Type:
Solution Manual
Resource:
Macroeconomics
Edition:
16th Edition
Author(s):
Christopher T.S. Ragan
INSTRUCTOR’S MANUAL Christopher T.S. Ragan McGill University
Macroeconomics Sixteenth Canadian Edition
Christopher T.S. Ragan
Contents Part One: What Is Economics? Chapter 1: Economic Issues and Concepts Chapter 2: Economic Theories, Data, and Graphs
1 3 13
Part Two: An Introduction to Demand and Supply Chapter 3: Demand, Supply, and Price
26 27
Part Seven: An Introduction to Macroeconomics Chapter 19: What Macroeconomics Is All About Chapter 20: The Measurement of National Income
209 211 218
Part Eight: The Economy in the Short Run Chapter 21: The Simplest Short-Run Macro Model Chapter 22: Adding Government and Trade to the Simple Macro Model Chapter 23: Real GDP and the Price Level in the Short Run
226 228 239 250
Part Nine: The Economy in the Long Run Chapter 24: From the Short Run to the Long Run: The Adjustment of Factor Prices Chapter 25: Long-Run Economic Growth
261 262 272
Part Ten: Money, Banking, and Monetary Policy Chapter 26: Money and Banking Chapter 27: Money, Interest Rates, and Economic Activity Chapter 28: Monetary Policy in Canada
281 283 291 300
Part Eleven: Macroeconomic Problems and Policies Chapter 29: Inflation and Disinflation Chapter 30: Unemployment Fluctuations and the NAIRU Chapter 31: Government Debt and Deficits
307 308 316 325
Part Twelve: Canada in the Global Economy Chapter 32: The Gains from International Trade Chapter 33: Trade Policy Chapter 34: Exchange Rates and the Balance of Payments
334 335 344 352
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________________________________________ Part One What Is Economics?
________________________________________ This opening Part of the book provides an introduction to economics. The central themes of Chapter 1 are scarcity, choice, opportunity cost, and the self-organizing role of markets. The chapter also examines the gains from specialization and trade, the role of money, the effects of globalization, and ends with a discussion of the various types of economic systems. Chapter 2 examines how economists build their models and test their theories. It also addresses central methodological issues, the most important being the idea that the progress of economics (like all scientific disciplines) depends on relating our theories to what we observe in the world around us. Finally, the chapter has an extensive section on graphing. *** Chapter 1 opens with a brief tour of some key economic issues in Canada and other countries—from rising protectionism and the dangers of climate change to accelerating technological change and growing income inequality. The purpose is to whet the reader’s appetite for the kinds of issues economists are thinking about today. This offers a natural segue to the discussion of scarcity, without which few of these issues would be very interesting. The chapter addresses the fundamental concepts of scarcity, choice, and opportunity cost, illustrating these ideas with a production possibilities boundary. (It is worth noting that these concepts are relevant to all economies, whether they are organized by central planning or by free markets.) We then examine the complexity of modern market economies, examining the decision makers, production, trade, money, and globalization. Finally, we examine different types of economic systems, including traditional, command, and freemarket systems. We emphasize that all actual economies are mixtures, containing elements of all three pure systems. Chapter 2 provides a longer introduction to the methodological issues of economics than is usually included in introductory texts. We do this because most students believe that the scientific method is limited to the natural sciences. But to appreciate economics, they must understand that its theories are also open to empirical testing and that these theories continually change as a result of what the empirical evidence shows. We understand that some instructors feel their time is so limited that they cannot spend class time on Chapter 2. We believe that even if it is not covered in class, students’ attention should be called to the issues addressed in the chapter. Our experience is that students benefit from some discussion of the scientific method and from the insight that the social sciences are not all that different from the “hard” sciences, at least in their basic approaches.
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The chapter begins by making the distinction between positive and normative statements. We then work carefully through the various elements of economic theories, including definitions, assumptions, and predictions. Testing theories is as important as developing them, so we emphasize the interaction between theorizing and empirical observation. We then present various types of economic data, and this gets us into a detailed discussion of index numbers, time-series and crosssection data, and graphs. The final section of the chapter goes through graphing in detail.
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_______________________________________ Chapter 1: Economic Issues and Concepts _______________________________________ This chapter is in three main sections, after a short introductory mention of some key economic issues of the day. The first substantive section develops the concepts of scarcity, choice, and opportunity cost. To ensure the student really understands what opportunity cost is all about, we have a box that examines the opportunity cost of a university or college degree. This should be a familiar example to which students can easily relate. The production possibilities boundary is then introduced, and it is shown to embody the three key concepts of scarcity, choice and opportunity cost. Its nature as a frontier between attainable and unattainable is worth stressing, as is the fact that what is attainable is itself subject to change. Four key economic problems are then discussed, and each one is expressed in terms of the production possibilities boundary. These questions give the student an inkling of the types of questions addressed both in microeconomics and in macroeconomics. The chapter’s second section examines the complexity of modern economies, asking why the things we want to purchase are almost always available. What produces this remarkable coordination? We discuss the market as an instrument that brings order to the economy as a whole. Along the way, the student is introduced to Adam Smith’s “invisible hand”. The section also discusses who makes the choices in a market economy, and why incentives matter. We show the circular flow of income and expenditure as a way of showing the interaction between consumers and producers. We also examine the nature of maximizing decisions (both utility and profit), and the importance of decisions at the margin. Finally, on the production side, we examine the role of specialization, the division of labour, globalization, and the importance of money in facilitating trade. The chapter’s third and final section deals with comparative economic systems. Students will read in almost every chapter of this book about a market economy. Contrasting it with planned and traditional economies is a good way to gain some insight into the concept at the outset. We emphasize that actual economies are rarely, if ever, well represented by the extremes; instead, actual economies are mixed economies, with varying degrees of government ownership and planning. Students are introduced to Karl Marx’s argument for a centrally planned economy. While Marx had many things right, we argue that central planning has not been successful in proving itself as an efficient way of organizing an economy, allocating resources, or generating prosperity for a large fraction of the population.
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Answers to Study Exercises Fill-in-the-Blank Questions Question 1 a) land, labour, capital; factors b) opportunity cost c) production possibilities boundary d) scarcity (because points outside the boundary are unattainable); downward (or negative); the opportunity cost associated with any choice e) constant; increasing f) increases (meaning that more units of good B must be given up to get an extra unit of good A)
Question 2 a) self; self-interest b) incentives created by market prices c) firms; households; governments d) increase (maximize); increase (maximize) e) margin; (marginal) cost Question 3 a) division; specialization b) trade c) money d) globalization
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Review Questions Question 4 Any realistic production possibilities boundary displays scarcity, the need for choice, and opportunity cost. Scarcity: The production possibilities boundary (PPB) separates attainable combinations of goods from those that are unattainable. Thus scarcity is shown by the existence of some unattainable bundles of goods. Choice: Because of scarcity, societies must somehow choose how resources are to be allocated; thus a particular point on the PPB must be chosen. Opportunity Cost: The slope of the PPB is negative, revealing the opportunity cost that is unavoidable every time a choice is made. For the economy as a whole, the decision to produce more of one good must involve a decision to produce less of some other good.
Question 5 Consider any country’s production possibilities boundary, and suppose the two products are X and Y. A technological improvement in industry X shifts the PPB out (along the X axis), increasing the maximum amount of X that can be produced. Note that the maximum amount of Y that can be produced has not changed. But since the PPB has shifted out, there are many combinations of both goods that are now available that were not before, and some of these involve producing more of both goods. Thus, even though the technology for producing Y has not changed, the technological improvement in X does allow the country to choose to produce more of both products. Question 6 The central ideas illustrated by the two-good version of the production possibilities boundary (PPB) are scarcity, choice, and opportunity cost. Exactly the same ideas can be illustrated in a more realistic three-good version of the model, which is more complicated to draw, or by the much more realistic N-good version of the model (with N 4), which is impossible to draw. Thus the assumption of only two goods is merely a simplifying one: it allows us to easily grasp and illustrate some central points that would be more difficult to understand in the more general N-good case. Question 7 a) If all Canadian families had $80,000 of after-tax income (roughly the Canadian average), it would be difficult to say that real poverty existed in Canada. At this level of income, all families would easily have enough income to provide the essentials of food, shelter, and clothing, and could also have much beyond these essentials. However, there would still be many things that these families could not afford, such as expensive university education, expensive vacations, a cottage
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in the country, etc. Defining poverty with any precision is difficult, and we will say more about this in Chapter 18. b) Would scarcity exist in such a setting? Yes, certainly. By scarcity we mean simply an excess of wants over the resources available to satisfy those wants. And scarcity would exist for each of those families because most (if not all) of them would still desire to have more than they actually had. c) Scarcity is an excess of wants over the resources available to satisfy those wants. Poverty—at least in its “absolute form”—is concerned with a level of resources below some threshold of sufficiency. One can conceivably eliminate poverty, as in part (a), but that would not eliminate scarcity. Question 8 Microeconomics is the study of the allocation of resources within and across individual markets, and the determination of relative prices and quantities in those specific markets. Little or no attention is paid to the behaviour of the aggregate economy. Macroeconomics is the study of the determination of aggregates such as aggregate output, employment, the price level, the unemployment rate, and the exchange rate. When doing macroeconomics, little or no attention is paid to what is going on in the individual markets for specific products. Question 9 In the answers that follow, note that the statements are made ceteris paribus. In other words, the predicted result of a change in some specific price is made under the assumption that nothing else changes. a) As the price of ski-lift tickets rises, you are likely to substitute toward other leisure activities (whose price has not increased) and thus reduce your purchases of ski-lift tickets. b) As the hourly wage for your weekend job rises, the opportunity cost of not working rises. So you are more likely than before to decide not to go skiing, and to work instead. c) As the fine for speeding rises, the cost of being caught speeding clearly increases. The benefit of driving over the speed limit is presumably unchanged, however. So an increase in the value of speeding tickets is likely to cause you to reduce your speed (and to watch more carefully for hidden police cars!). d) The higher the weight placed on the assignment, the greater is the incentive for you to work hard on that assignment (and thus hopefully receive a higher grade on the assignment and on the course). This is one obvious reason why professors like to put significant weight on midterm exams – to get students to work hard early in the course rather than leaving all the work to the few days before the final exam! e) As tuition fees for one specific institution increase, you are likely to substitute toward other institutions whose fees have not increased, and thus reduce your desire to attend the first institution. .
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(For small changes in tuition fees, this effect may be very small because of the perceived large differences between some educational institutions.) Question 10 There are two reasons why the specialization of labour is more efficient than self-sufficiency. First, since individual abilities differ, specializing allows each person to focus their energies on what they do best, leaving everything else to be done by others. As a result, total output will rise. Second, as people specialize, they often “learn by doing” and become even better at their specific task. Thus specialization often leads to improvements in ability that would not otherwise occur. Question 11 The market for doctors’ services depends heavily on the specialization of labour. A person with back pain will not know what is wrong. They go to a general practitioner (GP) who is somewhat familiar with a broad range of symptoms and illnesses. The GP may rule out the simplest possible causes for the pain, and in the process determine that the patient requires the services of a specialist who diagnoses and treats the patient’s back. The patient is referred to this specialist who may diagnose a ruptured disk and perform the delicate surgery necessary to solve the problem. Given this reliance on specialization, the market depends on having relatively more GPs who see a large number of patients and act as “gatekeepers” for patients to the more specific specialists. Question 12 Traditional systems: Behaviour is based primarily on tradition, custom, and habit. Command systems: Decisions about production and consumption are determined by a central planning authority. Free-market systems: Production and consumption decisions are made privately, by decentralized producers and consumers. Mixed systems: These economic systems contain elements of tradition, command, and free markets. Question 13 This quote, if put to a group of students, would stimulate much interesting discussion, not only about views on how alternative economic systems work, but also about the words used to describe them. The term planned economy, for example, describes the conscious use of centralized decision making for key economic decisions, but the results of that process often look anything but planned, with shortages in some sectors, surpluses in others, and often a rather dispirited and unmotivated private sector. On the other hand, the unplanned decentralized market economy––though surely not perfect—creates a much more orderly looking set of outcomes.
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Problems Question 14 In general, the opportunity cost (measured in dollars) for any activity includes three things: • the direct (dollar) cost of the activity, plus • the dollar value of whatever you give up in order to do the activity, minus • whatever dollar “savings” the activity generates In this case, the direct cost of transportation, lift tickets and accommodation of $300 is definitely included. The income of $120 that you give up also counts. Finally, we must deal with the restaurant meals of $75. Surely you would have eaten some food even if you hadn’t gone skiing, so the full $75 is not included. But given the relatively high price of restaurant meals compared to buying your own groceries, you will probably include most of the $75. Thus the opportunity cost of the ski trip is $420 plus some (large) fraction of the $75. Question 15 a) The budget line is shown below. If all $240,000 is spent on ATVs, you could purchase 30 of them; if all the money is spent on snowmobiles, you could purchase 20 of them. The downward sloping line divides the attainable from the unattainable combinations of ATVs and snowmobiles.
b) The opportunity cost of one ATV is the number of snowmobiles that must be given up to purchase an additional ATV. Since each ATV costs $8000 and each snowmobile costs $12000, the opportunity cost of one ATV is 2/3 of a snowmobile. c) The opportunity cost of one snowmobile is the number of ATVs that must be given up to purchase an additional snowmobile. It is equal to 1.5 ATVs. Note that the opportunity cost of an ATV (in terms of forgone snowmobiles) is the inverse of the opportunity cost of a snowmobile (in terms of forgone ATVs).
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d) In this case, the prices of ATVs and snowmobiles are independent of how many are purchased. This fact is reflected by the budget line being linear (of constant slope). So both of the opportunity costs are independent of how many are purchased. Question 16 In each scenario, one could choose to plot the production possibilities boundary, where the two numbers provided are the two intercepts along the two axes. The slope of the boundary would show the opportunity cost of each door (or each window). Alternatively, one can compare the two maximum values, as provided in the question. a) The factory could produce either 1000 windows or 250 doors (or many intermediate combinations). In order to produce one extra door, it must give up 4 (=1000/250) windows. In other words, the opportunity cost of one extra door is 4 windows. b) The opportunity cost of one extra door is 1 window (=500/500). c) The opportunity cost of one extra door is 3 windows (=1200/400). d) The opportunity cost of one extra door is 1.35 windows (=942/697). e) The opportunity cost of one extra door is 1.33 windows (=600/450). Question 17 This question is good for forcing students to think through the computation of opportunity cost and also in showing how the allocation of labour in particular ways can maximize total output. a) You can catch 6 fish or collect 3 bundles of firewood in one day’s work. Thus, your opportunity cost of one additional bundle of firewood is 2 fish. For your friend, the opportunity cost of one additional bundle of firewood is 4 fish. b) To allocate tasks in the output-maximizing way, each person should do the task for which they have the lower opportunity cost. You have the lower opportunity cost of collecting firewood. Your friend has the lower opportunity cost of catching fish (0.25 of a bundle for your friend as compared to 0.5 of a bundle for you). So for the two of you to collectively maximize output you should specialize in collecting firewood and your friend should specialize in catching fish. c) What is the total amount of output after two days, if you allocate labour as in part (b)? In two days, you would collect 6 bundles of firewood and your friend would catch 16 fish. The reverse pattern of specialization would yield only 4 bundles of firewood and 12 fish, which is clearly inferior.
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Question 18 a) At point A, 2.5 tonnes of clothing and 3 tonnes of food are being produced per year. At point B, annual production is 2.5 tonnes of clothing and 7 tonnes of food. At point C, annual production is 6.5 tonnes of clothing and 3 tonnes of food. b) At point A the economy is either using its resources inefficiently or it is not using all of its available resources. Point B and C represent full and efficient use of available resources because they are on the PPB. c) At point B, the opportunity cost of producing one more tonne of food (and increase from 7 to 8) is the 2.5 tonnes of clothing that must be given up. The opportunity cost of producing one more tonne of clothing (from 2.5 to 3.5) appears, from the graph, to be approximately 0.75 tonnes of food that must be given up. d) Point D is unattainable given the economy’s current technology and resources. Point D can become attainable with a sufficient improvement in technology or increase in available resources.
Question 19 a) As the table shows, there are only 250 workers in Choiceland, and to construct the production possibilities boundary (PPB) we must imagine all the combinations of workers in each sector. Using the two middle columns from the table, we can plot the output levels on a graph to get the following PPB:
b) If the economy is already producing 45 units of X and 900 units of Y, then 15 extra units of X can only be produced by reducing the production of Y by 300 units. The opportunity cost of 15 units of X is therefore 300 units of Y (or 300/15 = 20 units of Y per unit of X). If the economy is already producing 60 units of X (and 600 units of Y), the opportunity cost of producing an additional 15 units of X is the full 600 units of Y that must be given up. This implies an opportunity cost of 600/15 = 40 units of Y per extra unit of X. Thus, we see that the opportunity cost of X rises when more of X is already being produced. .
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c) If the economy is producing 40 units of X and 600 units of Y, then either some resources are not being used or they are being used inefficiently; the economy is operating inside the production possibilities boundary. It would thus be possible to improve the use of resources and increase output of X by 20 units without reducing the output of Y at all. In this sense, the extra output of X has no opportunity cost in terms of forgone units of Y. d) If any given amount of labour can now produce 10 percent more of good Y, then the PPB shifts up in a particular way. Specifically, the Y values increase by 10 percent for any given X value, as shown below.
Question 20 a) It doesn’t matter how the two axes are labelled in this case; just label them X and Y. The long civil war destroys much of the country’s infrastructure and likely reduces the country’s ability to produce all products. So the PPB shifts inwards, as shown below in part (a) of the figure. b) The axes are now labelled Food and Clothing. The new technology doubles the maximum amount of food that can be produced, and so shifts the PPB outward in the manner shown in part (b) of the figure. Note that the vertical intercept (maximum amount of clothing) does not change. c) The axes are again labelled Food and Clothing, as in part (c). In this situation, the earthquake destroys many clothing factories and so shifts the PPB inward, reducing the maximum possible amount of clothing (but leaving unaffected the maximum possible amount of food). d) The axes are labelled X and Y, as shown in part (d) of the figure. The immigration increases the labour force and increases the country’s ability to produce all products. The PPB shifts outward, increasing the maximum possible amounts of both X and Y. Since the new level of immigration is occurring each year, every year will see such an outward shift in the PPB.
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*****
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______________________________________________ Chapter 2: Economic Theories, Data, and Graphs ______________________________________________ This chapter provides an introduction to the methods economists use in their research. We integrate a detailed discussion of graphing into our discussion of how economists present economic data and how they test economic theories. In our experience, students typically do not learn enough about the connection between theory and evidence, and how both are central to understanding economic phenomena. We therefore recommend that considerable emphasis be placed on Figure 2-1, illustrating the process of going from model building to generating hypotheses to confronting data and testing hypotheses, and then returning to model building (or rebuilding). There is no real beginning or end to this process, so it is difficult to call economics an entirely “theory driven” or “data driven” discipline. Without the theory and models, we don’t know what to look for in the data; but without experiencing the world around us, we can’t build sensible models of human behaviour and interaction through markets. The scientific approach in economics, as in the “hard” sciences, involves a close relationship between theory and evidence. *** The chapter is divided into four major sections. In the first section, we make the important distinction between positive and normative statements and advice. Students must understand this distinction, and that the progress of any scientific discipline relies on researchers’ ability to separate what evidence suggests is true from what they would like to be true. We conclude this section by explaining why economists are often seen to disagree even though there is a great deal of agreement among them on many specific issues. This leads to a box on where economists typically get jobs and the kind of work they often do. The second section explains the elements of economic theories and how they are tested. We emphasise how a theory’s or model’s definitions and assumptions lead, through a process of logical deduction, to a set of conditional predictions. We then examine the testing of theories. It is here that we focus on the interaction of theory and empirical observation (Figure 2-1). We emphasize the importance of the distinction between correlation and causation, with a simple example. The chapter’s third section deals with economic data. We begin by explaining the construction of index numbers, and we use them to compare the volatility of two sample time series. Index numbers are so pervasive in discussions of economic magnitudes that students must know what these are and how they are constructed. We then make the distinction between crosssectional and time-series data, and at this point students are introduced to two types of graph.
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This brings us to the chapter’s final section, on graphing. We show how a relation can be expressed in words, in a table, in an equation, or on a graph. We then go into considerable detail on linear functions, slope, non-linear functions, and functions with minima and maxima. In this discussion, the student is introduced to the concept of the margin, described as the change in Y in response to a one-unit change in X. In all cases, the graphs apply to real-world situations rather than abstract variables. Pollution abatement, hockey-stick production, firm profits, and fuel consumption are our main examples.
Answers to Study Exercises Fill-in-the-Blank Questions
Question 1 a) models (or theories) b) endogenous; exogenous c) (conditional) prediction; empirical d) (positively) correlated; causal e) self-interest; utility; profits Question 2 a) index; relative b) absolute value of the price; absolute value of the price c) cross-section d) scatter e) time-series
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Question 3 a) Y/X b) 500; positively; 4 c) 12; negatively; -0.2 d) tangent e) zero; zero Review Questions Question 4 a) normative (“The government should impose…” is inherently a value judgement.) b) positive (In principle, we could determine the impact that foreign aid actually has.) c) positive (In principle, we could determine the extent to which fee increases affect access.) d) normative (What is or is not unfair is clearly based on a value judgement.) e) normative (Use of the expression “too much” is a value judgement.) Question 5 a) In the Canadian wheat sector, the amount of rainfall on the Canadian prairies is an exogenous variable; the amount of wheat produced is an endogenous variable. b) To the Canadian market for coffee, the world price of coffee is exogenous; the price of a cup of coffee at Tim Horton’s is endogenous. c) To any individual student, the widespread unavailability of student loans is exogenous; their own attendance at university or college is endogenous. d) To any individual driver, the tax on gasoline is exogenous; his or her own decision regarding which vehicle to purchase is endogenous. Question 6 The observed correlation cannot lead to a certain inference about causality. It is consistent with the theory that the increase in demand for homes leads to an increase in the price of lumber (which is generally a pretty sensible theory!), but it is also consistent with a different theory – one in which some unobserved factor leads to both the increase in demand for homes and separately to the increase in the price of lumber. Correlation does not imply causality!
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Problems Question 7 a) Using 2009 as the base year means that we choose $85 as the base price. We thus divide the actual prices in all years by $85 and then multiply by 100. In this way, we will determine, in percentage terms, how prices in other years differ from prices in 2009. The index values are as follows: Year
Price ($)
Physics textbook price index
2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019
85 87 94 104 110 112 120 125 127 127 130
(85/85) 100 = 100 (87/85) 100 = 102.4 (94/85) 100 = 110.6 (104/85) 100 = 122.4 (110/85) 100 = 129.4 (112/85) 100 = 131.8 (120/85) 100 = 141.2 (125/85) 100 = 147.1 (127/85) 100 = 149.4 (127/85) 100 = 149.4 (130/85) × 100 = 152.9
b) The price index in 2014 is 131.8, meaning that the price of the physics textbook is 31.8 percent higher in 2014 than in the base year, 2009. c) From 2016 to 2019, the price index increases from 147.1 to 152.9⎯but this is not an increase of 5.8 percent. The percentage increase in the price index from 2016 to 2019 is equal to [(152.9147.1)/147.1]×100 = 3.94 percent. d) These are time-series data because the data are for the same product at the same place but at different points in time. Question 8 a) Using Calgary as the “base university” means that we choose $6.25 as the base price. Thus we divide all actual prices by $6.25 and then multiply by 100. In this way, we will determine, in percentage terms, how prices at other universities differ from Calgary prices. The index values are as follows:
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University
Price per pizza
Index of pizza prices
Dalhousie Laval McGill Queen’s Waterloo Manitoba Saskatchewan Calgary UBC Victoria
$6.50 5.95 6.00 8.00 7.50 5.50 5.75 6.25 7.25 7.00
(6.50/6.25)100 = 104 (5.95/6.25)100 = 95.2 (6.00/6.25)100 = 96 (8.00/6.25)100 = 128 (7.50/6.25)100 = 120 (5.50/6.25)100 = 88 (5.75/6.25)100 = 92 (6.25/6.25)100 = 100 (7.25/6.25)100 = 116 (7.00/6.25)100 = 112
b) The university with the most expensive pizza is Queen’s, at $8.00 per pizza. The index value for Queen’s is 128, indicating that pizza there is 28 percent more expensive than at Calgary. c) The university with the least expensive pizza is Manitoba, at $5.50 per pizza. The index value for Manitoba is 88, indicating that the price of pizza there is only 88 percent of the price at Calgary. It is therefore 12 percent cheaper than at Calgary. d) These are cross-sectional data. The variable is the price of pizza, collected at different places at a given point in time (March 1, 2016). If the data had been the prices of pizza at a single university at various points in time, they would be time-series data.
Question 9 a) Using 2012 as the base year for an index number requires that we divide the value of exports (and imports) in each year by the value in 2012, and then multiply the result by 100. This is done in the table below.
Year 2012 2013 2014 2015 2016
Exports 11225 11687 11821 12219 12507
Export Index (11225/11225)(100) = 100 (11687/11225)(100) = 104.1 (11821/11225)(100) = 105.3 (12219/11225)(100) = 108.9 (12507/11225)(100) = 111.4
Imports 3706 3550 3262 3447 3659
Import Index (3706/3706)(100) = 100 (3550/3706)(100) = 95.8 (3262/3706)(100) = 88.0 (3447/3706)(100) = 93.0 (3659/3706)(100) = 98.7
b) It appears that imports were more volatile over this period than exports. Imports fell by about 12 percent in the first two years, and then increased by about 10 percent in the next two. In contrast, exports increased fairly steadily, by a total of over 11 percent over the five years.
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c) From 2014 to 2016, the export index increases from 105.3 to 111.4. The percentage change is equal to (111.4 – 105.3)/105.3 which is 5.8 percent. For imports the percentage change is (98.7 88.0)/88.0 which is 12.2 percent. Question 10 This is a good question to make sure students understand the importance of using weighted averages rather than simple averages in some situations. a) The simple average of the three regional unemployment rates is equal to (5.5 + 7.2 + 12.5)/3 = 8.4. Is 8.4% the “right” unemployment rate for the country as a whole? The answer is no because this simple, unweighted (or, more correctly, equally weighted) average does not account for the fact that the Centre is much larger in terms of the labour force than either the West or East, and thus should be given more weight than the other two regions. b) To solve this problem, we construct a weighted average unemployment rate. We do so by constructing a weight for each region equal to that region’s share in the total labour force. From the data provided, the country’s total labour force is 17.2 million (5.3 + 8.4 + 3.5). The three weights are therefore: West: weight = 5.3/17.2 = 0.308 Centre: weight = 8.4/17.2 = 0.488 East:
weight = 3.5/17.2 = 0.203
These weights should sum exactly to 1.0, but due to rounding they do not quite do so. Using these weights, we now construct the average unemployment rate as the weighted sum of the three regional unemployment rates. Canadian weighted unemployment rate = (.308 5.5) + (.488 7.2) + (.203 12.5) = 7.75 This is a better measure of the Canadian unemployment rate because it correctly weights each region’s influence in the national total. Keep in mind, however, that for many situations the relevant unemployment rate for an individual or a firm may be the more local one rather than the national average. Question 11 a) These data are best illustrated with a time-series graph, with the month shown on the horizontal axis and the exchange rate shown on the vertical axis.
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b) These cross-sectional data are best illustrated with a bar chart.
c) These cross-sectional data are best illustrated in a scatter diagram; the “line of best fit” is clearly upward sloping, indicating a positive relationship between average investment rates and average growth rates.
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20 Instructor’s Manual for Ragan, Economics, Sixteenth Canadian Edition
Question 12 a) Along Line A, Y falls as X rises; thus the slope of Line A is negative. For Line B, the value of Y rises as X rises; thus the slope of Line B is positive. b) Along Line A, the change in Y is –4 when the change in X is 6. Thus the slope of Line A is ΔY/ΔX = -4/6 = -2/3. The equation for Line A is: Y = 4 – (2/3)X c) Along Line B, the change in Y is 7 when the change in X is 6. Thus the slope of Line B is ΔY/ΔX = 7/6. The equation for Line B is: Y = 0 + (7/6)X Question 13 Given the tax-revenue function T = 10 + .25Y, the plotted curve will have a vertical intercept of 10 and a slope of 0.25. The interpretation is that when Y is zero, tax revenue will be $10 billion. And for every increase in Y of $100 billion, tax revenue will rise by $25 billion. The diagram is as shown below:
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