitution effect toward increased labor supply. The person making $30,000 faces the same marginal tax rate, so there’s no substitution effect, but has a lower average tax rate, so the income effect tends to reduce labor supply.

5. If workers value their leisure at 90 goods per day, then 90 goods per day must be the equilibrium value of the after-tax real wage. (a) The after-tax real wage equals (1 - t) ´ pre-tax real wage; so 90 = (1 - 0) ´ pre-tax real wage; so the pre-tax real-wage = 90. Setting the pre-tax real wage equal to the marginal product of labor gives 90 = 250 - N, or N = 160. Output is Y = 250N - 0.5N2 = (250 ´ 160) - (0.5 ´ 1602) = 27,200.

The after-tax real wage equals (1 - t) ´ pre-tax real wage; so 90 = (1 - 0) ´ pre-tax real wage; so the pre-tax real-wage = 90. (b) The after-tax real wage equals (1 - t) ´ pre-tax real wage; so 90 = (1 - 0.25) ´ pre-tax real wage; so the pre-tax real-wage = 90/0.75 = 120. Setting the pre-tax real wage equal to the marginal product of labor gives 120 = 250 - N, or N = 130. Output is Y = (250 ´ 130) - (0.5 ´ 1302) = 24,050. The cost of the distortion in terms of lost output is 27,200 - 24,050 = 3150. (c) The after-tax real wage equals (1 - t) ´ pre-tax real wage; so 90 = (1 - 0.5) ´ pre-tax real wage; so the pre-tax real-wage = 90/0.5 = 180. Setting the pre-tax real wage equal to the marginal product of labor gives 180 = 250 - N, or N = 70. Output is Y = (250 ´ 70) - (0.5 ´ 702) = 15,050.

The cost of the distortion in terms of lost output is 27,200 - 15,050 = 12,150, for changing the tax rate from 0% to 50%. Doubling the tax rate from 25% to 50% makes the distortion nearly four times as big. This suggests that taxes should be smoothed over time, since high tax rates increase the distortion more than proportionately.

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6.

(a) To find the largest nominal deficit that the government can run without raising the debt-GDP ratio, use Eq. (15.4) and set the change in the debt-GDP ratio equal to zero. The equation is: Change in debt–GDP ratio = deficit/nominal GDP - [(total debt/nominal GDP) ´ growth rate of nominal GDP]. Plugging in the values of the known variables and setting the change in the debtGDP ratio equal to zero gives: 0 = (deficit/nominal GDP) - [(1000/nominal GDP) ´ 0.10].

Multiplying both sides of the equation by nominal GDP eliminates that term from the equation, leaving 0 = deficit - 100. This has the solution: deficit = 100. (b) Since the debt-GDP ratio is initially 0.6, and nominal GDP is initially 10,000, then debt must initially be 6,000. If real GDP is initially 5,000 and remains constant, then with inflation of 5%, nominal GDP must increase 5% to 10,500. The equation is: Change in debt–GDP ratio = deficit/nominal GDP - [(total debt/nominal GDP) ´ growth rate of nominal GDP]. Plugging in the values of the known variables and setting the change in the debt-GDP ratio equal to zero gives: 0 = (deficit/10,000) - [(6,000/10,000) ´ 0.05], so deficit = 300.

7.

(a) The debt-GDP ratio is .10 at the start. After n years it is .10(1.07/1.05)n. After one year it is .102, after two years it is .104, after five years it is .110, and after ten years it is .121.

If after n years the debt-GDP ratio is 10, we want to find n such that .10(1.07/1.05)n ³ 10. Taking logarithms of both sides of this equation and solving shows that the debt-GDP ratio exceeds 10 after 245 years. So the government must run a primary surplus at some point, as the public won’t continue to buy government bonds forever. (b) Now, after n years the debt-GDP ratio is .10(1.07/1.08)n. After one year it is .099, after two years it is .098, after five years it is .095, and after ten years it is .091. The debt-GDP ratio is declining over time, so it will never exceed 10, and the government can roll over its debt forever. The crucial difference from part (a) is that here the growth rate of GDP exceeds the interest rate.

8.

L = 0.2Y - 500i = 0.2Y - 500r - 500p. With Y = 1000, L = 200 - 500r - 500p. (a) When r = 0.04, equating real money supply to money demand gives: M/P = L = 200 - (500 ´ 0.04) - 500p = 180 - 500p. Real seignorage revenue R = pM/P = 180p - 500p 2. The following table shows seignorage revenue (R) for inflation rates between 0 and 0.30. These values are plotted in Figure 15.3.

Figure 15.3

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p

R

p

R

p

R

0.00 0.02 0.04 0.06 0.08 0.10

0.0 3.4 6.4 9.0 11.2 13.0

0.12 0.14 0.16 0.18 0.20

14.4 15.4 16.0 16.2 16.0

0.22 0.24 0.26 0.28 0.30

15.4 14.4 13.0 11.2 9.0

(b) Seignorage is maximized at p = 0.18. (c) The maximum amount of seignorage revenue is 16.2. (d) When r = 0.08, equating real money supply to money demand gives: M/P = L = 200 - (500 ´ 0.08) - 500p = 160 - 500p. Real seignorage revenue R = pM/P = 160p - 500p 2. The following table shows seignorage revenue (R) for inflation rates between 0 and 0.30. These values are plotted in Figure 15.4.

Figure 15.4

p

R

p

R

p

R

0.00 0.02 0.04 0.06 0.08 0.10

0.0 3.0 5.6 7.8 9.6 11.0

0.12 0.14 0.16 0.18 0.20

12.0 12.6 12.8 12.6 12.0

0.22 0.24 0.26 0.28 0.30

11.0 9.6 7.8 5.6 3.0

The maximum seignorage of 12.8 is attained when p = 0.16.

9.

(a) The monetary base is growing at a 10% rate, so it increases by 0.1 ´ $250 = $25. The nominal value of seignorage over the year is $25. (b) Deposit holders pay the inflation tax on their non-interest-bearing deposits of $600 ´ 0.10 = $60.

This amount is received by banks. Banks pay the inflation tax on their non-interest-bearing reserves of $50 ´ 0.10 = $5. Currency holders pay the inflation tax on their non-interest-bearing currency of $200 ´ 0.10 = $20.

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Overall, deposit holders pay an inflation tax of $60, banks pay an inflation tax of -$60 + $5 = -$55, and currency holders pay an inflation tax of $20. The total inflation tax is $60 - $55 + $20 = $25. (c) If deposit holders get the market rate of interest on their accounts, and the market rate of interest rises with inflation, then deposit holders pay no inflation tax to banks. In this case the inflation tax is borne entirely by banks ($5) and currency holders ($20).

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Analytical Problems 1.

The main reason for having a system of grants in aid from the federal government to state and local governments is that there are nationwide benefits to education, transportation, and welfare programs, but these programs are most efficiently administered at the state and local level. Since the benefits are nationwide, the programs should be paid for at the national level. However, since it takes local knowledge to provide the programs at the right level, state and local governments should decide the best way to provide the services.

The advantage of such a system is that the national government can identify the external effects, that is, the features that make these programs have nationwide benefits, and provide appropriate funding to pay for those benefits. The disadvantage of such a system is that the administration of the programs may become politicized. The grants may go to the regions with the most powerful politicians rather than the regions with the greatest needs and external benefits.

2.

This program has very bad incentive effects. For income (y) below $10,000, a person gets a transfer equal to $10,000 - y. So for every dollar of income a person earns, he or she loses a dollar of transfers. This is like having a marginal tax rate of 100%! The program makes it unlikely that a person with low-income opportunities would want to work at all.

A program with a better incentive effect would be to provide a subsidy to labor income. For example, suppose the program said that it would subsidize labor income at a 25% rate. If a person worked 2000 hours per year at a wage of $4 per hour, to get labor income of $8000, the subsidy would increase the person’s wage by 25% to $5 per hour, so he or she would earn $10,000 per year.

Unlike the first program, which increased the effective marginal tax rate on labor income to 100%, this program increases the after-tax real wage rate by 25%, encouraging work effort.

The advantage of this system is that it increases the effective after-tax real wage rate, so there is a substitution effect toward greater work effort. The disadvantages are that (1) there is an income effect toward lower work effort; and (2) if the program is cut off at a particular income level, then the effective marginal tax rate suddenly rises once people reach that level. This means there is a kink in the budget constraint, so people are likely to choose the point at which the kink occurs; and (3) it does not offer much help to those most in need: the unemployable and those with only very small potential income.

3.

(a) Begin with Eq. (15.4): Change in debt–GDP ratio = deficit/nominal GDP - [(total debt/nominal GDP) ´ growth rate of nominal GDP]. To make things easier, replace the words with symbols, where the debt-GDP ratio = B/PY, with debt = B, nominal GDP = PY, let i = nominal interest rate, and the primary deficit is Bp. Then Eq. (15.4) is D(B/PY) = DB/PY - [(B/PY) ´ (DPY/PY)].

In symbols, the equation that the nominal deficit equals the nominal primary deficit plus nominal interest payments on government debt is DB = DBp + iB. Substitute this expression into Eq. (15.4) and do some algebra: D(B/PY) = DB/PY - [(B/PY) ´ (DPY/PY)] = (DB p + iB)/PY - [(B/PY) ´ (DPY/PY)] = DB p/PY + (B/PY ´ i) - [(B/PY) ´ (DPY/PY)] = DB p/PY - [(B/PY) ´ (DPY/PY - i)].

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(b) If the primary deficit is zero, then DBp/PY = 0, so the equation above is: D(B/PY) = - [(B/PY) ´ (DPY/PY - i)] = (B/PY) ´ (i - DPY/PY) Thus changes to the debt-GDP ratio depend on whether the nominal interest rate is larger or smaller than the growth rate of nominal GDP. 4.

A balanced-budget amendment might prove useful if the government otherwise had a tendency to run a perpetual budget deficit. The amendment would provide a mechanism for fiscal discipline, forcing policymakers to balance the budget. But there could be significant disadvantages, since fiscal policy wouldn’t be as flexible. In particular, automatic stabilizers kick in during a recession to increase spending and reduce taxes, creating a budget deficit but stimulating the economy; however, these effects would have to be offset if the budget were to be balanced. Also, instead of smoothing taxes over time, the government would have to raise taxes when times were bad and incomes were low and reduce taxes when times were good and incomes were high, thus creating distortions to the economy.

Finally, a balanced-budget amendment would fail to recognize that capital formation would help future generations, so deficit financing that’s paid off by taxes on future generations would be appropriate.

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Working with Macroeconomic Data 1.

State and local government spending and taxes have generally grown faster than federal government spending. The federal government has a tendency to run larger overall deficits as a percent of GDP than state and local governments do.

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2.

In recessions, the budget surpluses of both federal and state & local governments generally decrease. The federal government has budget surpluses (as a percent of GDP) that are more affected by the business cycle. Note that the scales are very different in the two graphs.

3.

In 2017, projected deficits and full-employment deficits for the coming five years were rising compared with the average historical deficit. They were slightly lower than those in the aftermath of the Great Recession, however. [Note that the CBO did not produce its normal annual analysis in January 2018, so it is not clear if this question will continue to be viable.]

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4.

The monetary base relative to GDP and the federal debt to GDP ratio do not seem to be related from 1970 to 2008. Beginning in 2008, both began moving in the same direction, as both fiscal policy and monetary policy became expansionary.

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Hyperinflation in the United States Although extreme inflations have not occurred for a very long time in the United States, they are not completely absent from U.S. history. Before declaring independence from Great Britain, the British colonies that would eventually become the United States issued their own money. In the first half of the eighteenth century, several colonies (including South Carolina and the New England colonies as a group) experienced very significant inflations.

A more widespread inflation began in 1776, when the Continental Congress started issuing large amounts of currency to help pay for the war against England (the individual colonies were simultaneously printing their own moneys as quickly as possible). The amount of Continental currency put into circulation went from $6,000,000 in 1775 to $124,800,000 in 1779, and average prices increased more than one hundred-fold between the signing of the Declaration of Independence and the end of the Revolutionary War. The Continental currency’s precipitous decline in value gave rise to a common expression, “not worth a continental.”

Another severe inflationary episode (on what is now American soil, although not involving the government of the United States) occurred in the Confederacy during the Civil War.1 The Confederacy found it very difficult to collect taxes, due to lack of cooperation from the individual Confederate states, the inroads of the invading Union forces, and a lack of experienced and reliable tax collectors. (In one incident, when agents of the Confederate Treasury attempted to contact the state collector in Arkansas, A. B. Greenwood, they were informed that “Mr. Greenwood fled with his property from the state to avoid capture by the enemy and has settled in Texas.” [cited in Lerner, p. 165].) Tax evasion was widespread, and up to October 1864 less than 5% of all revenue entering the Confederate Treasury came from taxes. In a desperate attempt to pay its bills, the Confederate government printed large quantities of paper money. As the war continued, even the printing of money became a problem, as sufficient paper and engravings for new bills became ever harder to find. At one point the Confederate government began paying 6 cents on the dollar for counterfeit notes, which were in wide circulation. The counterfeit notes were then stamped “valid” and reissued as legitimate money.

In April 1865, when Robert E. Lee surrendered to Ulysses Grant at Appomattox Courthouse, Virginia, prices in the Southern states were ninety-two times their level at the beginning of the war.

1 For an account, see Eugene M. Lerner, “Inflation in the Confederacy, 1861-65,” in Milton Friedman, ed., Studies in the Quantity Theory of Money, Chicago: University of Chicago Press, 1956.

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