Solution Manual for Labor Economics, 8th Edition George Borjas

Solution Manual for Labor Economics, 8th Edition By George J. Borjas

CHAPTER 2 2-1. The table below reports the unemployment rate, labor force participation rate, and (working-age) population for the United States in January 2008, 2011, and 2016. Using the data, answer the following questions. a. What was the size of the labor force at the start of each year? b. How many people were officially unemployed at the start of each year? c. What about these numbers may cause some concern even though the unemployment rate to start 2016 was a notch below the unemployment rate in 2008 as the economy was entering the Great Recession?

2008 5.0% 66.2% 234m

Unemployment Rate Labor Force Participation Rate Working-age Population

2011 9.1% 64.2% 238m

2016 4.9% 62.7% 251m

Parts (a) and (b) require some mathematical manipulations. As the labor force participation rate equals the LF / P, the size of the labor force (LF) each year is simply the working age population (P) times the labor force participation rate. Once the size of the labor force (LF) is know, the number of unemployed individuals is calculated by multiplying the labor force by the unemployment rate. For 2008, for example, LF = 234m × 0.662 = 154.9 million, and therefore U = 154.9m × 0.05 = 7.745 million. The numbers for the other years are found similarly. The answers are contained in the following table: 2008 154.9m 7.745m

Labor Force (LF) Unemployed Population (U)

2011 152.8m 13.9m

2016 157.4m 7.713m

As for part (c), these numbers are concerning despite the unemployment rate returning to something less than 5%. The concern is that the labor force participation rate has fallen drastically. According to the above numbers, the labor force consisted of 157.4 million individuals in 2016. Of these, only 4.9% were unemployed. Put differently, 95.9% × 157.4 = 150.9 million individuals were employed. Had the labor force participation rate remained at 66.2% in 2016, the labor force would have consisted of 251m × 0.662 = 166.2 million individuals. Of these, only 150.9 million were employed. Taking into account these individuals who have left the labor force (i.e., the hidden unemployed), the unemployment rate in 2016 could have been as high as (166.2 – 150.9) / 166.2 = 9.2%.

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2-2. 2-2. Charlie and Larry both face the same budget line for consumption and leisure. At every possible consumption-leisure bundle on the budget line, Charlie always requires marginally more leisure than does Larry in order to be equally happy when asked to forego a dollar of consumption. Using a standard budget line, graph several indifference curves and the optimal consumption-leisure bundle for both people. Which person optimally chooses more consumption? Which feature of indifference curves guarantees this result?

Because Charlie requires receiving more leisure than Larry when giving up consumption, Charlie’s indifference curves are flatter relative to Larry’s. This feature – shallower or flatter indifference curves – results in that person (Charlie) optimally choosing more of the Y-axis good.

Similarly, Larry’s indifference curves are steeper relative to Charlie’s, because Larry does not need to receive as much leisure when giving up consumption. This feature – steeper indifference curves – results in that person (Larry) optimally choosing more of the X-axis good. These ideas are all incorporated in the graph below where the solid lines represent an assortment of indifference curves for Charlie while the dashed lines represent an assortment of indifference curves for Larry.

Consumption

Charlie’s ICs

Larry’s ICs

C*Charlie

C*Larry

L*Charlie

L*Larry

Leisure

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2-3. Tom earns $15 per hour for up to 40 hours of work each week and $30 per hour for every hour in excess of 40. Tom also faces a 20 percent tax rate, pays $4 per hour in child care expenses for each hour he works, and receives $80 in child support payments each week. There are 110 (non-sleeping) hours in the week. Graph Tom’s weekly budget line.

• • •

If Tom does not work, he leisures for 110 hours and consumes $80.

For all hours Tom works up to his first 40, his after-tax and after-child care wage equals (80 percent of $15) – $4 = $8 per hour. Thus, if he works for 40 hours, he will be able to leisure for 70 hours and consume $80 + $8(40) = $400.

For all hours Tom works over 40, his after-tax and after-child care wage equals (80 percent of $30) – $4 = $20. Thus, if he works for 110 hours (70 hours at the overtime wage), he will not leisure at all, but he will consume $80 + $8(40) + $20(70) = $1,800.

Tom’s weekly budget line is pictured below.

Dollars of Consumption $1,400

$400 $80 70

110

Hours of Leisure

2-4. Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 110 hours. Her utility function is U(C, L) = C  L. This functional form implies that Cindy’s marginal rate of substitution is C / L. Cindy receives $660 each week from her great-grandmother–regardless of how much Cindy works. What is Cindy’s reservation wage?

The reservation wage is the MRS when not working at all. Thus, wRES = MRS at maximum leisure equals C/L = $660/110 = $6.00.

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2-5. Currently a firm pays 10% of each employee’s salary into a retirement account, regardless of whether the employee also contributes to the account. The firm is considering changing this system to a 10% match meaning that the firm will match the employee’s contribution into the account up to 10% of each employee’s salary. Some people at the firm think this change will lead employees to save more and therefore be more able to afford to retire at a younger age, while others believe this change will lead employees to have less retirement savings and therefore be less able to afford to retire. Explain why either point of view could be correct.

Either point of view may be correct. The first assumes that the new matching system will encourage workers to save at least 10% of their salary into the retirement account, because it is matched. In essence, each dollar of personal savings receives an automatic and immediate 100% return. Alternatively, if the workers feel that they simply cannot save for retirement, then the change to a matching system may result in fewer dollars saved for retirement as the workers save very little (say 2%) and the firm then only matches the 2%. With this example, a worker’s retirement account is receiving 4% of his or her salary each year compared to the 10% it received before the change. Clearly, the matching system provides fewer funds for retirement if the workers are not “savers” during their worklife.

2-6. Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = (C – 100)  (L – 40).

This utility function implies that Shelly’s marginal utility of leisure is C – 100 and her marginal utility of consumption is L – 40. There are 110 hours in the week available to split between work and leisure. Shelly earns $10 per hour after taxes. She also receives $320 worth of assistance benefits each week regardless of how much she works. (a) Graph Shelly’s budget line.

If Shelly does not work, she leisures for 110 hours and consumes $320. If she does not leisure at all, she consumes $320 + $10(110) = $1,420. Shelly’s weekly budget line, therefore, is: Dollars of Consumption $1,420

$320 110 Hours of Leisure

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(b) What is Shelly’s marginal rate of substitution when L = 100 and she is on her budget line?

If Shelly leisures for 100 hours, she works for 10 hours and consumes $320 + $10(10) = $420.

Thus, her MRS when doing this is:

MRS =

MU L C − 100 420 − 100 320 = = = = $5.33 .

MUc L − 40 100 − 40 60

(c) What is Shelly’s reservation wage?

The reservation wage is defined as the MRS when working no hours. When working no hours, Shelly leisures for 110 hours and consumes $320. Thus,

wRES =

MU L C − 100 320 − 100 220 = = = = $3.14 .

MUc L − 40 110 − 40 70

(d) Find Shelly’s optimal amount of consumption and leisure.

Her optimal mix of consumption and leisure is found by setting her MRS equal to her wage and solving for hours of leisure given the budget line: C = 320 + 10(110 – L). w = MRS 10 = 10 =

C − 100 L − 40

320 + 10(110 − L) − 100 L − 40

10 L − 400 = 1320 − 10 L L = 86.

Thus, Shelly will choose to leisure 86 hours, work 24 hours, and consume $320 + $10(24) = $560 each week.

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2-7. Explain why receiving a cash grant from the government can entice some workers to stop working (and entices no one to start working) while the earned income tax credit can entice some people who otherwise would not work to start working (and entices no one to stop working).

A lump sum transfer is associated with an income effect but not a substitution effect, because it doesn’t affect the wage rate. Thus, if leisure is a normal good, a lump sum transfer will likely cause workers to work fewer hours (and certainly not cause them to work more hours) while possibly enticing some workers to exit the labor force all together. On the other hand, the Earned Income Tax Credit raises the effective wage of low-income workers by 40 percent (at least for the poorest workers). Thus, someone who had not been working faces a wage that is 40 percent higher than it otherwise was. This increase may be enough to encourage the person to start working. For example, if a worker’s reservation wage is $10.00 per hour but the only job she can find pays $8.00 per hour, she will not work. Under the earned income tax credit, however, the worker views this same job as paying $11.20 per hour, which exceeds her reservation wage.

Furthermore, the EITC cannot encourage a worker to exit the labor force, as the benefits of the EITC are received only by workers.

2-8. In 1999, 4,860 TANF recipients were asked how many hours they worked in the previous week. In 2000, 4,392 of these recipients were again subject to the same TANF rules and were again asked their hours of work during the previous week. The remaining 468 individuals were randomly assigned to a “Negative Income Tax” (NIT) experiment which gave out financial incentives for welfare recipients to work and were subject to its rules.

Like the other group, they were asked about their hours of work during the previous week.

The data from the experiment are contained in the table below.

Number Of Recipients TANF NIT Total

4,392 468 4,860

Number of Recipients Who Worked At Some Time in the Survey Week

Total Hours Of Work By All Recipients in the Survey Week

1999

2000

1999

2000

1,217 131 1,348

1,568 213 1,781

15,578 1,638 17,216

20,698 2,535 23,233

(a) What effect did the NIT experiment have on the employment rate of public assistance recipients? Develop a standard difference-in-differences table to support your answer.

Employment Rate TANF NIT

1999 27.7% 28.0%

2000 35.7% 45.5%

Diff 8.0% 17.5%

Diff-in-Diff 9.5%

The NIT increased the probability of employment by 9.5 percentage points. Note that the percent numbers are found by dividing the “Number of Recipient” columns (2nd and 3rd columns of the original table) by the Number of Recipients column (1st column of the original original).

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(b) What effect did the NIT experiment have on the weekly hours worked of public assistance recipients who worked positive hours during the survey week? Develop a standard difference-in-differences table to support your answer.

Weekly Hours Worked Per Working Person TANF NIT

1999 12.8 12.5

2000 13.2 11.9

Diff 0.4 -0.6

Diff-in-Diff -1.0

The NIT decreased weekly hours worked, of those working, by 1 hour. Note that the average weekly hours of work per persons is found by dividing the “Total Hours of Work” columns (4th and 5th columns of the original table) by the Number of Recipients column (1st column of the original table).

2-9. Consider two workers with identical preferences, Phil and Bill. Both workers have the same life cycle wage path in that they face the same wage at every age, and they know what their future wages will be. Leisure and consumption are both normal goods. (a) Compare the life cycle path of hours of work between the two workers if Bill receives a one-time, unexpected inheritance at the age of 35.

Because the workers have the same life cycle wage path and the same preferences, they will have the same life cycle path of hours of work up to the unexpected event. An inheritance provides an income effect for Bill with no substitution effect, and thus, he will work fewer hours (or at least not more hours) than Phil from the age of 35 forward. See the following graph.

Hours Worked

Life Cycle Path of Hours Worked After Age 35: Before Age 35: Phil

Bill

Bill and Phil

35

Age

(b) Compare the life cycle path of hours of work between the two workers if Bill had always known he would receive (and, in fact, does receive) a one-time inheritance at the age of 35.

In this case, because the inheritance is fully anticipated, and because it offers the same income effect with no substitution effect, Bill will work fewer hours (or at least not more hours) than Phil over their entire work lives. See the following graph.

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Hours Worked

Life Cycle Path of Hours Worked

Phil

Bill

35

Age

2-10. Under current law, most Social Security recipients do not pay federal or state income taxes on their Social Security benefits. Suppose the government proposes to tax these benefits at the same rate as other types of income. What is the impact of the proposed tax on the optimal retirement age?

Suppose social security benefits are the only pension benefits available to a retiree. The tax, therefore, can be interpreted as a cut in pension benefits. The cut in pension benefits shifts the budget line from FH to FE in the figure below, shifting the worker from point P to point R. (Note that FE and FH are both downward sloping, indicating that total retirement consumption is greater the later in life one retires meaning that one has fewer years of retirement.) This shift from FH to FE generates both income and substitution effects. Both of these effects, however, work in the same direction. First, the tax reduces the retiree’s wealth, reducing her demand for leisure, and leading her to retire later (the income effect). At the same time, the tax reduces the “wage” that retirees receive when retired, effectively increasing (in relative terms) the wage they earn while working and generating a substitution effect that leads to more work hours, thus further delaying retirement. Under normal conditions, therefore, a tax on pension benefits will increase the optimal retirement age (i.e., workers will delay retirement and have fewer years of retirement).

Consumption During Retirement F

U1

P R H U0

E 20

Years of Retirement

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2-11. A worker plans to retire at the age of 65, at which time he will start collecting his retirement benefits. Then there is a sudden change in the forecast of inflation when the worker is 63 years old. In particular, inflation is now predicted to be higher than it had been expected so that the average price level of market goods and wages is now expected to be higher. What effect does this announcement have on the person’s preferred retirement age: (a) if retirement benefits are fully adjusted for inflation?

There will be no effect on the person’s retirement decision if retirement benefits are fully adjusted for inflation as nothing changes in the person’s calculations in real terms: the relative magnitudes of prices, wages and retirement benefits are the same with or without inflation. The person faces the same choice set, so his decision does not change. (b) if retirement benefits are not fully adjusted for inflation?

If retirement benefits are not adjusted for inflation, the purchasing power of retirement benefits falls. If the person does not retire, he can enjoy the same consumption as he would without inflation as wages are assumed to fully adjust for inflation. If he retires at 65, his benefits are worth less in real terms (they can buy him less consumption) with inflation than without, so he cannot afford the same consumption path as before. Hence, his choice set over the years of retirement and consumption lies below the original (pre-inflation) choice set except at one point—where he does not retire at all. Thus, as long as leisure (i.e., years of retirement) and consumption are normal goods, the income and substitution effects both lead to the individual retiring later in life.

2-12. Presently, there is a minimum and maximum social security benefit paid to retirees.

Between these two bounds, a retiree’s benefit level depends on how much she contributed to the system over her work life. Suppose Social Security was changed so that everyone aged 65 or older was paid $12,000 per year regardless of how much she earned over her working life or whether she continued to work after the age of 65. How would this likely affect the number of hours worked by retirees?

Labor force participation is likely greatest for those retirees whose social security income is low (below $12,000 per year). Thus, the change in benefits offers these retirees a pure (positive) income effect. These retirees should reduce their hours worked if not leave the labor force all together after the age of 65.

In contrast, the policy change offers all retirees who would have earned more than $12,000 per month a pure (negative) income effect. These retirees will become more likely to work, or, if already working, more likely to work more hours after the age of 65.

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2-13. Over the last 100 years, real household income and standards of living have increased substantially in the United States. At the same time, the total fertility rate, the average number of children born to a woman during her lifetime, has fallen in the United States from about three children per woman in the early twentieth century to about two children per woman in the early twenty-first century. Does this suggest that children are inferior goods?

The conventional wisdom (and empirical evidence) suggests that children are normal goods.

Economically, children are a lot more expensive today than they were 100 years ago (consider education, housing, clothing, entertainment expenses, etc.). Children also produce less for the household in the 21st century than they did 100 years ago.

There is also a biology/evolution argument is that infant mortality rates have fallen dramatically over the last 100 years, so a woman needs to have fewer children to be more confident that some of her children will reach adulthood. This argues against children being an inferior good as the “good” in question can be thought of as the number of offspring who live long enough to procreate.

2-14. Consider a person who can work up to 80 hours each week at a pre-tax wage of $20 per hour but faces a constant 20% payroll tax. Under these conditions, the worker maximizes her utility by choosing to work 50 hours each week. The government proposes a negative income tax whereby everyone is given $300 each week and anyone can supplement her income further by working. To pay for the negative income tax, the payroll tax rate will be increased to 50%. (a) On a single graph, draw the worker’s original budget line and her budget line under the negative income tax.

Under the original scenario, let I be total weekly income, L be hours of leisure, and H be hours worked. The worker’s after-tax wage rate is 80% of $20 which equals $16 per hour. Thus, when the worker works all 80 hours in the week, she earns $16 x 80 = $1,280 and her budget line is described by I = 1280 – 16L. Notice that when L = 80, the worker earns $0. And when L = 30, the worker earns $16 × 50 = $800.

Under the negative income tax, the worker is given $300 each week, but now her after-tax wage rate is 50% of $20 which equals $10 per hour. In this case, when the worker works all 80 hours in the week, she earns $10 × 80 + $300 = $1,100 and her budget line is properly described by I = 1100 – 10L. Notice that when L = 80, the worker receives $300. And when L = 30, the worker receives $300 + $10 x 50 = $800.

The two budget lines for both scenarios are graphed on the next page.

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Weekly Budget Lines Weekly $1,280 Income $1,100

Original Scenario

$800

Negative Income Tax $300

30

80

Hours of Leisure

(b) Show that the worker will choose to work fewer hours if the negative income tax is adopted.

To answer this question, one needs to find where the budget lines intersect. Setting the budget lines equal and solving for L reveals that the budget lines intersect at L = 30. Thus, the indifference curve that is tangent to the original budget line at L = 30 must not be tangent to the budget line under the negative income tax (because L = 30 was the optimal choice without the negative income tax). In particular, the worker’s original indifference curve must be below the new budget line to the right of L = 30. Therefore, when faced with the negative income tax, the worker will move in that direction, which requires her to increase L (hours of leisure) and concurrently decrease H (hours of work). (c) Will the worker’s utility be greater under the negative income tax?

In this particular case, the worker’s utility will increase under the negative income tax because she could have continued to leisure 30 hours each week and receive $800 (which was her outcome before the negative income tax) but instead the worker decides to leisure more (and consume less). This change in behavior must increase her utility.

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2-15. The absolute value of the slope of the consumption-leisure budget line is the after-tax wage, w. Suppose some workers earn w for up to 40 hours of work each week, and then earn 2w for any hours worked thereafter (called overtime). Other workers earn w for up to 40 hours of work each week, and then only earn 0.5w thereafter as working more than 40 hours requires getting a second job which pays an hourly wage less than their primary job.

Both types of workers experience a “kink” in their consumption-leisure budget line. (a) Graph in general terms the budget line for each type of worker.

Weekly Budget Lines Weekly Income The wage increases (to 2w) for hours of work in excess of 40.

The wage falls (to 0.5w) for hours of work in excess of 40.

Both face a wage of w for 40 hours

T - 40

T

Hours of Leisure

(b) Which type of worker is likely to work up to the point of the kink, and which type of worker is likely to choose a consumption-leisure bundle far away from the kink?

The worker who experiences a decrease in her wage after working 40 hours is more likely to work exactly 40 hours as the marginal benefit of working experiences a negative jump down at this point.

In contrast, the worker who experiences an overtime premium after working 40 hours is more likely to not work exactly 40 hours. Because of the overtime premium, once the worker hits 40 hours of work, the worker experiences a positive jump up in the marginal benefit of working. Put differently, this worker may opt to only work 20 or 30 hours, but if she finds herself having worked 40 hours because the T – 40th hour of leisure was not as valuable as w, then it is very likely that she will also find that the T – 41st hour of leisure is not as valuable as 2w, and therefore she works the 41st hour (and possibly quite more).

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CHAPTER 3 3-1. Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 1 machine to do the work of 3 workers. The firm wants to produce 100 units of output. Suppose the price of capital is $750 per machine per week. What combination of inputs will the firm use if the weekly salary of each worker is $300? What combination of inputs will the firm use if the weekly salary of each worker is $225? What is the elasticity of labor demand as the wage falls from $300 to $225?

Because labor and capital are perfect substitutes, the isoquant for producing 100 units of output (in bold in the figure below) is linear and the firm will use only labor or only capital, depending on which is relatively cheaper in producing 100 units of output.

The (absolute value of the) slope of the isoquant (MPE / MPK) is 1/3 because 1 machine does the work of 3 workers. When the wage is $300, the slope of the isocost is 300/750. The isocost curve, therefore, is steeper than the isoquant, and the firm only hires capital (at point A). To calculate this in a different way, one machine does the work of three workers. The one machine costs $750; the three workers cost $300 × 3 = $900. Clearly the firm should hire only machines.

When the weekly wage is $225, the isoquant is steeper than the isocost and the firm hires only labor (at point B). To calculate this in a different way, one machine does the work of three workers. The one machine costs $750; the three workers cost $225 × 3 = $675. Clearly the firm should hire only workers.

Capital Smallest isocost line that achieves 100 units of output when the wage is $225 per week: w / r = 225 / 750 < 1/3.

Output = 100 Units Isoquant A Smallest isocost line that achieves 100 units of output when the wage is $300 per week: w / r = 300 / 750 > 1/3.

Labor

B

The elasticity of labor demand is defined as the percentage change in labor divided by the percentage change in the wage. Because the demand for labor goes from 0 to a positive quantity when the wage drops to $225, the (absolute value of the) elasticity of labor demand is infinity.

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3-2. Figure 3-18 in the text shows the ratio of the federal minimum wage to the average hourly manufacturing wage. (a) Describe how this ratio has changed from the 1950s to the 1990s. What might have caused this apparent shift in fundamental economic behavior in the United States?

The ratio of the federal minimum wage to the average hourly manufacturing wage averaged about 0.5 from 1950 to 1968. That is, a manufacturing job paid about 2 times as much as a minimum wage job. Since 1968, however, the ratio has steadily fallen. In the last quarter of the 20th century, the ratio approached 0.3, meaning that a manufacturing job paid about 3 times as much as a minimum wage job.

Consider three (of the many possible) explanations for this behavior. First, although the nominal minimum wage has risen over time, the real minimum wage fell quit a bit from 1968 to 1990.

Second, the U.S. economy has lost a lot of manufacturing jobs recently, ostensibly due to globalization. Economic theory suggests that the jobs most likely to be lost are those with the least productive workers (relative to foreign workers), which likely correlates to the lowest paid manufacturing jobs. Thus, when the lowest paid manufacturing jobs are lost, the average manufacturing wage will increase, which in turn increases the ratio presented in Figure 3-18.

Third, one might point toward the return to skills. Most low-wage, minimum wage jobs require very little skill (and some of these jobs are becoming more and more automated). Manufacturing jobs, however, still require skill in terms of using high-tech equipment and machines. (b) This ratio fell steadily from 1968 to 1974 and again from 1980 to 1990, but the underlying dynamics of the minimum wage and the average manufacturing wage were different during the two time periods. Explain.

First, notice that over both of these periods that the federal minimum wage was unchanged.

The earlier period (1968-1974) was a time of stagflation, war, and an oil price shock. High levels of inflation led to higher nominal wages (for those who had jobs), thus lowering the ratio of the minimum wage to the average manufacturing wage. That is, the decreasing ratio was largely a product of an eroding real minimum wage during an inflationary period.

The later period (1980-1990) is generally characterized as a time of economic growth and prosperity. Thus, while inflation was largely in check, wages were increasing substantially as a result of productivity growth. This productivity growth (and in turn wage growth) resulted in a lower ratio. (c) What has been happening to the ratio of the federal minimum wage (nominal) to the average hourly manufacturing wage from 1990 to today?

More or less, it has been holding steady between 0.3 and 0.4, depending on the timing of legislative increases in the minimum wage.

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3-3. Firm would hire 20,000 workers if the wage rate is $12 but will hire 10,000 workers if the wage rate is $15. Firm B will hire 30,000 workers if the wage is $20 but will hire 33,000 workers if the wage is $15. The workers in which firm are more likely to organize and form a union?

The union will be more likely to attract the workers’ support when the elasticity of labor demand (in absolute value) is small. The elasticity of labor demand facing firm A is given by:

A =

%E (20,000 − 10,000) 20,000 = = −2 . %w (12 − 15) 12

The elasticity of labor demand facing firm B is given by:

B =

%E (33,000 − 30,000) 33,000 =  −0.45 %w (15 − 20) 15

Workers at Firm B, therefore, are more likely to organize as |-0.45| < |-2|.

3-4. Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4.

These prices then shift to w = 4 and r = 2. (a) In which direction will the substitution effect change the firm’s employment and capital stock?

Prior to the price shift, the absolute value of the slope of the isocost line (w/r) was 1.5. After the price shift, the slope is 2. In other words, labor has become relatively more expensive than capital. As a result, there will be a substitution away from labor and towards capital (the substitution effect). (b) In which direction will the scale effect change the firm’s employment and capital stock?

Because both prices fall, the marginal cost of production falls, and the firm will want to expand.

The scale effect, therefore, increases the demand for both labor and capital as both are normal inputs. (c) Can we say conclusively whether the firm will use more or less labor? More or less capital?

The firm will certainly use more capital as the substitution and scale effects reinforce each other in the direction of using more capital. The change in labor hired, however, will depend on whether the substitution or the scale effect dominates for labor.

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3-5. What happens to employment in a competitive firm that experiences a technology shock such that at every level of employment its output is 200 units/hour greater than before?

Because output increases by the same amount at every level of employment, the marginal product of labor does not change (and hence, the value of the marginal product of labor does not change).

Therefore, as the value of the marginal product of labor will equal the wage rate at the same level of employment as before, the level of employment will not change.

3-6. Consider each of the following, and explain why it is or is not a valid instrument for estimating labor supply elasticity and/or labor demand elasticity in the United States. (1) Variation in state income tax rates. (2) Variation in state corporate tax rates. (3) Changes in federal income tax rates over time.

A valid instrumental variable for estimating labor supply elasticity must be something that shifts labor demand but not labor supply. Similarly, a valid instrumental variable for estimating labor demand elasticity must be something that shifts labor supply but not labor demand. For each of the options above: (1) State income taxes affect labor supply (because income taxes affect the wage), and therefore variation in state income taxes would be a valid instrument for estimating the elasticity of labor demand but not for estimating labor supply.

(2) State corporate taxes affect labor demand (because corporate taxes affect profits and the value of marginal product of labor), and therefore variation in state corporate taxes would be a valid instrument for estimating the elasticity of labor supply but not for estimating labor demand.

(3) Changes in the federal income tax rate over time is not a valid instrument for estimating either elasticity. The goal is to estimate either elasticity for the United States. Therefore, one needs something that changes within the United States for different workers or firms.

One cannot use a nation-wide variable to do this. Moreover, using time as the variation is dangerous as it requires assuming everything else is constant over time, which likely is not the case.

3-7. Suppose a firm purchases labor in a competitive labor market and sells its product in a competitive product market. The firm’s elasticity of demand for labor is −0.4. Suppose the wage increases by 5 percent. What will happen to the amount of labor hired by the firm?

What will happen to the marginal productivity of the last worker hired by the firm?

Given the estimates of the elasticity of labor demand and the change in the wage, we have that

=

%E %E = −0.4 => = −0.4 => %E = −2% . %w 5%

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Thus, the firm hires 2 percent fewer workers when wages increase by 5%. Furthermore, because fewer workers are hired, under normal conditions the marginal productivity of the last worker hired will increase. (More formally, because the labor market is competitive, the marginal worker is paid the value of his marginal product. As the product market is competitive, we also know that the output price does not change so that the marginal productivity of the marginal worker increases by 5 percent as well.)

3-8. A firm’s technology requires it to combine 5 person-hours of labor with 3 machinehours to produce 1 unit of output. The firm has 15 machines in place when the wage rate rises from $10 per hour to $20 per hour. What is the firm’s short-run elasticity of labor demand?

Unless the firm shuts down (i.e., goes out of business in the short run), it will combine 25 persons with the 15 machines it has in place regardless of the wage rate. Therefore, employment will not change in response to the movement of the wage rate, and the short-run elasticity of labor demand is zero.

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3-9. In a particular industry, labor supply is ES = 10 + w and labor demand is ED = 40 − 4w, where E is the level of employment and w is the hourly wage. (a) What is the equilibrium wage and employment if the labor market is competitive? What is the unemployment rate?

In equilibrium, the quantity of labor supplied equals the quantity of labor demanded, so that ES = ED. This implies that 10 + w = 40 – 4w. The wage rate that equates supply and demand is $6.

When the wage is $6, 16 persons are employed. There is no unemployment because the number of persons looking for work equals the number of persons employers are willing to hire at the going wage rate of $6 per hour. (b) Suppose the government sets a minimum hourly wage of $8. How many workers would lose their jobs? How many additional workers would want a job at the minimum wage?

What is the unemployment rate?

If employers must pay an hourly wage of $8, employers would only want to hire ED = 40 – 4(8) = 8 workers, while ES = 10 + 8 = 18 persons would like to work. Thus, 8 workers lose their job following the minimum wage as 16 workers used to be employed but now only 8 are; and 2 additional people enter the labor force following the minimum wage as 16 workers used to want a job but now 18 do. Under the minimum wage, the unemployment rate would be 10/18, or 55.6 percent.

3-10. Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The production function is f(E,K) = E½K ½, so that the marginal product of labor is MPE = (½)(K/E) ½ .

If the current capital stock is fixed at 1,600 units, how much labor should the firm employ in the short run? How much profit will the firm earn?

The firm’s labor demand curve is its value of marginal product curve, VMPE, which equals the marginal productivity of labor, MPE, times the marginal revenue of the firm’s product. But as price is fixed at $50, MR = 50. Thus, we have: 1600 1,000 1 .

VMPE = MPE  MR =     50 = E 2 E

Now, by setting VMPE = w and solving for E, we find that the optimal number of workers for the firm to hire is 10,000 workers (i.e., 1000/sqrt(E) = 10 solves as E = 10,000). The firm then makes (1,600)½(10,000)½ = 4,000 units of output and earns a profit of π = 4,000($50) – 1,600($25) – 10,000 ($10) = $60,000.

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3-11. Several states set their own minimum hourly wage above the federal minimum wage.

To offset higher minimum wages, many of these states offer firms tax incentives that lower the cost of borrowing and/or lower the firm’s tax liability on profits. In general, how do these kinds of state policies (i.e., higher minimum wages and lower taxes) distort the firm’s profit-maximization decisions? Why might we expect to see such policies attract firms in “high tech” industries?

High minimum wages provide an incentive to hire fewer low-skilled workers than the firm would otherwise choose to hire if it faced the lower federal minimum wage. Similarly, receiving tax incentives that lower the cost of borrowing or the firm’s tax liability provides an incentive for firms to invest more in non-labor inputs, such as capital and technology. As “high tech” firms tend to hire very skilled workers (paid well in excess of the minimum wage) and employ a lot of capital/technology while employing very little minimum wage labor, it is exactly these kinds of firms that would find a state that offered these kinds of tax incentives appealing (and who don’t really care about the higher minimum wage).

3-12. How does the amount of unemployment created by an increase in the minimum wage depend on the elasticity of labor demand? Do you think an increase in the minimum wage will have a greater unemployment effect in the fast food industry or in the lawn care/landscaping industry?

The elasticity of demand (for low-skill workers) is the percent change in labor demanded over the percent change in the wage. When this is low (in absolute value), labor demand is not very responsive to increases in the (minimum) wage. In this case, there will be very small unemployment effects from increasing the minimum wage. When the elasticity of demand is large in absolute value, however, there will be substantial unemployment effects when the minimum wage is increased.

It is probably likely that the unemployment effect from an increase in the minimum wage would be more pronounced in the fast food industry than in the lawn care/landscaping industry. The fast food industry has witnessed a large amount of automation (and even outsourcing), and could experience more. Such possible reactions make labor demand more elastic. In contrast, the lawn care/landscaping industry requires workers to cut lawns, install sprinklers, etc. Such reliance on labor, therefore, may result in more inelastic demand for labor.

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3-13. Which one of Marshall’s rules suggests why labor demand should be relatively inelastic for public school teachers and nurses? Explain.

Public school teachers and nurses both help produce a good that is price inelastic – in the United States, at least, society will always purchase education and health care. Likewise, education and healthcare do not face strong competition from substitute goods. Finally, the production processes for education and healthcare both require teachers and nurses. And though these talents can be substituted for to some degree by other forms of labor or capital, both are crucial to the production process. Thus, other inputs (computers, doctors, etc.) cannot readily replace teaching or nursing services, and therefore the supply elasticity of other factors of production is not very elastic for teachers or nurses. For all three of these rules, therefore, the labor demand for public school teachers and nurses is likely fairly inelastic.

As an aside, however, we can make a distinction between teachers and nurses. These two occupations likely differ in Marshall’s fourth rule. Public school teacher salaries are estimated to be between 50% and 80% of all expenditures on primary and secondary education. In contrast, expenditures on nursing are a much lower percentage of the total cost of heath care. For this rule, therefore, the demand for nurses is likely to be even more inelastic than is the demand for public school teachers.

3-14. Many large cities have recently enacted living wage ordinances that require paying a minimum wage that is higher than the state or federal minimum wage. Moreover, sometimes living wage ordinances state two different minimum wages – one for workers who also receive employer-paid health insurance and one for workers who do not receive health insurance. (a) Why would living wages distinguish between workers based on their health insurance?

In particular, what “problem” might the local government be trying to solve?

Living wage ordinances came about (largely in the 1990s) as advocates argued that people could not live in the city on the federal minimum wage. Therefore, these advocate groups tried to change the discussion from an hourly wage issue to discussing what it takes to actually live – wages, housing, education, healthcare, etc. When making these arguments, it quickly becomes clear that there is a huge difference between people with healthcare insurance and those without.

Therefore, in recognition of this difference, living wage advocates started proposing a policy of , say, $18 per hour if health insurance is not provided and $15 per hour if health insurance is provided, in order to remain true to their goals. Put differently, without this provision it isn’t a stretch to think that many firms would stop providing health insurance in order to save money now that they are being asked to pay a much higher minimum wage. , (b) Sometimes living wage ordinances apply only to the city government, meaning that the city is required to pay all city workers a high minimum wage while private firms are only subject to state or federal minimum wages. In this case, the living wage creates a covered sector and an uncovered sector. Which workers are in the covered sector? Which workers are in the uncovered sector? What might city officials, who have to manage to a budget, do in response to a living wage ordinance that only applies to city workers?

The covered sector are all city workers. The uncovered sector is everyone else working in the city. City officials who are trying to make the budget work out may decide to lay-off any city worker whose job can be replaced with contracted work. For example, a city may hire 1,000 8 ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

landscapers at $10 per hour to maintain all of the natural patches of grass, trees, and flowers throughout the city. But should it be forced to pay a minimum wage of $18 per hour, the city could (optimally) respond by firing those 1,000 workers and rather contract out landscaping work. These 1,000 workers then flow to the uncovered sector where they are paid $10 per hour (or even less if the flow of labor competes down the wage.) In response to this shift by the city, some living wage ordinances apply to all city workers as well as to all firms that do business with the city. This doesn’t completely prevent the labor migration issue discussed in this paragraph, but it is thought to reduce the abuse somewhat.

As a side note, many colleges and universities have done exactly the same thing (though not due to a formal living wage ordinance but rather due to accusations of paying staff way too little).

Thus, many campuses now contract out food preparation, janitorial services, and lawn care.

3-15. Consider a production model with two inputs–domestic labor (EDom) and foreign labor (EFor). The market is originally in equilibrium in that

MPEdom MPEfor . = wdom w for (a) Suppose a shock occurs that increases the marginal product of foreign labor. Assuming no changes in domestic or foreign wages, explain what will happen to domestic and foreign labor in order to restore the above condition.

We are told that the marginal productivity of foreign labor has increased. Therefore, before labor adjustments, we will have a situation in which

MPEdom MPEfor  . wdom w for As we are further told that wages don’t adjust, the only way to restore the original equation is to have MPEdom increase and/or MPEfor to decrease. And these changes occur through labor mobility. In particular, for MPEdom to increase, we need EDom to decrease; and similarly for MPEfor to decrease we need EFor to increase. Therefore, to answer the question, following a positive shock to the marginal product of foreign labor, firms will respond by employing fewer units of domestic labor and more units of foreign labor. (b) In the years following the shock, what are three (significantly different) policies that the domestic country could employ if it wanted to reverse the outflow of labor?

In order to reverse the outflow of labor, there are generally two things that can be done: •

Reverse the change in relative wages, which requires the domestic wage to decrease relative to the foreign wage.

•

Reverse the previous change in relative marginal products, which requires domestic marginal product to increase relative to foreign marginal product.

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The first, therefore, requires lowering wDom or increasing wFor. The second requires increasing MPEdom or decreasing MPEfor. Of these four options, the only one the domestic country probably would not pursue is decreasing MPEfor. To provide an example using the United States, the government could: •

Decrease wdom by allowing the minimum wage to be eroded by inflation, by reducing hiring rules and regulations, by allowing firms to cut medical benefits, by offering hiring subsidies, etc.

•

Increase wfor by lobbying the WTO and UN to have developing countries adopt minimum wage laws, environmental standards, child labor laws, etc.

•

Increase MPEdom by improving K – 12 and university education in the United States. (In words, the standard economic argument here is that outsourcing would stop if American workers became more productive.)

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CHAPTER 4 4-1. Figure 4-9 discusses the changes to a labor market equilibrium when the government mandates an employee benefit for which the cost exceeds the worker’s valuation (panel a) and for which the cost equals the worker’s valuation (panel b). (a) Provide a similar graph to those in Figure 4-9 when the cost of the benefit is less than the worker’s valuation, and discuss how the equilibrium level of employment and wages change. Is there deadweight loss associated with the mandated benefit?

The Impact of a Mandated Benefit (C < B) S0 Dollars P B

w0

S1

w1 Q

R

w*

C

D1

E1 E0

E*

D0

Employment

Without the mandate, the original equilibrium is at point P with an employment level of E0 and a wage level of w0. When the government mandates the benefit, labor demand shifts down by C as C is the per employee cost of the mandate. At the same time, however, supply shifts down by B as each worker values the benefit at B. As drawn, the cost is less than the benefit as stipulated in the problem. In this case, the new equilibrium is at R with an employment level of E* and a wage level of w*. Notice that the mandate has increased employment. It has also lowered the wage, by more than C but not by more than B. Consequently, firms and workers both benefit from this form of government intervention. Thus, there is no deadweight loss but rather new found surplus to be shared by firms and workers. Note: all of this analysis is predicated on firms and workers being unable to recognize the surplus gain without the government’s assistance (see part b below). (b) Why is the situation in part (a) in which a mandated benefit would cost less than the worker’s valuation less important for public policy purposes than when the cost of the mandated benefit exceeds the worker’s valuation?

The reason why this situation is less important for public policy purposes is that this is a situation of a “free lunch” that is not taken advantage of by firms and workers but it is observed by the government. Economists don’t tend to devote much attention to such problems as it is believed that the firms and workers would come to realize the potential for mutual gain (in which case the above figure would have originally been at point R with the benefit supplied for the worker by the firm, making the mandate unnecessary).

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4-2. In the United States, labor supply tends to be inelastic relative to labor demand, and according to law, payroll taxes are essentially assessed evenly between workers and firms.

Given the above situation, are workers or firms more likely to bear the additional burden of an increased payroll tax in the United States? Could this burden be shifted to the firms by assessing the increase in payroll taxes on just firms rather than having firms and workers continue to be assessed payroll taxes equally?

As labor supply is relatively more inelastic than labor demand, workers will bear a greater percentage of payroll taxes than employers regardless of how the law stipulates the amount be split. Most estimates suggest that workers in the United States bear about 80 to 85 percent of payroll taxes. Again, tax incidence does not depend on who legally is required to pay the tax, so levying a greater percentage of payroll taxes on firms will not have any real economic effect.

4-3. Suppose the supply curve of physicists is given by w = 10 + 5E, while the demand curve is given by w = 50 – 3E. Calculate the equilibrium wage and employment level. Suppose now that the demand for physicists increases to w = 70 – 3E. Assume the market is subject to cobwebs. Calculate the wage and employment level in each round as the wage and employment levels adjust to the demand shock. What is the new equilibrium wage and employment level?

The initial equilibrium requires 10 + 5E = 50 – 3E. Solving yields w = $35 and ES = ED = 5.

When demand increases to w = 70 – 3E, the new equilibrium wage is $47.5 and the equilibrium level of employment is 7.5, which is found by solving 10 + 5E = 70 – 3E. The table below gives the values for the wage and employment levels in each round. The values in the table are calculated by noting that in any given period the number of physicists is inelastically supplied, so that the wage is determined by the demand curve. Given this wage, the number of physicists available in the next period is calculated. By round 7, the market wage rate is within 30 cents of the new equilibrium.

Round 1 2 3 4 5 6 7 8

Wage $55.0 $43.0 $50.2 $45.9 $48.4 $46.9 $47.8 $47.2

Employment 5 9 6.6 8.0 7.2 7.7 7.4 7.6

Scratch work for some of the math: • Original employment of 5 implies that when labor demand increases, the new posted wage will be 70 – 3E = 70 – 3(5) = $55. (The round 1 wage.)

• At this wage, 55 = 10 + 5E implies E = 9 workers will supply their labor. Given these 9 workers, the firm, using its new demand function, will post a wage of 70 – 3(9) = $43.

(The round 2 wage.)

• At this wage, 43 = 10 + 5E implies E = 6.6 workers will supply their labor. Given these 6.6 workers, the firm, using its new demand function, will post a wage of 70 – 3(6.6) = $50.20. (The round 3 wage.)

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•

And so on.

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4-4. Suppose labor demand for low-skilled workers in the United States is w = 24 – 0.1E where E is the number of workers (in millions) and w is the hourly wage. There are 120 million domestic U.S. low-skilled workers who supply labor inelastically. If the U.S. opened its borders to immigration, 20 million low-skill immigrants would enter the U.S. and supply labor inelastically. What is the market-clearing wage if immigration is not allowed? What is the market-clearing wage with open borders? How much is the immigration surplus when the U.S. opens its borders? How much surplus is transferred from domestic workers to domestic firms?

Without immigration, the market-clearing wage is $12 as 24 – 0.1(120) = $12, at which all 120 million low-skill U.S. workers are employed. With immigration, the market-clearing wage is $10 as 24 – 0.1(140) = $10, at which all 120 million low-skill U.S. workers and all 20 million immigrants are employed. Both surplus values are easy to see in Figure 4–15. The additional surplus received by the U.S. economy is the area of triangle BCF in the figure. Thus, the additional surplus received by the U.S. because of the immigration equals ($12 – $10) × (140m – 120m) / 2 = $20 million.

Likewise, the total transfer from U.S. workers to U.S. firms is represented in the figure by the rectangle captered by w0w1BF. Thus, the total transfer from U.S. workers to U.S. firms because of the immigration equals ($12 – $10) × (120m) = $240 million.

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4-5. There are two reasons why the immigration surplus is greater when

immigration is accompanied by human capital externalities compared to when there are no human capital externalities associated with immigration. Both reasons are evident in Figure 4-16. The first is represented by triangle BCD. The second is represented by trapezoid ABEF. Explain the underlying source of each area.

Explain why human capital externalities are important to each region.

Triangle BCD represents the additional benefit domestic firms receive from employing immigrants. This is compared to the much smaller triangle equal to the change in the number of immigrants times the change in the wage (times one-half) that would have resulted had the demand for high-skilled workers (in this case, high-skilled immigrant labor) had not increased due to the human capital externalities.

Trapezoid ABEF represents the additional benefit domestic firms receive from employing highskilled domestic workers which comes about because of human capital externalities. This trapezoid exists only because demand for high skilled workers increased because of immigration.

4-6. Let total market demand for labor be represented by ED = 1,000 – 50w where ED is total employment and w is the hourly wage. (a) What is the market clearing wage when total labor supply is represented by ES = 100w – 800? How many workers are employed? How much producer surplus is received at the equilibrium wage?

Set ED = ES and solve for w yields w* = $12. At this wage, ED = 400 and ES = 400, which is the equilibrium level of employment.

Lastly, producer surplus is the area below the demand curve but above the wage.

Mathematically, producer surplus = (0.5) × ($20 – $12) × 400 = $1,600 where the $20 comes from solving for w when ED = 0.

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(b) Suppose the government imposes a minimum wage of $16. What is the new level of employment? How much producer surplus is received under the minimum wage?

At a minimum wage of $16, labor demand will equal 200 (while labor supply will equal 800). As firms are not required to hire workers if they don’t want to, the new level of employment will be 200 workers. In this case, producer surplus = (0.5) × ($20 – $16) × 200 = $400.

4-7. Let total market demand for labor be represented by ED = 1,200 – 30w where ED is total employment and w is the hourly wage. Suppose 750 workers supply their labor to the market perfectly inelastically. How many workers will be employed? What will be the market clearing wage? How much producer surplus is received?

As the 750 workers supply their labor perfectly inelastically, all 750 will be employed. The wage that the firms must pay satisfies 750 = 1,200 – 30w which solves as w* = $15. In this case, producer surplus = (0.5) × ($40 – $15) × 750 = $9,375 where the $40 comes from solving for w when ED = 0.

4-8. A firm faces perfectly elastic demand for its output at a price of $6 per unit of output.

The firm, however, faces an upward-sloped labor supply curve of E = 20w – 120 where E is the number of workers hired each hour and w is the hourly wage rate. Thus, the firm faces an upward-sloped marginal cost of labor curve of MCE = 6 + 0.1E Each hour of labor produces five units of output. How many workers should the firm hire each hour to maximize profits? What wage will the firm pay? What are the firm’s hourly profits?

First, solve for the labor demand curve: VMPE = P · MPE = $6 x 5 = $30. Thus, every worker is valued at $30 per hour by the firm. Now, setting VMPE = MCE yields 30 = 6 + .1E which yields E* = 240. Thus, the firm will hire 240 workers every hour. Further, according to the labor supply curve, 240 workers can be hired at an hourly wage of $18 as 240 = 20w – 120 → 240 = 20(18) – 120 → w = $18.

Finally, as Q = 5L = 5 × 240 = 1,200, the firm’s hourly profits are: π = pQ – wL = $5 × 1,200 – $18 × 240 = $2, 880.

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4-9. Ann owns a lawn mowing company. She has 400 lawns she needs to cut each week. Her weekly revenue from these 400 lawns is $20,000. If given an 18-inch deck push mower, a laborer can cut each lawn in two hours. If given a 60-inch deck riding mower, a laborer can cut each lawn in 30 minutes. Labor is supplied inelastically at $10 per hour. Each laborer works 8 hours a day and 5 days each week. (a) If Ann decides to have her workers use push mowers, how many push mowers will Ann rent and how many workers will she hire?

As each worker can cut a lawn in 2 hours, it follows that each worker can cut 4 lawns in a day or 20 lawns in a week. Therefore, Ann would need to hire 20 workers (400 ÷ 20) and rent 20 push mowers (one for each worker) in order to cut all 400 lawns each week. (b) If she decides to have her workers use riding mowers, how many riding mowers will Ann rent and how many workers will she hire?

As each worker can cut a lawn in 30 minutes, it follows that each worker can cut 16 lawns in a day or 80 lawns in a week. Therefore, Ann would need to hire 5 workers (400 ÷ 80) and rent 5 riding mowers (one for each worker) to cut all 400 lawns each week. (c) Suppose the weekly rental cost (including gas and maintenance) for each push mower is $250 and for each riding mower is $2,400. What equipment will Ann rent? How many workers will she employ? How much profit will she earn?

If Ann uses push mowers, her weekly cost of mowers is $250(20) = $5,000 while her weekly labor cost is $10(20)(40) = $8,000. Under this scenario, her weekly profit is $7,000. If Ann uses riding mowers, her weekly cost of mowers is $2,400(5) = $12,000 while her weekly labor cost is $10(5)(40) = $2,000. Thus, under this scenario, her weekly profit is $6,000. Therefore, under these conditions, Ann will rent 20 push mowers and employ 20 workers. (d) Suppose the government imposes a 20 percent payroll tax (paid by employers) on all labor and offers a 20 percent subsidy on the rental cost of capital. What equipment will Ann rent? How many workers will she employ? How much profit will she earn?

Under these conditions, the cost of labor has increased to $12 per hour, while the rental costs for a push mower and a riding mower have decreased to 0.8 × $250 = $200 and 0.8 × $2,400 = $1,920 respectively. Ann’s profits under the two options, therefore, are Push-Profit = $20,000 – $200(20) – $12(20)(40) = $6,400.

Rider-Profit = $20,000 – $1,920(5) – $12(5)(40) = $8,480.

Thus, under these conditions, Ann rents riding mowers, hires 5 workers, and earns a weekly profit of $11,600.

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4-10. Figure 4-6 shows that a payroll tax will be completely shifted to workers when the labor supply curve is perfectly inelastic. In this case, for example, a new $2 payroll tax will lower the wage by $2, will not affect employment, and will not result in any deadweight loss.

Suppose instead that labor supply is perfectly elastic at a wage of $10. In this case, what would be the effect on wages, employment, and deadweight loss from a $2 payroll tax?

If the labor supply curve is perfectly elastic, the firm will pay the entire tax, so the effective wage earned by workers will remain at $10 but the effective wage paid by firms will increase to $12.

However, because the firm pays the entire tax increase, it will respond by reducing employment (from E0 to E1 in the figure below). This reduction in employment results in a substantial deadweight loss.

Wage $12

Deadweight Loss

$10

S

D1

E1

E0

D0

Employment

4-11. In the Cobweb model of labor market equilibrium (Figure 4-19), the adjustments in employment can be small with adjustment being fast, or the adjustments in employment can be large with adjustment being slow. The result that comes about depends on the elasticity of labor supply. Which result (small and fast vs. large and slow) is associated with very inelastic labor supply? Which result is associated with elastic labor supply? What is the economic intuition behind this result?

Intuitively, we should expect the adjustments in employment to be large (and therefore slow) when the labor supply curve is elastic, because by definition when the labor supply curve is elastic (i.e., responsive), changes in employment will be large (large and positive for small positive wage changes; large and negative for small negative wage changes).

Inelastic Supply

Elastic Supply

Wage

Wage S S

Employment

Employment

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4-12. A monopsonist’s demand for labor can be written as VMPE = 40 – 0.005ED. Labor is supplied to the firm according to w = 5 + 0.01ES. Thus, the firm’s marginal cost of hiring workers when it hires off of this supply schedule is MCE = 5 + 0.02ES. (a) How much labor does the monopsony firm hire and at what wage when there is no minimum wage?

The monopsonist sets MCE equal to VMPE and solves. In this case, 5 + 0.02E = 40 – 0.005E solves as E* = 1,400. At this employment level, the firm pays a wage off of the supply curve, which is 5 + 0.01×1,400 = $19. (b) How much labor does the monopsony firm hire and at what wage when it must pay a minimum wage of $25?

When the minimum wage is $25, the firm’s marginal cost curve also equals $25 until this wage hits the supply curve. When it does, the firm then faces the original marginal cost curve. To check: at a wage of $25, solve 25 = 5 + 0.01E → E = 2,000 units of labor are supplied. At 2,000 units of labor, VMPE = 40 – 0.005×2,000 = $30. Therefore, we know that the minimum wage of $25 hits the supply curve before it hits the demand curve.

With the firm facing a marginal cost of $25, set marginal cost equal to the supply curve (see Figure 4-22). In this case, this requires 25 = 5 + 0.01E, which solves as E* = 2,000. Therefore, when facing a wage of $25, the firm pays a wage of $25 and hires 2,000 workers.

The lesson here is that, compared to part (a), a minimum wage can cause a monopsony firm to respond by hiring more workers.

4-13. Suppose the economy’s labor market is competitive and that labor demand can be written as w = 50 – 0.3E while labor supply can be written as w = 8 + 0.2E where E is the total amount of employment in millions. What is the market clearly wage? How many people are employed? What is the total value of producer surplus? What is the total amount of worker surplus?

The picture of market clearing equilibrium is given in Figure 4–1. To find E*, set labor demand equal to labor supply and solve: 8 + 0.2E = 50 – 0.3E 0.5E = 42 E* = 84 million workers Use E* and either equation to then solve for the market equilibrium wage: w* = 50 – 0.3(84) = $24.80 or w* = 8 + 0.2(84) = $24.80 Therefore, the market equilibrium is that 84 million workers are hired at an hourly wage of $24.80.

Looking at Figure 4–1, producer surplus is the area designate by triangle P. Thus: 9 ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

P = (½ ) × ($50 – $24.80) × 84 million = $1,058.4 million.

Looking at Figure 4–1 again, worker surplus is the area designate by triangle Q. Thus: Q = (½ ) × ($24.80 – $8) × 84 million = $705.6 million.

4-14. Suppose the Cobb-Douglas production function given in equation 4-1 applies to a developing country. Instead of thinking of immigration from a developing to a developed country, suppose a developed country invests large amounts of capital (foreign direct investment, or FDI) in a developing country. (a) How does an increase in FDI affect labor productivity in the developing country? How will wages respond in the short-run?

FDI is an increase in capital, K. As equation 4-5 shows, the marginal product of labor increases as K increases. Thus, wages (which equal the marginal product of labor in a competitive market) will increase in the developing nation in response to FDI inflows. (b) What are the long-run implications of FDI, especially in terms of potential future immigration from the developing country?

Intuitively, there will be less migration out of the developing country in the long run due to FDI inflows because the domestic wage (and standards of living) will have increased. Thought of differently, as r is constant in the long run, the capital to labor ratio is also constant in the long run (see the text). Thus, FDI ↑→ K ↑→ L ↑in the long run. There are several ways to increase L in the long run, but an obvious candidate is to have less migration out of the developing country.

4-15. Empirical work suggests that labor demand is very elastic while labor supply is very inelastic. Assume too that payroll taxes are about 15% and legislated to be paid half by the employee and half by the employer. (a) What would happen to worker wages if payroll taxes were eliminated?

Because labor supply is relatively inelastic while labor demand is relatively elastic, workers bear most of the tax burden of payroll taxes, regardless of who is legislated to pay the tax. Therefore, a good estimate might be that workers bear 12 percentage points of the tax while firms bear 3 percentage points of the tax. If so, average wages would increase by 12 percentage points if payroll taxes were eliminated. (b) What would happen to employment costs paid by firms if payroll taxes were eliminated?

Using the description from part A, it is likely that employer wage costs would fall by only 3 percentage points if payroll taxes were eliminated.

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(c) What would happen to producer and worker surplus if payroll taxes were eliminated?

Which measure is relatively more sensitive to payroll taxes? Why? Both producer surplus and worker surplus would increase if payroll taxes were eliminated, but in terms of a percent change, the change would be much greater (maybe as much as 4 times greater) for workers than for firms. (d) Why might workers not want payroll taxes eliminated?

Despite the increase in worker surplus that would accrue from an elimination of payroll taxes, workers may still not want them to be eliminated if workers value the programs these taxes fund – in particular payroll taxes fund social security, Medicare, and Medicaid.

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CHAPTER 5 5-1. Politicians who support the green movement often argue that it is profitable for firms to pursue a strategy that is “environmentally friendly” (for example, by building factories that do not pollute), because workers will be willing to work in environmentally friendly factories at a lower wage rate. Evaluate the validity of this claim.

If it is profitable for firms to build factories that do not pollute, firms would build these factories without government interference as doing so would maximize profits. After all, firms could build these profit-maximizing factories and attract persons to work at these factories at lower wages because no compensating differential would be needed. The fact that compensating differentials exist and that governments attempt to regulate the quality of the workplace implies that providing these amenities to workers is more costly than cost-saving.

This idea/argument is related to part b of question 4-1 in which the government mandates a benefit that costs C to firms but is valued at B by workers where C < B.

5-2. Consider the demand for and supply of risky jobs. (a) Derive the algebra that leads from equations (5-4) and (5-5) to equation (5-6).

(5-4) (5-5)

π0 = pα0E* – w0E*, π1 = pα1E* – w1E*,

Now,

π1 – π0 = (pα1E* – w1E*) – ( pα0E* – w0E*) = (pα1 – pα0)E* – (w1 – w0)E* = [θ – (w1 – w0)]E*.

This difference in profits, therefore, is positive (which means the firm will offer a risky work environment) if θ > w1 – w0 and is negative (which means the firm will offer a safe work environment) if θ < w1 – w0. Thus, we have shown equation (5-6). (b) Describe why the supply curve in Figure 5-2 is upward sloping. How does your explanation incorporate θ? Why? The y-axis in Figure 5-2 is the difference in wages between the risky job (w1) and the safe job (w0). The higher one is on the y-axis, the greater is this difference. The greater this difference, the more people there are who are willing to work the risky job. For example, when the difference equals $5, maybe only 30 people are willing to work the risky job. When the differential increases to $6, though, these same 30 people plus some others will be willing to work the risky job. The “plus some others” is what makes the supply curve in Figure 5-2 upward sloping.

Notice that the explanation of why the supply curve in Figure 5-2 is upward sloping has absolutely nothing to do with θ where θ = pα1 – pα0. In particular, θ is a technology parameter as it is the difference (measured in dollars) in worker productivity. This is an important idea for the firm, but it is not important to the worker who is providing the same level of effort in either case.

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(c) Using a graph similar to Figure 5-2, demonstrate how the number of dirty jobs changes as technological advances allow the cost of making worksites cleaner to fall for all firms.

w1 – w0

ˆ A

SA = SB

ˆB (w1 – w0)*A (w1 – w0)*B

DB

E*B

E*A

DA

Number of Workers in Risky Job

In the above graph, the original market equilibrium is determined by SA and DA. What is important is that the demand for workers in the risky job originally is a function of ˆ A , which is a technology parameter. In particular, it is the lowest wage differential at which the worst (or least able firm) becomes willing to offer a safe work environment. Then, suppose that technology improves so that even the worst firms find it profitable to offer a safe environment at a lower differential. This implies that ˆ has been reduced, from ˆ A to ˆB . After this shift in the demand for risky jobs, the equilibrium adjusts appropriately: employment in the risky sector falls and the equilibrium wage differential falls.

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5-3. Suppose there are 100 workers in the economy in which all workers must choose to work a risky or a safe job. Worker 1’s reservation price for accepting the risky job is $1; worker 2’s reservation price is $2, and so on. Because of technological reasons, there are only 10 risky jobs. (a) What is the equilibrium wage differential between safe and risky jobs? Which workers will be employed at the risky firm?

The supply curve to the risky job is given by the fact that worker 1 has a reservation price of $1, worker 2 has a reservation price of $2, and so on. As the figure below illustrates, this supply curve (given by S) is upward sloping, and has a slope of 1. The demand curve (D) for risky jobs is perfectly inelastic at 10 jobs. Market equilibrium is attained where supply equals demand so that 10 workers are employed in risky jobs; the market compensating wage differential is $10 (or, at least some number at least $10 at not yet $11) since this is what it takes to entice the marginal (tenth) worker to accept a job offer from a risky firm. Note that the firm employs those workers who least mind being exposed to risk. (b) Suppose now that an advertising campaign, paid for by the employers who offer risky jobs, stresses the excitement associated with “the thrill of injury,” and this campaign changes the attitudes of the work force toward being employed in a risky job. Worker 1 now has a reservation price of -$10 (that is, she is willing to pay $10 for the right to work in the risky job); worker 2’s reservation price is -$9, and so on. There are still only 10 risky jobs. What is the new equilibrium wage differential?

If tastes towards risk change, the supply curve shifts down to S and the market equilibrium is attained when the compensating wage differential is -$1. This is the compensating differential required to hire the marginal worker (that is, the 10th worker). Note that this compensating differential implies that even though most workers (from worker 12 onwards) dislike risk, the market determines that risky jobs will pay less than safe jobs.

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5-4. Suppose all workers have the same preferences represented by

U = w − 2x , where w is the wage and x is the proportion of the firm’s air that is composed of toxic pollutants. There are only two types of jobs in the economy, a clean job (x = 0) and a dirty job (x = 1). Let w0 be the wage paid by the clean job and w1 be the wage paid for doing the dirty job. If the clean job pays $16 per hour, what is the wage in dirty jobs? What is the compensating wage differential?

If all persons have the same preferences regarding working in a job with polluted air, market equilibrium requires that the utility offered by the clean job be the same as the utility offered by the dirty job, otherwise all workers would move to the job that offers the higher utility. This implies that:

w0 − 2(0) = w1 − 2(1) =>

16 = w1 − 2.

Solving for w1 implies that w1 = $36. The compensating wage differential, therefore, is $20 as the risky job pays $36 per hour and the clean job pays $16 per hour.

5-5. Suppose a drop in the compensating wage differential between risky jobs and safe jobs has been observed. Two explanations have been put forward: • •

Engineering advances have made it less costly to create a safe working environment.

The phenomenal success of a new action serial “Die On The Job!” has imbued millions of viewers with a romantic perception of work-related risks.

Using supply and demand diagrams show how each of the two developments can explain the drop in the compensating wage differential. Can information on the number of workers employed in the risky occupation help determine which explanation is more plausible?

The engineering advances make it cheaper for firms to offer safe jobs, and hence reduce the gain from switching from a safe environment to a risky one (or reduce the cost of switching from a risky environment to a safe one). This will decrease (shift in) the demand curve for risky jobs and reduce the compensating wage differential (Figure 1 below). Note that the equilibrium number of workers in risky jobs goes down.

The glamorization of job-related risks may make people more willing to take these risks. This increases the supply (shift out) of workers to risky jobs and reduces the compensating differential (Figure 2 below). Note that the equilibrium number of workers in risky jobs goes up.

Thus, information on whether employment in the risky sector increased or decreased can help discern between the two competing explanations: if employment in risky jobs went down then it is likely due to technology; if employment in risky jobs went up it is likely due to preferences.

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Figure 1. Labor Market for Risky Jobs

Compensating Differential

Supply

(w1 – w0 )old (w1 – w0 )new

Old Demand New Demand Enew Eold

Number of Workers in Risky Jobs

Figure 2. Labor Market for Risky Jobs

Compensating Differential

Old Supply New Supply

(w1 – w0 )old (w1 – w0 )new Demand

Eold

Enew

Number of Workers in Risky Jobs

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5-6. Consider a competitive economy that has four different jobs that vary by their wage and risk level. The table below describes each of the four jobs.

Job A B C D

Risk ( r ) 1/5 1/4 1/3 1/2

Wage ( w ) $3 $12 $23 $25

All workers are equally productive, but workers vary in their preferences. Consider a worker who values his wage and the risk level according to the following utility function:

u( w, r ) = w +

1 . r2

Where does the worker choose to work? Suppose the government regulated the workplace and required all jobs to have a risk factor of 1/5 (that is, all jobs become A jobs). What wage would the worker now need to earn in the A job to be equally happy following the regulation?

Calculate the utility level for each job by using the wage and the risk level: U(A) = 28, U(B) = 28, U(C) = 32, and U(D) = 29. Therefore, the worker chooses a type C job and receives 32 units of happiness. If she is forced to work a type A job, the worker needs to receive a wage of $7 in order to maintain her 32 units of happiness as 7 + 25 = 32.

5-7. AB Consulting and DF Partners are two identical consulting firms in all aspects except that AB Consulting fires all new hires who don’t bring in at least $5 million in revenue during their 4-year probationary term while DF Partners fires all new hires who don’t bring in at least $2 million in revenue during their 4-year probationary term. (a) Assuming no worker likes to take on the risk of being fired, what would you expect salaries to look like across the two firms? That is, how do you expect the compensating differential to appear?

Assuming no worker likes to take on the risk of being fired, jobs at DF Partners are preferred to jobs at AB Consulting. Therefore, the compensating differential should be that salaries are higher at AB Consulting compared to salaries at DF Partners. (b) Suppose rather than seeing what you predicted in part (a), it terms out that salaries are the same in both firms. Provide a few explanations as to why this might be the case.

There are several reasons why the expected compensating differential may not come about in the data. First and foremost, preferences may not be as clear-cut as described above. In particular, if workers differ in their ability (and they know their ability), it may be that enough workers are confident in their ability to hit the revenue targets that they are willing to work at AB Consulting without a compensating differential. If the number of such workers is smaller than the number of jobs offered by AB Consulting, we would expect there to be no compensating differential. A 6 ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

second reason could be the labor market itself. If there is an over-supply of workers to the market, the hedonic wage function will be less steeply sloped (or not sloped at all).

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5-8. The EPA wants to investigate the value workers place on being able to work in “clean” mines over “dirty” mines. The EPA conducts a study and finds the average annual wage in clean mines to be $42,250 and the average annual wage in dirty mines to be $47,250. (a) According to the EPA, how much does the average worker value working in a clean mine?

The average value is $47,250 - $42,250 = $5,000. (b) Suppose the EPA could mandate that all dirty mines become clean mines and that all workers who were in a dirty mine must therefore accept a $5,000 pay decrease. Are these workers helped by the intervention, hurt by the intervention, or indifferent to the intervention?

All except the marginal worker are hurt by the intervention. The workers who sort themselves into the dirty jobs are those workers who prefer to work in a dirty mine than in a clean mine when the wage differential is $5,000. These workers, in essence, value working in a dirty job at less than $5,000, and therefore being required to give up $5,000 to have a clean job is a bad deal for them. (Similarly, if all of the workers in the clean jobs were forced to accept dirty jobs for $5,000 more, all of them except the marginal worker would be hurt as they all value working in a clean job at more than $5,000.)

5-9. There are two types of farming tractors on the market, the FT250 and the FT500. The only difference between the two is that the FT250 is more prone to accidents than the FT500. Over their lifetime, one in ten FT250s is expected to result in an accident, as compared to one in twenty-five FT500s. Further, one in one-thousand FT250s is expected to result in a fatal accident, as compared to only one in five-thousand FT500s. The FT250 sells for $125,000 while the FT500 sells for $137,000. At these prices, 2,000 of each model are purchased each year. What is the statistical value farmers place on avoiding a tractor accident? What is the statistical value of a life of a farmer?

The FT500 is associated with an extra cost of $12,000, but its accident rate is only 4% compared to the 10% accident rate of the FT250. Also, each farmer that buys the FT250 is willing to accept the additional risk in order to save $12,000. These workers are willing to receive $24 million ($12,000 x 2,000) in exchange for (0.1 – 0.04) · 2000 = 120 more accidents. Thus, the value placed on each accident is $24 million ÷ 120 = $200,000.

Likewise, the 2,000 farmers who buy the FT250 are willing to receive $24 million in exchange for (0.001 – 0.0002) · 2000 = 1.6 more fatal accidents. Thus, the value placed on each life is 24 million ÷ 1.6 = $15 million.

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5-10. Consider the labor market for public school teachers. Teachers have preferences over their salary, amenities, and school characteristics. (a) One would reasonably expect that high-crime school districts pay higher wages than low-crime school districts. But the data consistently reveal that high-crime school districts pay lower wages than low-crime school districts. Why? (Hint: in many cities the primary source of funding for teacher salaries is local property taxes.)

The likely reason for this is not that teachers do not care about crime–they almost certainly do– but rather that school funding is determined in large part by local property taxes. If high-crime schools are located in low-income cities, there is nothing (or at least very little) the local school board can do to raise more money to pay the compensating differential. (b) Does your discussion suggest anything about the relation between teacher salaries and school quality?

In the end, because high-crime schools cannot offer the necessary compensating differential, they will not be able to attract the highest quality workers. Therefore, one would expect that the worst schools with the worst teachers are located in the poorest communities with the most crime. This is the typical story told by proponents of replacing the local property tax scheme to fund public education with state or federal funds.

5-11. (a) On a graph with the probability of injury on the x-axis and the wage level on the y-axis plot two indifference curves, labeled UA and UB, so that the person associated with UA is less willing to take on risk relative to the person associated with UB. Include an arrow on the graph showing which direction is associated with higher levels of utility.Explain what it is about the indifference curves that reveals person A is less willing to take on risk relative to person B.

Wage UA

UB

Probability of Injury

In the graph above, the person with indifference curves represented by UA is less willing to take on risk than a person with indifference curves represented by UB. This can be seen by looking at the point where the two indifference curves intersect. Suppose both workers are offered this job, and then asked how much extra they need to be paid to accept a different job that is associated

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with some extra risk. Worker A demands a greater payment to take on additional risk (because UA is higher than UB at all points to the right of the intersection) compared to worker B. The directional arrow points toward the northwest (up and to the left), because both types of workers prefer a higher wage (north) and a lower probability of injury (left). (b) Consider a third person who doesn’t care about the risk associated with the job. That is, he doesn’t seek to limit risk or to expose himself to risk. On a new graph, draw several of this person’s indifference curves. Include an arrow on the graph showing which direction is associated with higher levels of utility.

Wage

As worker C does not care about risk, his indifference curves increase to the north (and not to the northwest as would be the case for someone who disliked risk.)

Probability of Injury

As this worker does not care about risk, his indifference curve increases strictly to the north (up), and not to the northwest as would be the case for someone who disliked risk.

(c) Consider a wage-risk equilibrium that is characterized by an upward-sloping hedonic wage function. Now suppose there is a government campaign that successfully alters people’s perception of risk. In particular, each worker adjusts her preferences so that she now needs to be more highly compensated to take on risk. Discuss, and show on a single graph, how the government’s campaign affects indifference curves, isoprofit lines, the equilibrium hedonic wage function, and the distribution of workers to firms.

The proposed campaign will not alter iso-profit lines, but it will make indifference curves more steeply sloped.

In terms of the equilibrium, here are two possible answers as to what will happen to the hedonic wage function, depending on what one considers about the product market. If the product market is competitive, then the hedonic wage function will not change in shape as all firms compete and earn zero long-run profits. However, part of the hedonic wage function will disappear as certain types of firms (i.e., the ones that find it most costly to offer safe jobs) end up going out of business. That is, although the steepness doesn’t change, the top part of the function disappears.

As a result of the campaign, more workers work in safe environments and the equilibrium differential will fall (simply because the most risky jobs no longer exist).

If one assumes that profits can be positive, the result is a more steeply sloped hedonic wage function because of more steeply sloped indifference curves. Moreover, because the hedonic 10 ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

wage function is more steeply sloped (indicating that it is more expensive to offer a risky work environment), more firms will opt to offer safer jobs and more workers will take safer jobs because that is what they now prefer. However, the equilibrium wage differential will increase, meaning that those firms that find it very expensive to offer a safe job will have to pay higher wages.

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5-12. Suppose everyone is highly productive, college educated, hard-working, etc. People still differ in their preferences for jobs—while some would prefer to be doctors than lawyers, others prefer to be lawyers than doctors, and so on—and everyone prefers to be a professional to being a trash collector, but as usual preferences vary across individuals. In order for this economy to function at all, someone needs to choose to be the trash collector.

Who will be the trash collector, and in general terms how much will the job of trash collector pay?

In order for this economy to function at all, someone needs to choose to be the trash collector, so the salary paid to the trash collector will adjust until someone willing chooses to do the job. The person will be highly productive, college educated, hard-working, etc. The person will most likely earn a lot of money, as the salary must be high enough to encourage someone to take the job. Moreover, the person will be, of all people in the economy, the one who least objects to being a trash collector. So, to recap, because of other people’s aversion to collecting trash and the necessity to have someone collect the trash, the person with preferences far from the norm (i.e., most willingto pick up trash) earns a very high wage.

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5-13. Consider two identical jobs, but some jobs are located in Ashton while others are located in Benton. Everyone prefers working in Ashton, but the degree of this preference varies across people. In particular, the preference (or reservation price) is distributed uniformly from $0 to $5. Thus, if the Benton wage is $2 more than the Ashton wage, then 40 percent (or two-fifths) of the worker population will choose to work in Benton. Labor supply is perfectly inelastic, but firms compete for labor. There are a total of 25,000 workers to be distributed between the two cities. Demand for labor in both locations is described by the following inverse labor demand functions: Ashton: wA = 20 – 0.0024EA. Benton: wB = 20 – 0.0004EB. Solve for the labor market equilibrium by finding the number of workers employed in both cities, the wage paid in both cities, and the equilibrium wage differential.

There are five equations that must hold simultaneously to make the equilibrium. In particular, and defining Δ = wB – wA, the equations are: (1) wA = 20 – 0.0024EA, (2) wB = 20 – 0.0004EB, (3) Δ = wB – wA, (4) EA + EB = 25,000, (5) EB = 25000Δ ÷ 5 = 5000Δ.

Equation (5) is the most difficult for most students to see. And once they see it, they wonder why a sixth equation of EA = 25,000 – 5,000Δ isn’t also included. Of course, this sixth equation plus (4) and (5) are perfectly collinear, so only two of the three can be used.

Now consider the following algebraic manipulations: (2) – (1) → wB – wA = Δ = 0.0024EA – 0.0004EB. Substituting in (4) yields: Δ = 0.0024(25000 – EB) – 0.0004EB = 60 – 0.0028EB. Substituting (5) into this last equation yields: Δ = 60 – 0.0028EB. Δ = 60 – 0.0028 · 5000Δ Δ = 60 - 14Δ 15Δ = 60 Δ = $4.

A little more work, now provides the entire equilibrium: Equation (5) → EB = 5000Δ = 5000(4) = 20,000.

Equation (4) → EA = 5,000.

Equation (2) → wB = 20 – 0.0004EB = 20 – 0.0004(20,000) = $12 Equation (1) → wA = 20 – 0.0024EA = 20 – 0.0024(5,000) = $8.

Thus, the labor market equilibrium is for 20,000 workers to work in Benton, each being paid $12 per hour; for 5,000 workers to work in Ashton, each being paid $8; and for the equilibrium wage differential to be $4.

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5-14. U.S. Trucking pays its drivers $40,000 per year, while American Trucking pays its drivers $38,000 per year. For both firms, truck drivers average 240,000 miles per year.

Truck driving jobs are the same regardless of which firm one works for, except that U.S. Trucking gives each of its trucks a safety inspection every 50,000 miles while American Trucking gives each of its trucks a safety inspection every 36,000 miles. This difference in safety inspection rates results in a different rate of fatal accidents between the two companies. In particular, one driver for U.S Trucking dies in an accident every 24 million miles while one driver for American Trucking dies in an accident every 30 million miles.

What is the value of a trucker’s life implied by the compensating differential between the two firms?

To make things easy, suppose both firms require driving 120 million miles each year. This requires each firm hiring 120 million miles ÷ 240,000 miles per driver = 500 drivers. U.S. Trucking expects to experience 5 deaths in a year (120 ÷ 24) while American Trucking expects to experience 4 deaths in a year (120 ÷ 30). The 500 drivers for U.S. Trucking, therefore, are each paid $2,000 more than drivers for American Trucking to take on the expected risk of having one more death. Thus, the 1 expected life is worth 500 × $2,000 = $1,000,000. Thus, the value of a trucker’s life implied by the compensating differential between the two firms is $1 million.

5-15. When trying to quantify the compensating differential associated with a desirable fringe benefit such as health insurance, it is important to try to collect data on an equally productive set of workers. Why? Is it also true that it is important to try to collect data on an equally productive set of workers when trying to quantify the compensating differential associated with a firm characteristic that is disliked by most workers (e.g., exposure to risk of injury on the job)?

The issue, as demonstrated in Figure 5–10 in the text, is that workers with higher ability are worth more to the firm. So, for example, a low-skill worker may be worth $50,000 to the firm while a high-skill worker may be worth $100,000. Ultimately, in a competitive labor market, the lowskill worker will be compensated a total of $50,000 in some mixture of salary and fringe benefits, while the high-skill worker will be compensated a total of $100,000 in some mixture of salary and fringe benefits. Assuming that workers value fringe benefits more than cash for some reason (e.g., a tax incentive), it is quite likely that the high-skill worker will be compensate with more salary AND more fringe benefits than the low-skill worker. This is precisely the result in Figure 5 – 10 of the text between points Q (the low-skill worker) and Q* (the high-skill worker).

There is still a problem when the compensating differential is being paid for something that is disliked for precisely the same reason–different types of workers have different value to the firm, so comparing salary or wage compensation to identify compensating differentials is flawed because the observed differences will necessarily take into account differences in ability as well.

Using the case above, suppose all workers are willing to forego $10,000 in annual salary to avoid the disliked job amenity, and assume that removing the disliked amenity costs most than $10,000 in the workplace of low-skilled workers (e.g., in the mine) while removal costs must less than $10,000 in the workplace of high-skilled workers (e.g., in the office). In this case, all high-skilled workers will be paid $90,000 and not encounter the bad job amenity while all low-skill workers will be paid $50,000 but have to experience the bad job amenity. In this case, raw data would suggest that the compensating differential to avoid the bad job amenity is $40,000 when in fact it is $10,000 for both types of workers. The $40,000 number, however comes about largely because of the vast difference in value both types of workers provide the firm.

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CHAPTER 6 6-1. Debbie is about to choose a career path. She has narrowed her options to two alternatives. She can either become a marine biologist or a concert pianist. Debbie lives two periods. In the first, she gets an education. In the second, she works in the labor market. If Debbie becomes a marine biologist, she will spend $15,000 on education in the first period and earn $472,000 in the second period. If she becomes a concert pianist, she will spend $40,000 on education in the first period and then earn $500,000 in the second period.Suppose Debbie can lend and borrow money at a 5 percent rate of interest between the two periods. Which career will she pursue? What if she can lend and borrow money at a 15 percent rate of interest? Describe in general terms how Debbie’s decision depends on the interest rate.

Debbie will compare the present value of income for each career choice and choose the career with the greater present value. If the interest rate is 5 percent, PVBiologist = –$15,000 + $472,000/(1.05) = $434,523.81 and PVPianist = –$40,000 + $500,000/(1.05) = $436,190.48.

Therefore, she will become a concert pianist. If the rate of interest is 15 percent, however, the present value calculations become PVBiologist = –$15,000 + $472,000/(1.15) = $395,434.78 and PVPianist = –$40,000 + $500,000/(1.15) = $394,782.61.

In this case, Debbie becomes a biologist.

As the interest rate increases, the worker discounts future earnings more, lowering the returns from investing in education. In this case, the higher interest rate makes the payoff from the $50,000 investment into becoming a concert pianist less valuable.

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6-2. Peter lives for three periods. He is currently considering three alternative educationwork options. He can start working immediately, earning $100,000 in period 1, $110,000 in period 2 (as his work experience leads to higher productivity), and $90,000 in period 3 (as his skills become obsolete and physical abilities deteriorate). Alternatively, he can spend $50,000 to attend college in period 1 and then earn $180,000 in periods 2 and 3. Finally, he can receive a doctorate degree in period 2 after completing his college education in period 1.

This last option will cost him nothing when he is attending graduate school in the second period as his expenses on tuition and books will be covered by a research assistantship.

After receiving his doctorate, he will become a professor in a business school and earn $400,000 in period 3. Peter’s discount rate is 20 percent per period. What education path maximizes Peter’s net present value of his lifetime earnings?

The present discounted values of Peter’s earnings associated with each of the alternatives are

PV HS = 100,000 +

110,000 90,000 + = $254,167 , 1.2 1.2 2

PVCOL = −50,000 +

180,000 180,000 + = $225,000 , 1.2 1.2 2

PV PhD = −50,000 +

0 400,000 + = $227,778 .

1.2 1.2 2

and

Thus, the best option for Peter is to start working immediately upon completely high school.

6-3. Jane has three years of college, Pam has two, and Mary has one. Jane earns $21 per hour, Pam earns $19, and Mary earns $16. The difference in educational attainment is due completely to different discount rates. How much can the available information reveal about each woman’s discount rate?

The returns to increasing one’s education from one to two years of college and then from two to three years of college are

r1to 2 =

$19 − $16 $21 − $19 = 18.75% and r2to 3 = = 10.53% . $16 $19

Having observed their educational choices, we know that Mary’s discount rate is greater than 18.75 percent (otherwise she would have invested in a second year of education and earned 18.75% on the investment), Pam’s discount rate is between 10.53 percent and 18.75 percent, and Jane’s discount rate is less than 10.53 percent.

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6-4. Suppose the skills acquired in school depreciate over time, perhaps because technological change makes the things learned in school obsolete. What happens to a worker’s optimal amount of schooling if the rate of depreciation increases?

If the rate of depreciation is very high, the payoff to educational investments declines. As a result, a worker’s optimal amount of schooling will also fall as the benefits of education erode more rapidly.

6-5. (a) Describe the basic self-selection issue involved whenever discussing the returns to education.

People choose their level of education knowing their own abilities, preferences, and financial situation. Most important here is knowing one’s abilities. Highly capable people would likely earn a large salary even if they didn’t attend college, but they choose to attend because they earn even more (net of the cost of college) by doing so. Likewise, less capable people know they are less capable and that they will not get very high paying jobs even with a college degree.

Consequently, highly capably people tend to go to college while less capable people are less likely to go to college, and the average wage of college graduates is higher than the average wage of non-college graduates largely because of self-selected education levels due to innate skills or abilities.

To put numbers with the problem, suppose highly capable person would earn $50,000 without a college education and $65,000 with a college education. Similarly, a less capably person would earn $20,000 without a college education and $35,000 with a college education. All high ability people go to college, while none of the low ability people do. Clearly in this example, if one knows the numbers, one would say that the return to college is $15,000 (for either group). If one just saw the raw data of who went to college (and who did not) and each person’s income, one would falsely conclude that the return to college is $45,000. (b) Does the fact that some high school or college dropouts go on to earn vast amounts of money (e.g., Bill Gates dropped out of Harvard without ever graduating) contradict the self-selection story?

No. One, there are always exceptions. And two, if the cost of education gets large enough (or the returns to education get small enough), even high ability people will forego college.

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6-6. Suppose Carl’s wage-schooling locus is given by Years of Schooling 9 10 11 12 13 14

Earnings $18,500 $20,350 $22,000 $23,100 $23,900 $24,000

Derive the marginal rate of return schedule. When will Carl quit school if his discount rate is 4 percent? What if the discount rate is 9 percent?

The marginal rate of return is given by the percentage increase in earnings if the worker goes to school one additional year.

Schooling 9 10 11 12 13 14

Earnings $18,500 $20,350 $22,000 $23,100 $23,900 $24,000

MRR 10.0 8.1 5.0 3.5 0.4

Carl will quit school when the marginal rate of return to schooling falls below his discount rate. If his discount rate is 4 percent, therefore, he will quit after 12 years of schooling; if his discount rate is 9 percent, he will quit after 10 years of schooling.

6-7. Suppose people with 15 years of schooling average earnings of $60,000 while people with 16 years of education average $66,000. (a) What is the annual rate of return associated with the 16th year of education?

The annual rate of return is ($66,000 - $60,000) / $60,000 = 10%. (b) It is typically thought that this type of calculation of the returns to schooling is biased, because it doesn’t take into account innate ability or innate motivation. If this criticism is true, is the actual return to the 16th year of schooling more than or less than your answer in part (a)?

It is typically argued that people who are innately skilled or motivated pursue more education than those who are less innately skilled or motivated, because the cost (psychic and in terms of the time spent in college) are less for the innately skilled or motivated. If true, then the returns to education are over-estimated by this type of simple calculation (i.e., a 10% rate of return is too high). Of course, the typical story might be wrong. The innately skilled or motivated might have to give up a lot in terms of foregone earnings in order to attend college, which they might not need in the first place (e.g., Bill Gates, NBA players). If so, then the returns to education could be under-estimated.

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6-8. Suppose there are two types of people: high-ability and low-ability. A particular diploma costs a high-ability person $8,000 and costs a low-ability person $20,000. Firms wish to use education as a screening device where they intend to pay $25,000 to workers without a diploma and $K to those with a diploma. In what range must K be to make this an effective screening device?

In order for a low-ability worker to not pursue education, it must be that $25,000  K – $20,000, otherwise pursuing the diploma would be better than not pursuing the diploma for low-ability people. Thus, it must be that K  $45,000 to make sure low-ability people don’t pursue the diploma.

Similarly, in order for a high-ability worker to pursue education, it must be that K – $8,000  $25,000, otherwise not pursuing the diploma would be better than pursuing the diploma for high-ability people. Thus, it must be that K  $33,000 to make sure high-ability people pursue the diploma.

Thus, in order to use education as a signaling device in this example, it must be that educated workers are paid between $33,000 and $45,000.

6-9. Some economists maintain that the returns to additional years of education are actually quite small but that there is a substantial “sheepskin” effect whereby one receives a higher salary with the successful completion of degrees or the earning of diplomas (i.e., sheepskins). (a) Explain how the sheepskin effect is analogous to a signaling model.

The sheepskin effect is analogous (in fact it is identical) to the signaling model in that purchasing the signal doesn’t actually change the person’s skills or productivity. Rather, purchasing the signal in effect documents or reveals that the person is a high-ability person. This is exactly the same as the sheepskin effect. That is, paying the money and sitting through classes and doing the work doesn’t change the person. Rather, no one without high skills would choose to do this, so acquiring a sheepskin is a tool by which to “signal” one’s productivity even though achieving the sheepskin had not direct effect on the individual. (b) Typically in the United States, a high school diploma is earned after 12 years of schooling while a college degree is earned after 16 years of school. Graduate degrees are earned with between 2 and 6 years of post-college schooling. Redraw Figure 6-2 under the assumption that there are no returns to years of schooling but there are significant returns to receiving diplomas.

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The Wage-Schooling Locus with Sheepskin Effects Dollars

$68,000

$42,000 $30,000

$18,000 12

16

20

Years of Schooling

The bold line in the above graph gives the wage-schooling locus with sheepskin effects. In particular, anyone without a high school diploma earns $18,000; anyone with a high school diploma (and no college diploma) earns $30,000; someone with a college diploma (but not a graduate school diploma) earns $42,000; and people with a graduate degree earn $68,000.

6-10. Consider a model with two periods—the first time period is the four years after high school and the second time period is the next 40 years. A person without a college education receives $120,000 of income during the first period and $1.2 million of income during the second period. A college graduate pays $200,000 during the first period to obtain a college degree and forgoes all earnings but then earns $2 million of income during the second period. Will the individual work or go to college in the first period if her individual rate of return between the two periods is 40%?

The present value of working immediately (not going to college) is: PVNoCollege = 120,000 + 1,200,000/1.4 = $977,143 while the present value of getting a college degree is PVCollege = –200,000 + 2,000,000/1.4 = $9$1,228,571.

Therefore, as PVNoCollege < PVCollege, the individual will choose to attend college.

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6-11. One policy objective of the federal government is to provide greater access to college education for those who are less able to afford it. Recently many state governments have passed budgets that have significantly reduced funding for state universities. Using supply and demand analysis, what is the likely effect on the price of a university education to potential students? What does your model predict in terms of the number of people who will complete a university education?

Less state funding will not change the demand for education; however, less state funding means that universities will need to pay for more expenses out of their own revenue, meaning that the marginal cost of providing a university education will increase. With the supply of university educations shifting in (up), the equilibrium will be associated with a higher price for a university education and imply that fewer people will complete a university education.

Price of Education S1 P1 S0 P0

D

E1

E0

Education

6-12. In 1970, men aged 18 to 25 were subject to the military draft to serve in the Vietnam War. A man could qualify for a student deferment, however, if he was enrolled in college and made satisfactory progress on obtaining a degree. By 1975, the draft was no longer in existence. The draft did not pertain to women. According to the 2008 edition of the U.S. Statistical Abstract, 55.2% of male high school graduates enrolled in college in 1970, but only 52.6% were enrolled in 1975. Similarly, 48.5% of female high school graduates were enrolled in college in 1970, while 49.0% were enrolled in 1975. Use women as the control group to estimate (using the difference-in-differences methodology) the effect abolishing the draft had on male college enrollment.

The difference-in-differences table is

Men Women

1970 55.2 48.5

College Enrollment (percentage) 1975 Diff Diff-in-diff 52.6 -2.6 -3.1 49.0 0.5

Thus, abolishing the draft is estimated to have lowered the college enrollment rate of men by 3.1 percentage points.

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6-13. The textbook discusses in section 6–5 some strategies for correcting for ability bias when trying to estimate the rate of return to education. (a) What is the main argument for why using data on identical twins can control for ability bias? What problem arises if most pairs of identical twins pursue different levels of education? What problem arises if most pairs of identical twins pursue the same level of education?

The main argument for why using data on identical twins can control for ability bias rests on the assumption that identical twins are also identical in ability. As long as this assumption is true, then wage models can be differenced between twins, the ability portion drops out, and the true rate of return remains. (This is shown in the textbook.) There are two issues with this method.

First, if most pairs of identical twins actually pursue different levels of education, this calls into question the assumption that identical twins are identical in ability as differences in ability are a likely reason for the difference in education. Alternatively, if most pairs of identical twins pursue the same amount of education, then the rate of return to education is left to be estimated by just the small handful of twins in the sample who have pursued different levels of education. Looking at the equation in the text, Δs = 0 for any pair of twins with identical education, and therefore that observation lends no predictive information for b. (b) What is the main argument for why using certain birthdates can control for the bias?

Do you think this method will be better as identifying the rate of return to different years of high school education or college education? Why? The main idea for using birthdates (or birth quarter as is common in the literature) is that education enrollment laws provide differences in kindergarten enrollment ages. Therefore, two people can be born relatively close together in time but have up to a year different in education when they drop out of high school at age 16. This method is likely better at estimating the rate of return to additional years of a high school education than additional years of a college education, because the mechanism by which birthdate is argued to serve this role pertains to dropping out of high school. It could be useful for college as well using maturity arguments, but this is a much less clear mechanism.

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6-14. A high school graduate has to decide between working and going to college. If he works, he will work for the next 50 years of his life. If he goes to college, he will be in college for 5 years, and then work for 45 years. In this model, the rate of discount that equates the lifetime present value of not going to college and going to college is 8.24% when the cost of each year of college is $15,000, each year of non-college work pays $35,000, and each year of post-college work pays $60,000. For each of the parts below, discuss how the rate of discount that equalizes the two options would change and who would make a different schooling decision based on the change. (Extra credit: Use Excel to show that the rate of return to schooling is 8.24% in the above case, and solve for the rates of discount associated with each of the parts below.)

Calculating the rate of return for each case is straightforward in Excel by using the IRR function.

In particular, list Years from 0 to 49. Then list the salary for co college in the next column. In the next list the cost of college or the salary from college for each year. Finally, create a fourth column that is the difference in value (college minus no college). Assuming the difference values are in cells E4 through E53, the Excel command is: =IRR(E4:E53). (a) Each year of college still costs $15,000 and each year of post-college work still pays $60,000, but each year of non-college work now pays $40,000.

As the dollar benefit from not attending college has increased (from $35,000 to $40,000 annually), the return to college must fall. In fact, it falls to 5.98%. (b) Each year of college still costs $15,000 and each year of non-college work still pays $35,000, but each year of post-college work now pays $80,000.

As the dollar benefit from college has increased (from $60,000 to $80,000 annually), the return to college must also increase. In fact, it increases to 13.66%. (c) Each year of non-college work and post-college work still pays $35,000 and $60,000 respectively, but now each year of college costs $35,000.

As the dollar cost to college has increased (from $15,000 for four years to $35,000 for four years), the return to college must fall. In fact, it falls to 5.86%. (d) Each year of college still costs $15,000. The first year of non-college work pays $35,000 but then increases by 3 percent each year thereafter. The first year of post-college work pays $60,000 but then increases by 5 percent each year thereafter.

This problem boils down to the rates of change in salaries. As the non-college salary is increasing at a lower rate than the college salary is increasing, the benefits from attending college are increasing relative to the benefits from not attending college. Thus, the return to college must increase. In fact, it increases to 12.73%.

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6-15. Suppose the decision to acquire schooling depends on three factors–preferences (joy of learning), costs (monetary and psychic), and individual-specific returns to education. (a) Explain how each of these factors affects one’s optimal amount of schooling?

People who receive more joy from learning are more likely to acquire more schooling. People who face higher costs of schooling are likely to acquire less schooling. People who benefit from a greater individual-specific return to additional years of education are likely to acquire more schooling. (b) Using these three factors, explain why someone who faces a very steep returns to education function may still opt to obtain very little schooling.

Someone who faces a very steep returns to education function (so that the person benefits from a very high individual-specific return to education) might still opt to acquire very little schooling if the person absolutely hates the process of acquiring schooling or if the person faces extraordinarily high costs to schooling. At the extreme, for example, someone who faces insurmountable costs to schooling–extremely high tuition, a family situation that requires the person to work rather than go to college, laws that facilitate segregation, etc.–simply cannot acquire more schooling regardless of what the individual rate of return is. (c) Consider two groups of people – Alphas and Betas. The cost of schooling is the same for each. The average level of schooling and salary for Alpha types is 15 years and $120,000, while the average level of schooling and salary for Beta types is 13 years and $100,000. Why is it that 10%, which is calculated as ($120,000 - $100,000) / (15 – 13), is not a good estimate of the annual return to an additional year of education?

This is not a good estimate of the annual return to an additional year of education because the two groups may differ in their preferences, costs, or returns. For example, if Alpha types are more highly motivated, their average salary if only 13 years were acquired may be $116,000 (not the Beta’s average of $100,000). Similarly, if Beta types are less motivated, their average salary if 15 years were acquired may be $104,000 (not the Alpha’s average of $120,000). In this case, the annual rate of return is roughly 2%, not 10%.

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CHAPTER 7 7-1. Evaluate the validity of the following claim: The increasing wage gap between highly educated and less educated workers will itself generate shifts in the U.S. labor market over the next decade. As a result of these responses, much of the “excess” gain currently accruing to highly educated workers will soon disappear.

The incentives for young workers to stay in school rose as a result of the increasing wage differential across schooling groups. The widening wage inequality, therefore, would be expected to increase the number of young persons who obtain a college education. This increase in the supply of highly educated workers will eventually narrow the wage gap between the highly educated and the less educated. The extent to which the supply response narrows the “excess gain” depends on two parameters: (1) the elasticity of supply measuring how college enrollments respond to the increasing relative wage of college graduates; and (2) the elasticity of demand measuring the responsiveness of the relative wage of college graduates to an increase in their supply. The greater these elasticities are in the coming years, the greater role the “self-correcting” mechanism will play in reducing wage inequality in the future.

7-2. What effect will each of the following proposed changes have on wage inequality? (a) Indexing the minimum wage to inflation.

Indexing the minimum wage to inflation should reduce wage inequality because the minimum wage helps prop up the wages of less skilled workers. Note that an increase in the minimum wage may have negative employment effects, but the proposed policy is not to increase the minimum wage but rather simply to prevent it from falling in real terms. (b) Increasing the benefit level paid to welfare recipients.

Wage inequality measures the dispersion of wages in the working population. An increase in welfare benefits would likely induce less-skilled workers out of the labor force, and would reduce measured wage inequality by effectively eliminating the bottom of the wage distribution. (c) Increasing wage subsidies paid to firms that hire low-skill workers.

Wage subsidies would increase the demand for less skilled workers, reducing wage inequality.

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7-3. From 1970 to 2000, the supply of college graduates to the labor market increased dramatically, while the supply of high school (no college) graduates shrunk. At the same time, the average real wage of college graduates stayed relatively stable, while the average real wage of high school graduates fell. How can these wage patterns be explained?

The graphs below show equilibrium movements in the market for high school graduates and in the market for college graduates. The decrease in labor supply among high school graduates and the increase in labor supply among college graduates is taken as given. The analysis, therefore, focuses on labor demand for each type of labor.

Given a lower supply of high school graduates, the only way for their average wage to fall is for labor demand for high school graduates to have decreased (shifted in).

Labor Market for High School Graduates LS2000 LS1970 w1970 w2000 LD1970

LD2000 L2000

L1970

Given a greater supply of college graduates, the only way for their average wage to stay the same is for labor demand for college graduates to have increased (shifted out).

Labor Market for College Graduates

LD1970

LD

LS1970 LS2000

2000

w1970 = w2000

L1970

L2000

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7-4. (a) Is the presence of an underground economy likely to result in a Gini coefficient that over-states or under-states poverty?

The larger the underground economy, the more the Gini coefficient is likely to over-state poverty as the underground economy tends to employ low-skill, low-income workers. (b) Consider a simple economy where 90 percent of citizens report an annual income of $10,000 while the remaining 10 percent report an annual income of $110,000. What is the Gini coefficient associated with this economy?

As all citizens in each group receive an equal income, the actual Lorenz curve will be a straight line within each group. Let’s suppose there are 1,000 citizens. The 90% of poorest citizens, therefore, receive 0.90 × 1,000 × $10,000 = $9 million. The entire economy, though, earns 0.90 × $10,000 + 0.1 × $110,000 = $20 million. Therefore, the bottom 90% receives 9 ÷ 20 = 45% of total income. The perfect and actual Lorenz curves can now be drawn rather easily.

Share of Income 1.00 Perfect-Equality Lorenz Curve

Actual Lorenz Curve

0.45

0.00 0

0.9 Share of Citizens

1.00

The Gini coefficient is now easily calculated by seeing that the area beneath the actual Lorenz curve is two triangles and one rectangle. . (c) Suppose the poorest 90 percent of citizens actually have an income of $15,000 because each receives $5,000 of unreported income from the underground economy. What is the Gini coefficient now?

The problem is identical to that above, but the income levels change. In this case, per capita GDP is 0.9 x 15,000 + 0.1 x 110,000 = $24,500 so total income of the 1,000 citizens is $24,500,000.

Lastly, the total income share of the poorest 90% of citizens is 900 x 15000 ÷ 24.5 million = 55.1%. (That is, in the graph on the previous page, the income share at 90% of citizens increases from 45% to 55.1%.) The Gini coefficient is not calculated as it was before:

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7-5. Use the two wage ratios for each country in Table 7-4 to calculate each country’s percent increase in the 90-10 wage ratio from 1984 to 1994. Which countries experienced a compression in the wage distribution over this time? Which three countries experienced the greatest percent increase in wage dispersion over this time?

The results are: 90-10 Wage Gaps Country Germany Canada Norway Japan Finland France Netherlands Australia Sweden United States United Kingdom New Zealand Italy

1984 138.7 301.5 105.4 177.3 150.9 232 150.9 174.6 103.4 266.9 177.3 171.8 129.3

1994 124.8 278.1 97.4 177.3 153.5 242.1 158.6 194.5 120.3 326.3 222.2 215.8 163.8

Percent Change -10.02% -7.76% -7.59% 0.00% 1.72% 4.35% 5.10% 11.40% 16.34% 22.26% 25.32% 25.61% 26.68%

Thus, Germany, Canada, and Norway (with Japan holding constant) all experienced a compression in the wage distribution over this time. The United Kingdom, New Zealand, and Italy experienced the largest percent increases in wage dispersion.

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7-6. (a) What is the difference between income inequality and wealth inequality?

Income inequality refers to differences in earned income, sometimes just labor income, sometimes both labor and investment income. Wealth inequality refers to differences in accumulated wealth, which is driven in part by income inequality but also in part by saving and spending behavior. The difference is important, because wealth (accumulated savings) is almost always more unequal than income. (b) Most policies that target inequality either target it at the low end of the income distribution by trying to increase wages of low-income workers, or at the high end of the income distribution by limiting wages of high-income workers. List a few potential policies of each type.

Pell grants and guaranteed student loans are designed to fundamentally lessen inequality by giving children of low-income parents greater access to education. Policies like the minimum wage, the progressive tax system, and the Earned Income Tax Credit are all designed in part to partially offset income inequality by transferring resources from the rich to the poor. The estate tax is a primary policy aimed at alleviating inequality by targeting the high end as it is supposed to prohibit family dynasties in terms of wealth. (c) In your opinion, should the government focus on the low end or the high end? Why? In many people’s opinion, the government should focus most of its efforts at the low end for a couple of reasons. Most importantly, there are a lot more people at the low end than at the high end, so having effective policies in place (like Pell grants) can give everyone a chance to make decisions to help themselves economically. Also, many proposals to alleviate inequality targeted at the high end would, to some extent, stifle innovation. In simple terms, the question is whether inequality is a problem because Bill Gates created Microsoft or because 20% of minority students drop out of high school and don’t go to college. (d) In order to better understand how sensitive inequality measures are to the choice of measure, provide a graph of an economy with a 90-10 wage gap that is essentially zero but for which the Gini coefficient is close to 1.

Consider an economy where 95% of the economy earns essentially nothing, with 5% of the economic agents earning essentially everything. Such an economy will have a 90-10 wage gap that is essentially zero (as the 90 percentile person earns roughly what the 10 percentile person earns) but also has a Gini coefficient close to 1 as 5% of the agents earn almost all of the income.

Earnings Distribution Share of Income

100%

0% 0% Share of Households 95% 100%

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7-7. The two points for the international income distributions reported in Table 7-2 for countries in 2013 can be used to make a rough calculation of the Gini coefficient. Use a spreadsheet to estimate the Gini coefficient for each country. Which three countries had the most equal income distribution in 2013? Which three countries had the most unequal income distribution in 2013?

If one considers the percent of income received by the poorest and richest 10 percent of households called P and R respectively, the Gini coefficient is

Conveniently, this equation carefully reduces to Gini = 0.9(R – P). The results are: Country Australia Austria Belgium Canada Chile Dominican Republic France Germany Guatemala Hungary India Israel Italy Mexico Norway Sweden United Kingdom United States

P 3% 3% 3% 2% 2% 2% 3% 3% 1% 3% 4% 2% 2% 2% 4% 3% 3% 2%

R 27% 24% 22% 25% 36% 37% 26% 25% 42% 24% 30% 30% 26% 39% 21% 22% 25% 30%

Gini 0.216 0.189 0.171 0.207 0.306 0.315 0.207 0.198 0.369 0.189 0.234 0.252 0.216 0.333 0.153 0.171 0.198 0.252

The three countries in the sample with the most inequality in 2013 were Guatemala (0.369), Mexico (0.333), and the Dominican Republic (0.315). The three countries in the sample with the most equality in 2013 were Norway (0.153), Belgium (0.171), and Sweden (0.171). It should be emphasized that these are very crude measures as they rely on only two points in the income distribution.

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7-8. Most government-provided job training programs are optional to the worker. Describe how the self-selection issue might be used to call into question empirical results suggesting there are large economic benefits to be gained by requiring all workers to receive government-provided job training.

As job training programs are optional, and a desire or willingness to work or try to get a new job or to get retrained is probably the most important factor in a person’s success, there is certainly a self-selection story to be told. In particular, the successful people coming out of job training programs would likely have been successful even if left on their own because of their innate ability or motivation. Similarly, the people who did not choose job training and failed to get a job would likely have failed to get a job even if the government required them to pursue job training.

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7-9. Before 1990, the 80-50 and the 50-20 log wage gap was higher for women than for men (see Figure 7-7). What are some possible reasons for this?

This pattern is likely a result of three empirical facts. Before the 1990s (1) women had much lower labor force participation rates than males, (2) women were less likely to be professionals, and (3) women were more likely to work part-time. All of these “facts” are likely to lead to greater wage gaps across the wage distribution. Moreover, all of these patterns have reversed to some degree since 1990. In the 2000’s, for example, more women are in college than men, and in the near future there will be more female doctors and lawyers than male doctors and lawyers. As labor force attachment and professional options have converged for men and women since 1990, Figure 7-7 demonstrates convergence in the gender wage gaps as a result as well.

7-10. Jill is planning the timing of her on-the-job training investments over the life cycle.

What happens to Jill’s OJT investments if (a) the market-determined rental rate to an efficiency unit falls?

When the marginal revenue of investing in OJT declines, Jill will invest less at each age as the return to making the investment has fallen. (b) Jill’s discount rate increases?

If Jill’s discount rate increases she becomes more “present oriented”, reducing the future benefits associated with OJT. Thus her OJT investments fall as she no longer values the benefits from making the investment as much as she had before her discount rate fell. (c) the government passes legislation delaying the retirement age until age 70.

The marginal revenue of investing in OJT increases because the payoff period to the investment is longer. Thus, she undertakes more OJT in this case. (d) technological progress is such that much of the OJT acquired at any given age becomes obsolete within the next 10 years.

The marginal revenue to investing in OJT declines, so the amount of OJT acquired falls.

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7-11. Suppose two households earn $40,000 and $56,000 respectively. What is the expected percent difference in wages between the children, grandchildren, and great-grandchildren of the two households if the intergenerational correlation of earnings is 0.2, 0.4, or 0.6?

If the intergenerational correlation of earnings is r, the percent difference in earnings of the children is (56,000 – 40,000)r / 40,000 = 0.4r, of grandchildren is .4r2, and of great-grandchildren is .4r3. Therefore, we have that the expected percent difference in earnings is: Correlation 20% 40% 60%

Children 8% 16% 24%

Grandchildren 1.6% 6.4% 14.4%

Great-Grandchildren 0.32% 2.56% 8.64%

7-12. Suppose 50 percent of a population all receive an equal share of p percent of the nation’s income while the other 50 percent of the population all receive an equal share of 1 – p of the nation’s income where 0 ≤ p ≤ 50. (a) For any such p, what is the Gini coefficient for the country?

Calculating the Gini coefficient is most easily done with reference to a graph. Notice, given the set-up of the problem, there are two sections to the graph of the distribution of national income, and both are linear segments.

Share of Income

1

½

p

½

1

Share of Households

So, now the Gini coefficient is the area between the bold line and the dashed bold line divided by one-half. This is easiest to figure as the area below the bold line (one-half) less the area below the dashed bold line. The area below the dashed bold line equals (0.5)(0.5)p + 0.5p + (0.5)(0.5)(1 – p) = 0.25 + 0.5p.

Finally, the Gini coefficient is (0.5 – 0.25 – 0.5p) / 0.5 = 0.5 – p. (b) For any such p, what is the 90 – 10 wage gap?

Each person (percentile) in the lower half of the distribution receives 0.02pM, where M is national income. Similarly, each person (percentile) in the top half of the distribution receives 9 ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

0.02(1–p)M. As the 10th percentile person is in the lower half and the 90th percentile person is in the upper half, the 90 – 10 wage gap is 0.02(1–p)M / 0.02pM = (1–p)/p.

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7-13. Consider two developing countries. Country A, though quite poor, uses government resources and international aid to provide public access to quality education. Country B, though also quite poor, is unable to provide quality education for institutional reasons. The distribution of innate ability is identical in the two countries. (a) Which country is likely to have a more positively skewed income distribution? Why? Plot the hypothetical income distributions for both countries on the same graph.

At the outset, there is no reason to think the distribution of income is different between the two countries. However, one could argue that Country A collects more taxes than Country B, and as taxes are likely to fall more heavily on the rich, that the simple act of collecting taxes in Country A will cause it to lessen the skewness in its income distribution relative to Country B. Of course, one could make the alternative argument – that developing countries over-tax their poorest workers more than the rich. The graph below, however, assumes the first case.

Original Wage Distribution

Percent of Workers

Country A: Taxing the Rich Country B: Not Taxing the Rich

Earnings

(b) Which country is more likely to develop faster? Why? Plot the hypothetical income distributions in 20 years for both countries on the same graph.

Country A is likely to develop faster because of its savings and investments into education (human capital).

Wage Distribution after 20 Years

Percent of Workers

Country B Country A

Earnings

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7-14. Consider an economy with 10,000 individuals. Of them, 5,000 each earn $25,000; 3,000 each earn $40,000; and 2,000 each earn $100,000. (a) What is the Gini coefficient for this economy?

Total income in the economy is 5,000 × $25,000 + 3,000 × $40,000 + 2,000 × $100,000 = $445 million. The bottom group receives 5,000 × $25,000 / $445m = 28.09%. The middle group receives 3,000 × $40,000 / $445m = 26.97%. The top group receives 2,000 × $100,000 / $445m = 44.94%. Therefore, the Gini coefficient is calculated as:

The calculation produces a Gini coefficient equal to 0.30. (b) What would the Gini coefficient be if the wealthiest 2,000 individuals were taxed 30% of their income with the proceeds being transferred to the 5,000 poorest individuals?

To begin we need to know what the amount of the transfer is. As the wealthiest group is taxed at 30%, their $100,000 incomes will be reduced to $70,000. Moreover, as there are 2,000 people in this group, total tax revenue equals 2,000 × $30,000 = $60 million. This $60 million is equally distributed to the poorest 5,000 individuals, so each of these individuals receives an additional $60m / 5,000 = $12,000 in income for a total income of $37,000 per individual. Now the problem can be repeated as above.

Total income in the economy is 5,000 × $37,000 + 3,000 × $40,000 + 2,000 × $700,000 = $445 million. The bottom group receives 5,000 × $37,000 / $445m = 41.57%. The middle group receives 3,000 × $40,000 / $445m = 26.97%. The top group receives 2,000 × $70,000 / $445m = 31.46%. Therefore, the Gini coefficient is calculated as:

The calculation produces a Gini coefficient equal to 0.1247. Thus, the tax transfer reduced inequality quite substantially if one considers the Gini coefficients you produced in question 7 for a wide variety of countries.

7-15. Explain why the intergenerational correlation of earnings would likely be higher or lower than average for the following groups and factors in the United States: (a) Improved educational outcomes for all populations (e.g., minority, low-income, rural).

Improved educational outcomes for all populations should lower the intergenerational correlation of earnings as wealth becomes less of a factor in determining educational outcomes and economic success. (b) The elimination of legacy admits to colleges and universities.

The elimination of legacy admits to colleges and universities should lower the intergenerational correlation of earnings as parental education becomes less of a factor in determining educational outcomes and eventually economic success. (c) The implementation of a federal inheritance tax.

The implementation of a federal inheritance tax should lower the intergenerational correlation of earnings as children are less able to benefit from their parent’s wealth.

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CHAPTER 8 8-1. Suppose a worker with an annual discount rate of 10 percent currently resides in Pennsylvania and is deciding whether to remain there or to move to Illinois. There are three work periods left in the life cycle. If the worker remains in Pennsylvania, he will earn $20,000 in each of the three periods. If the worker moves to Illinois, he will earn $22,000 in each of the three periods. What is the highest cost of migration that a worker is willing to incur and still make the move?

The worker must compare the present value of staying in Pennsylvania to the present value of moving to Illinois. A worker will move if the present value of earnings in Illinois minus the costs of moving there exceed the present value of earnings in Pennsylvania: PV PA = 20,000 +

20,000 20,000 + = $54,710.74 1.1 (1.1) 2

PV IL = 22,000 +

22,000 22,000 + = $60,181.82 1.1 (1.1) 2

and

The worker will move, therefore, if PVIL – C > PVPA, where C denotes migration costs. Thus, the worker moves if C < 60,181.82 – 54,710.74 = $5,471.08

8-2. Suppose high-wage workers are more likely than low-wage workers to move to a new state for a better job. (a) Explain how this migration pattern can be due solely to differences in the distribution of wages.

Suppose migration costs are the same for all workers at $3,000. Suppose further that all lowwage workers are paid either $20,000 or $22,000 depending on productivity and location, and that all high-wage workers are paid either $40,000 or $45,000 depending on productivity and location. The immediate result is that no low-wage worker will ever migrate, while all high-wage workers who are not already earning $45,000 will migrate to a location where they are valued at $45,000. (b) Explain how this migration pattern can take place even if the cost to moving is greater for high-wage workers.

What matters is the difference in wages due to migration and the cost of migration. In the previous example, for instance, even if the cost to migration was $4,000 for high wage workers while it remained at $3,000 for low-wage workers, the same pattern of no low-wage workers migrating and all high-wage workers migrating until they find a job that pays $45,000.

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8-3. Patrick and Rachel live in Seattle. Patrick’s net present value of lifetime earnings in Seattle is $125,000, while Rachel’s is $500,000. The cost of moving to Atlanta is $25,000 per person. In Atlanta, Patrick’s net present value of lifetime earnings would be $155,000, while Rachel’s would be $510,000. If Patrick and Rachel choose where to live based on their joint well-being, will they move to Atlanta? Is Patrick a tied-mover or a tied-stayer or neither?

Is Rachel a tied-mover or a tied-stayer or neither?

As a couple, the net present value of lifetime earnings of staying in Seattle is $500,000 + $125,000 = $625,000 and of moving to Atlanta is $510,000 + $155,000 – $50,000 = $615,000.

Thus, as a couple, they would choose to stay in Seattle.

For Patrick, staying in Seattle is associated with a net present value of $125,000, while moving to Atlanta would yield a net present value of $155,000 – $25,000 = $130,000. So Patrick would choose to move to Atlanta. Therefore, Patrick is a tied-stayer.

For Rachel, staying in Seattle is associated with a net present value of $500,000, while moving to Atlanta would yield a net present value of $510,000 –$25,000 = $485,000. So Rachel would choose to remain in Seattle. Thus, Rachel is not a tied-stayer.

8-4. Consider a household consisting of four college friends. The friends have made a commitment to live together for the next five years. Presently they live in Milwaukee where Abby will earn $200,000, Bonnie will earn $120,000, Cathy will earn $315,000, and Donna will earn $150,000 over the next five years. They have the option of moving to Miami.

Moving to Miami would impose a one-time moving cost of $5,000 on each person. If they move to Miami, however, Abby will earn $180,000, Bonnie will earn $150,000, Cathy will earn $300,000, and Donna will earn $100,000 over the next five years. Moreover, each friend prefers to live in Miami over Milwaukee. In particular, Abby and Bonnie both value the quality of life in Miami versus Milwaukee over the next five years at $40,000 while Cathy and Donna place the value at $25,000 each. Should the household move to Miami or stay in Milwaukee? Is anyone a tied-mover or a tied stayer?

The present value of staying in Milwaukee is calculated in thousands of dollars as PVMIL = $200 + $120 + $315 + $150 = $785.

The present value of moving to Miami is calculated as PVMIAMI = $180 + $150 + $300 + $100 - $20 + $80 + $50 = $840.

Therefore, the household will move to Miami as PVMIAMI > PVMIL. As a result, no one can be a tied-stayer as the household doesn’t stay in Milwaukee. To determine if anyone is a tied-mover, one must calculate the present value calculations for each friend.

Abby: PVMIL = $200 vs PVMIAMI = $180 - $5 + $40 = $215 → Abby wants to move.

Bonnie: PVMIL = $120 vs PVMIAMI = $150 - $5 + $40 = $185 → Bonnie wants to move.

Cathy: PVMIL = $315 vs PVMIAMI = $300 - $5 + $25 = $329 → Cathy wants to move.

Donna: PVMIL = $150 vs PVMIAMI = $100 - $5 + $25 = $2120 → Bonnie wants to stay.

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Thus, Donna is the only tied-mover while the other three friends all strictly prefer to move to Miami.

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8-5. Suppose the United States enacts legislation granting all workers, including newly arrived immigrants, a minimum income floor of y dollars. (Assume there is positive selection of migrants from the home country to the U.S. before the policy change.) (a) Generalize the Roy model to show how this type of welfare program influences the incentive to migrate to the United States. Ignore any issues regarding how the welfare program is funded.

The introduction of a wage floor in the United States (at − y ) shifts the U.S. earnings-skill relationship from the straight line (U.S.) to the bold line (kinked) drawn in the figure below. The welfare program does not affect the incentives of foreigners with high or even moderate skills.

However, it does affect the incentives of those with the least skills as they earn very little in the home country and now can come to the United States and benefit from the welfare benefit.

U.S. Labor Market U.S. Dollars Home Country y αO

αU

Don’t Move

Move sL

Move SH

Skills

(b) Does this welfare program change the selection of the immigrant flow? In particular, are immigrants more likely to be negatively selected than in the absence of a welfare program?

As drawn above, before the welfare program was enacted there was only positive selection in terms of immigration to the United States. With the welfare benefit in place, though, foreigners with skills below sL now also find it profitable to migrate. Thus, the selection of immigrants becomes more negative. In fact, it is a bimodal distribution–foreigners with the highest skills continue to migrate and now those with the lowest skills also choose to migrate. (c) Which types of workers, the highly skilled or the less skilled, are most likely to be attracted by the welfare program?

As the returns to skills are higher in the United States, there are two sets of workers who find it profitable to move: those who have very high skill levels (above sH) as well as those workers who have very low skill levels (below sL). The welfare program, therefore, acts as a welfare magnet for workers originating in countries that generate “brain drains”, but not in countries where unskilled workers have incentives to migrate even in the absence of wage floors.

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8-6. In the absence of any legal barriers on immigration from Neolandia to the United States, the economic conditions in the two countries generate an immigrant flow that is negatively selected. In response, the United States enacts an immigration policy that restricts entry to Neolandians who are in the top 10 percent of Neolandia’s skill distribution. What type of Neolandian would now migrate to the United States?

No one would migrate from Neolandia. The policy does not change the cost-benefit analysis for the most skilled Neolandians. They did not want to migrate when they could enter the country freely, and they still will not want to migrate when they are the only ones who can obtain visas.

The lesson is that changes in immigration policy affect the skill composition of the immigrant flow only if policy changes target immigrants who wished to migrate to the United States in the first place or provide a new incentive to those who did not.

8-7. One trend in the U.S. labor market in the 2100s is telecommuting or working at home.

More and more firms allow working from home, and many firms even allow employees to live and work in one city for most of the year, flying to the firm’s headquarters for 3 or 4 days of work every quarter. How is this trend likely to affect job mobility (i.e., workers switching jobs)? How is this trend likely to affect internal migration raters in the U.S. (i.e., households moving cities)?

Using the standard migration model, when a worker doesn’t need to move cities to accept a new job, that worker faces a lower if not zero switching cost, which allows the worker to switch jobs more easily (i.e., imposing less cost and trauma on the entire household). So looking at the problem through a “migration cost” or “job switching cost” model, job turnover should increase.

One could make the argument that although more firms are allowing telecommuting because of technology advances, we know that workers value this option (otherwise it wouldn’t be a trend).

Viewing telecommuting as a benefit that workers value, therefore, likely makes workers more attached to their current job where telecommuting exists. Thus, lowering job mobility. This argument, though, is tenuous. Assuming a worker currently holds job A and is considering job B and both offer telecommuting, then this benefit does not place either job in a better position.

The trend in telecommuting should also manifest itself with lower internal migration raters in the U.S. as workers can switch jobs (increased mobility) without switching locations.

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8-8. In addition to it being illegal to enter the U.S. without a visa or to over-stay one’s visa, it is also illegal for U.S. employers to hire undocumented or “illegal” immigrants. Meanwhile, federal U.S. enforcement of immigration laws tends to concentrate resources on reducing illegal immigration rather than on prosecuting U.S. firms for employing undocumented workers. Using supply and demand analysis, show what would happen to the wage and employment level of undocumented workers if the government pursued more active enforcement of employers. According to your model, what would happen to the wage and employment level of documented workers?

This problem is best answered by considering two labor markets concurrently – the market for undocumented workers and the market for documented workers. Focusing enforcement on the employers (i.e., fining employers caught employing undocumented workers) would decrease the demand for undocumented workers. Essentially, if the cost of hiring undocumented workers increases because of potential fines, then in order to hire the same number of such workers, the wage will need to fall.

What would happen in the market for documented workers is a little unclear. Certainly employment wouldn’t fall, nor would wages. One could make the argument that nothing would happen in this market. (For example, maybe an employer will replace all undocumented workers with machines.) However, more likely is that the demand for documented workers will increase, not because such workers are all of a sudden more productive, but rather because the legal cost of hiring such workers has fallen, at least relatively.

In the analysis below, it is assumed that the enforcement mechanism lowers the demand for undocumented workers and increases the demand for documented workers. The result is that the employment and wage of undocumented workers both fall while the employment and wage of documented workers both increase.

Market of Undocumented Workers

Market for Documented Workers

ED0

ED1

Wage ES

WU0

WD,1

WU1

WD0

ES

ED1

EU1

EU0

ED0

Undoc. Wkrs

ED0

ED1

Doc. Wkrs

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8-9. Under 2001 tax legislation enacted in the United States, all income tax filers became eligible to deduct from their total income half of their expenses incurred when moving more than 50 miles to accept a new job. Prior to the change, only tax filers who itemized their deductions were allowed to deduct their moving expenses. (Typically, homeowners itemize their deductions and renters do not itemize.) How would this change in tax policy likely affect the mobility of homeowners and renters?

The policy change has no effect on homeowners, whereas the policy change reduces the cost of moving for renters. Therefore, the policy is predicted to increase the mobility of renters.

8-10. Suppose the immigrant flow from Lowland to Highland is positively selected. In order to mitigate the “brain drain” Lowland experiences as a result of this migration, public officials of Lowland successfully convince all Lowlanders who migrate to Highland to remit 10 percent of their wages to family members. (a) What effect will this policy have on the immigrant flow?

The policy, in essence, increases the cost of migration. In particular, the policy convinces everyone who is thinking about immigrating to act as if their wage in Highland will be 90% of what it actually is because immigrants “must” remit 10% of their earnings. Therefore, if all people in Lowland would have to agree to remittances before immigrating to the Highland, the selection would become even more positively skewed as people who used to be close to the margin but decided to immigrate will now be on the other side of the margin and decide to not immigrate (and these people are the least skilled of the original immigrants). (b) Provide a graph that details the extent to which this policy will limit the brain drain.

The implication is that fewer people will immigrate from Lowland to Highland, with the action taking place on the margin (section A in the graph below). Thus, the policy limits the brain drain partially as some high skill people who otherwise would have immigrated no longer do.

However, the policy will not prevent the most skilled people from still immigrating. Thus, Lowland still experiences brain drain of its best people.

In particular, the graph shows that Lowlanders with skills in A or B immigrate to Highland before the policy. After the policy, those in B still immigrate, but those in A no longer opt to do.

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Earnings

Return to Skill in Highland Pre-Policy

Return to Skill in Highland Post-Policy

Return to Skill in Lowland

A

B Skills

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8-11. (a) According to standard migration theory, how will skill selection (positive vs. negative) change on average as the distance between the source country and the destination country increases?

The further two countries are apart from each other, the greater are the monetary costs of migrating just in terms of traveling to the destination country, but also in terms of returning home for visits, possibly in terms of culture, etc. Thus, skill selection should be more and more positively selected the further the home country is from the destination country. (b) The 1990 U.S. Census data can be used to estimate the average wage differential between immigrants to the U.S. by country of origin, and compare those to the average native wage of workers with similar characterizes such as education, age, occubpation, etc.

The data suggest that the average Canadian immigrant earns about 25% more than Americans while the average Mexican immigrant earns about 40% less. Similarly, Indian immigrants earn about 12% more than Americans while Vietnamese immigrants earn almost 20% less. Do these empirical results support the idea that skill selection is a monotonic function of the distance between countries? If not, what might explain the differences?

If the theory held perfectly and skill selection was monotonic by distance, the estimates for Canadians and Mexicans should be similar, the estimates for Indians and Vietnamese should be similar, and the estimates for Indians/Vietnamese should be less (or more negative) than the estimates for Canadians/Mexicans. Therefore, these empirical results do not lend support that skill selection is monotonic with distance. One likely explanation is that, while distance matters, culture and or language matter more. It is probably no coincidence that the data from Canada and India, two English-speaking countries, suggest positive selection while the data from Mexico and Vietnam, two non-English-speaking countries, suggest negative selection.

8-12. (a) Explain how a universal healthcare system would likely cause a greater amount of efficient turnover.

Presently, many Americans receive employer-based health insurance. That is, employers pay a portion (or all of) the insurance premiums. The benefit of health insurance, therefore, would be lost if the employee separates from the job. In particular, many people would refuse to leave one job with health insurance benefits for another (even higher paying) job without health insurance benefits simply because of the risk. Under a universal healthcare system, everyone receives health benefits regardless of employment. Thus, workers would not feel tied to a particular job simply because they were currently receiving benefits. Consequently, a universal healthcare system would likely cause a greater amount of efficient labor turnover as workers seek out better employer matches without worry about losing healthcare benefits. (b) Defined-benefit retirement plans promise a fixed amount of retirement income to workers, but in order to receive benefits workers must be vested in the plan which usually requires working at the firm for 10 or 15 years. In contrast, a defined-contribution retirement plan specifies a fixed amount of money the firm contributes each pay period to a worker’s retirement fund which the worker then largely controls and can access even if she 9 ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

changes jobs. Do defined-benefit or defined-contribution retirement plans allow for more efficient turnover?

Defined-contribution retirement plans allow for more efficient labor turnover, because the money (i.e., value of the benefit/asset) is in the employee’s control and belongs to the employee even after separating from the job. So, just like in part (a), a defined-contribution plan follows the worker from job to job just like a universal healthcare system would, while a defined-benefit plan that requires the employee to become vested with the plan ties the employee to the firm just like employer provided health insurance. (c) When federal workers in Washington D.C. move jobs from one federal agency to another, the worker keeps her same health insurance and retirement benefits. In order to quantify the degree to which ease of transfer of benefits affects job sorting, two groups of new economists Ph.Ds. who accept a job in Washington D.C. are observed. The first group are US citizens. The second group are non-US residents who eventually received permanent resident status after 3 years of work experience. By law, several government agencies cannot hire non-residents. Among the group of US citizens, 42 percent changed jobs within the first 3 years of work while 33 percent changed jobs during their fourth to sixth years of work. Among the group of non-US residents, 17 percent changed jobs in the 3 years before becoming a resident while 29 percent changed jobs in the 3 years after becoming a US resident. Provide a difference-in-differences estimate of the effect of being a US resident/citizen in Washington D.C. for Ph.D. economists on job sorting.

The data generate the following table.

Group U.S. Citizens Non-Citizens

Turnover Years 0 – 3 0.42 0.17

Turnover Years 4 – 6 0.33 0.29

Difference -0.09 +0.12

Diff-in-Diff +0.21

Receiving a green card, which opens up job possibilities, therefore, is associated with a turnover rate that is 21 percentage points higher.

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8-13. The Immigration Reform Act of 2006 provided fewer work visas than were available in previous years for college graduates to remain in the United States. The exception is that work visas remained plentiful for college graduates who majored in technical areas such as math, computer programming, and physics. (a) How will this policy likely affect the skill distribution of immigrants to the United States and the age-earnings profile of immigrants in the United States?

The policy favors high-tech college majors, not so much in terms of attracting them to the United States but rather in terms of allowing them to stay once they were educated in the United States.

Thus, the policy will likely allow more high-tech (high-skill) immigrants to stay in the U.S. while requiring others to leave the U.S. after college. Measured in terms of wages, therefore, the policy will likely result in a greater positive skill-selection and result in a higher age-earnings profile of new immigrants. (b) In the future a demographer uses the 2010 U.S. census to study immigrant wages and concludes that the U.S. policy actually had the unintended consequence of attracting immigrants with lower levels of productivity as shown by a flatter age-earnings profile.

Using a graph similar to Figure 8-7, show why the demographer’s conclusions are sensitive to cohort effects.

Dollars

2000 Wave 1990 Wave

Cohort Implied AgeEarnings Profile

Age 22-28

32-38

In 2010 when using cohort analysis, the age-earnings profile will appear to be flatter than during similar previous studies. This is because the average wage of 20-something immigrants will be higher than it would have been without the policy and therefore the profile between 20somethings and 30-somethings will appear to be less steep. Put differently, because of the higher earnings of the younger cohort, the age-earnings profile implied by the 1990 and 2000 cohorts appears to be very flat.

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8-14. KAPC, a pharmaceutical company located in rural Kansas, is finding it difficult to retain its employees who frequently leave after just six months for jobs at pharmaceutical companies paying higher wages in Chicago. To address its problem with labor turnover, human resource officers at KAPC decide to run an experiment. Of their next 100 newly hired employees, 25 will randomly be selected to receive a housing voucher worth up to $4,000 per year to offset property taxes. To take advantage of this program, the employee must not only be randomly selected into the program but she must also purchase a home.

Of the 25 employees selected into the housing voucher program, 7 leave KAPC within 12 months of starting. Of the 75 employees not selected into the program, 37 leave KAPC within 12 months of starting. (a) Provide an estimate of the effect the housing voucher program has on retention at KAPC. The problem doesn’t give quite enough information to perform a pure diff-in-diff estimation, but we can make one simple assumption and then generate the results. The assumption is that 49.3% (37 out of 75) of all new employees leave KAPC within 1 year of being hired if they are not given a housing subsidy, and this rate applies pre- and post- subsidy. The data are now:

Group Control Group Rec. Subsidy

Leave in 1 Year Pre-Experiement 0.493 0.493

Leave in 1 Year Post-Experiment 0.493 0.280

Difference 0.00 -0.213

Diff-in-Diff -0.213

Notice that although the table above makes the estimate look like a difference-in-differences estimate, it really is just a difference estimate. That said, the policy seems to have a striking effect, reducing the probability someone leaves KAPC in the first year by 21.3 percentage points. (b) Suppose KAPC spends $10,000 in hiring costs each time a position is vacated. Would you endorse expanding the housing voucher program to all new employees? Justify your decision.

Consider 100 hires. Without the housing subsidy, KAPC expects to pay $10,000 on each hire and, after one year, to have 51 (50.7%) of these workers remain. Thus, it costs $1 million to hire 51 workers (100 × $10,000 = $1 million).

With the housing subsidy, as 72% of those hired remain, KAPC needs to hire 51 ÷ 0.72 = 71 workers in order to have 51 remain employed after one year. Thus, KAPC spends $710,000 on hiring costs. However, it also gives each worker a subsidy of $4,000, which totals $284,000. The total cost, therefore, is $994,000.

By the slimmest of margins, therefore, the policy is economically justifiable. If the housing voucher is renewable, however, then the policy is not efficient as KAPC would end up paying the remaining 51 workers each an additional $4,000 every year.

Lastly, the problem never specifies what percent of people who are offered the voucher actually use it (i.e., actually buy a house). Thus, $784,000 is the highest possible cost to the program.

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8-15. Consider the Roy model of potential immigrant flows as discussed in the chapter. (a) Why is it that a source country can experience both an outflow of low-skill workers and an outflow of high-skill workers at the same time?

In reality a source country will experience an outflow of low-skill and high-skill workers at the same time because of individual preferences–some people will want to immigrate regardless of the skills issue.

In theory and in practice, however, a source country can experience an outflow of low-skill and high-skill workers at the same time because the returns to skills in the two countries are not linear as the model in the text suggests. In the United States, for example, the returns to low-skills may be much greater than in Mexico. At the same time, the returns to high-skills may also be much greater in the United States than in Mexico. In the middle, though, the returns may be relatively higher in Mexico. If so, then Mexico will experience an outflow of low-skill and high-skill workers. (b) Provide a graph of the returns to skills in the destination and source countries that would suggest both behaviors occur simultaneously.

Returns in Destination Country Returns in Source Country

Move

Don’t Move

Move

Skills

(c) How do the social and economic (i.e., tax) policies of the United States encourage both types of flows?

The policies of the United States may encourage both types of flows in that the social safety net, working conditions, etc. are better for low-income, low-skill workers in the United States than in Mexico. At the same time, the highest tax rate is only 35% and wealth and liberty are wellprotected for everyone (including the wealthy) in the United States. In combination, these policies likely attract the lowest-skilled and highest-skilled Mexicans.

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CHAPTER 9 9-1. Feeling that local firms follow discriminatory hiring practices, a non-profit firm conducts the following experiment. It has 200 white individuals and 200 black individuals, all of whom are similar in age, experience, and education, apply for local retail jobs. Each individual applies to two jobs, one in a predominantly black part of town and one in a predominantly white part of town. Of the white applicants, 120 are offered jobs in the white part of town while only 80 are offered jobs in the black part of town. Meanwhile, 90 of the black applicants are offered jobs in the black part of town while only 50 are offered jobs in the white part of town. Using a difference-in-differences estimator, do you find evidence of discriminatory hiring practices? If there is evidence of discrimination, is it appropriate to conclude that all employers in the white part of town are discriminatory?

The data can be used to create the following table.

Type of Worker Black White

Chance of Receiving a Job Offer in the: Black part of town White part of town 90 ÷ 200 = 0.45 50 ÷ 200 = 0.25 80 ÷ 200 = 0.40 120 ÷ 200 = 0.60

Difference -0.20 0.20

Diff-in-Diff 0.40

There does appear to be discrimination as whites are 40% more likely to be offered jobs in the white part of town after controlling for differences elsewhere. Despite potential evidence of discrimination, it is inappropriate to conclude that all employers in the white part of town are discriminatory. Some may be, but others might not be. Even in the white part of town, 25% of black job candidates received an offer. These offers are likely not coming from discriminatory employers.

9-2. Suppose black and white workers are complements in that the marginal product of whites increases when more blacks are hired. Suppose also that white workers do not like working alongside black workers. Under what conditions will this employee discrimination lead to a segregated workforce? Under what conditions will it not?

As blacks and whites are complements in the production process, there is an incentive for employers to employ blacks and whites together in the work place. The question is whether the increase in productivity achieved by integrating the work force is higher than the extra wages employers must pay white workers to compensate them for working alongside blacks. Thus, as long as the differential needed to encourage white workers to work with black workers is not too large, the workplace will not be completely segregated. It is only if the differential needed to encourage white workers to work with black workers is larger than the productivity gain of having them work side-by-side that workplaces will be segregated.

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9-3. Suppose a restaurant hires only women to wait on tables, and only men to cook the food and clean the dishes. Is this most likely to be indicative of employer, employee, consumer, or statistical discrimination?

If this hiring pattern is due to discrimination at all, it is most likely due to customer discrimination. It is not employer discrimination as the employer is hiring both men and women.

It is further unlikely to be statistical discrimination as an employer would likely be able to determine in a short time what would happen if women became cooks or men waited on tables.

The hiring pattern could result from employee discrimination as well, but this seems unlikely as wait staff and chefs/dishwashers interact on the job.

9-4. A firm’s production function is given by Q = 40 ln(EW + EB + 1) where EW and EB are the number of whites and blacks employed by the firm respectively. From this it can be shown that the marginal product of labor is

Suppose the market wage for blacks is $50, the market wage for whites is $100, and the price of each unit of output is $20. (a) How many workers of each race would a non-discriminating firm hire? How much profit is earned if there are no other costs?

A non-discriminating firm will hire all black workers as labor enters the marginal product function as a sum and the black wage is less than the white wage. Therefore, the firm solves: VMPE = wB P × MPE = wB

EB + 1 = 16 EB = 15.

Given that the firm hires 15 black workers and 0 white workers, output is Q = 40ln(16) ≈ 111.

Therefore, profit is π = $20 × 110 – 15 × $50 = $1,450. (b) How many workers of each race would a firm with a discrimination coefficient of 0.6 against blacks hire? How much profit is earned if there are no other costs?

A discriminating firm with a discrimination coefficient of 0.6 will compare the white wage of $100 to the adjusted black wage of 1.6 × $50 = $80. As the adjusted black wage is still less than the white wage, this firm will also hire all black workers, but it will use the adjusted wage in the calculation. Therefore, the firm solves: 2 ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

VMPE = (1 + d) × wB P × MPE = (1 + d) × wB

EB + 1 = 10 EB = 9.

Given that the firm hires 9 black workers and 0 white workers, output is Q = 40ln(9) ≈ 88.

Therefore, profit is π = $20 × 88 – 9 × $50 = $1,310. (c) How many workers of each race would a firm with a discrimination coefficient of 1.2 against blacks hire? How much profit is earned if there are no other costs?

A discriminating firm with a discrimination coefficient of 1.2 will compare the white wage of $100 to the adjusted black wage of 2.2 × $50 = $110. As the adjusted black wage is more than the white wage, this firm will hire all white workers. Therefore, the firm solves: VMPE = wW P × MPE = wW

EW + 1 = 8 EW = 7.

Given that the firm hires 0 black workers and 7 white workers, output is Q = 40ln(7) ≈ 78.

Therefore, profit is π = $20 × 78 – 7 × $100 = $860.

9-5. Suppose years of schooling, s, is the only variable that affects earnings. The equations for the weekly salaries of male and female workers are given by: wm = 500 + 100s and wf = 300 + 75s.

On average, men have 14 years of schooling and women have 12 years of schooling. (a) What is the male-female wage differential in the labor market?

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The wage differential can be written as: w = wm − w f = 500 + 100s m − (300 + 75s f ) = 500 + 100(14) – 300 – 75(12) = $700.

(b) Using the Oaxaca-Blinder decomposition, calculate how much of this wage differential could be due to discrimination?

The raw wage differential is w = ( m − f )+(  m − f ) s f +    Differential Due to Discrimina tion

 ( s m −s f ) m  Differential Due to Difference in Skills

= (500−300)+(100−75)12 +   

100(14−12) 

Differential Due to Discrimina tion

Differential Due to Difference in Skills

= $500 + $200 = $700 .

The wage differential that could be due to discrimination equals $500, or 5/7ths of the raw differential.

9-6. Suppose the firm’s production function is given by

q = 10 Ew + Eb , where Ew and Eb are the number of whites and blacks employed by the firm respectively. It can be shown that the marginal product of labor is then

5 .

Ew + Eb

MPE =

Suppose the market wage for black workers is $10, the market wage for whites is $20, and the price of each unit of output is $100. (a) How many workers would a firm hire if it does not discriminate? How much profit does this non-discriminatory firm earn if there are no other costs?

There are no complementarities between the types of labor as the quantity of labor enters the production function as a sum, Ew + Eb. Further, the market-determined wage of black labor is less than the market-determined wage of white labor. Thus, a profit-maximizing firm will not hire any white workers and will hire black workers up to the point where the black wage equals the value of their marginal product: 10 = wb is set equal to VMPB = pMPE =

100(5) Eb

which solves as

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Eb = 2,500.

The 2,500 black workers produce q = 10(sqrt(2,500)) = 500 units of output, and profits are: π = pq – wbEb = 100(500) – 10(2,500) = $25,000. (b) Consider a firm that discriminates against blacks with a discrimination coefficient of .25. How many workers does this firm hire? How much profit does it earn?

The firm acts as if the black wage is wb(1 + d), where d is the discrimination coefficient. The employer’s hiring decision, therefore, is based on a comparison of ww and wb(1 + d). The employer will then hire whichever input has a lower utility-adjusted price. As d = 0.25, the employer is comparing a white wage of $20 to a black (adjusted) wage of $12.50. As $12.50 < $20, the firm will hire only blacks.

As before, the firm hires black workers up to the point where the utility-adjusted price of a black worker equals the value of marginal product, or 12.50 =

100(5) Eb

so that Eb= 1,600 workers. The 1,600 workers produce 400 units of output, and profits are π = 100(400) – 10(1,600) = $24,000. (c) Finally, consider a firm that has a discrimination coefficient equal to 1.25. How many workers does this firm hire? How much profit does it earn?

As d = 1.25, the employer compares a white wage of $20 against a black wage of $22.50. Thus, the firm hires only whites. The firm hires white workers up to the point where the price of a white worker equals the value of marginal product: 20 =

100(5) Ew

so the firm hires 625 whites, produces 250 units of output, and earns profits of π = 100(250) – 20(625) = $12,500.

9-7. Cindy, a tenured, full professor of French literature at a large university, is paid $60,000. The university reports median salaries by gender and rank as a new initiative on faculty compensation. From reading the report, Cindy learns that she is paid $20,000 below the median for male, tenured, full professors. She is also paid $12,000 below the median for female, tenured, full professors. What factors might explain Cindy’s position in the 5 ©McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.

wage distribution? Why might or might not the university be engaged in gender discrimination?

Many factors explain the distribution of wages. Gender discrimination could exist at the university. But additionally, her lower pay may be a result of her having been at the university for fewer years, her field of French literature is likely paid less than full professors in finance, and she may have received fewer grants for her research compared to her colleagues in Biology.

Even looking at the gender difference ($20,000 less than the median male vs. $12,000 less than the median female) may not be due to gender discrimination. The overall distribution of female salaries at a university would be expected to be lower than the overall distribution of male salaries if females are less likely to go into the hard sciences (which are known to pay more),

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9-8. Consider the following log-wage regression results for women (W) and men (M) where wages are predicted by schooling (S) and age (A). wW = 2.19 + 0.075SW + 0.023AW and wM = 2.42 + 0.072SM + 0.017AM. Sample means for the variables by gender are: women average a logged wage of 3.83, 13.5 years of schooling, and 41.2 years-old; men average a logged wage of 3.92, 13.2 years of schooling, and 44.3 years0old. Decompose the raw difference in average logged wages using the Oaxaca-Blinder decomposition. Specifically, decompose the raw difference into the portion due to differences in schooling, differences in age, and the portion left unexplained, possibly due to gender discrimination.

The raw logged wage gap is 3.92 – 3.83 = 0.09. For the two variables in the regression we have: School: βM = 0.072 and the difference in average schooling of 13.2 – 13.5 = –0.3 so that the decomposition due to schooling is –0.3 × 0.072 = –0.0216.

Age:

βM = 0.017 and the difference in average ages of 44.3 – 41.2 = 3.1 so that the decomposition due to age is 3.1 × 0.017 = 0.0527.

Thus, schooling and age explain –0.0216 + 0.0527 = 0.0311 of the wage gap. This leaves 0.09 – 0.0311 = 0.0589 of the wage gap left unexplained, possibly due to gender discrimination.

9-9. Each employer faces competitive weekly wages of $2,000 for whites and $1,400 for blacks. Suppose employers under-value the efforts/skills of blacks in the production process. In particular, every firm is associated with a discrimination coefficient, d where 0 ≤ d ≤ 1. In particular, although a firm’s actual production function is Q = 10(EW + EB), the firm manager acts as if its production function is Q = 10EW + 10(1 – d)EB. Every firm sells its output at a constant price of $240 per unit up to a weekly total of 150 units of output. No firm can sell more than 150 units of output without reducing its price to $0. (a) What is the value of the marginal product of each white worker?

The value of marginal product of each white worker is $2,400, because each white worker produces 10 units of output, and each unit of output (up to 150 units) can be sold for $240. (b) What is the value of the marginal product of each black worker?

The value of marginal product of each black worker is $2,400, because each black worker produces 10 units of output, and each unit of output (up to 150 units) can be sold for $240.

Notice that discriminatory beliefs on the part of the firm owner do not affect a black worker’s true marginal product.

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(c) Describe the employment decision made by firms for which d = 0.2 and d = 0.8 respectively.

The firm owner views each black worker as contributing 10(1 – d) units of production, and therefore views each black worker’s value of marginal product to be $2,400(1 – d). When d = 0.8, therefore, the firm views each black worker’s value of marginal product to be $480, and when d = 0.2 the firm views each black worker’s value of marginal product to be $1,920.

When d = 0.2.

Each white worker costs $2,000 and produces $2,400 of revenue for a net gain of $400. Each black worker costs $1,400 and is believed to produce $1,920 of revenue for a perceived net gain of $520. In this case, the firm employs 15 black workers (to exactly produce 150 units of output) and receives profit of 15 × ($1,920 – $1,400) = $7,800.

When d = 0.8.

Each white worker costs $2,000 and produces $2,400 of revenue for a net gain of $400. Each black worker costs $1,400 and is believed to produce $480 of revenue for a perceived net loss of $920. In this case, the firm employs 15 white workers (to exactly produce 150 units of output) and receives profit of 15 × ($2,400 – $2,000) = $6,000. (d) For what value(s) of d is a firm willing to hire blacks and whites?

Each white worker produces $400 of profit for the firm. Each black worker, while costing $1,400 is perceived to produce $2,400(1 – d) of revenue. Thus, each black worker is perceived as producing $2,400(1 – d) – $1,400 = $1,000 – $2,400d of profit. The firm is willing to hire black and white workers, therefore, if 1,000 – 2,400d = 400 600 = 2,400d 0.25 = d.

Thus, the firm hires both types if d = 0.25. If d > 0.25, the firm hires only whites. If d < 0.25, the firm hires only blacks.

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9-10. After controlling for age and education, it is found that the average woman earns $0.80 for every $1.00 earned by the average man. After controlling for occupation to control for compensating differentials (i.e., maybe men accept riskier or more stressful jobs than women, and therefore are paid more), the average woman earns $0.92 for every $1.00 earned by the average man. The conclusion is made that occupational choice reduces the wage gap 12 cents and discrimination is left to explain the remaining 8 cents. (a) Explain why discrimination may explain more than 8 cents of the 20 cent differential (and occupational choice may explain less than 12 cents of the differential).

Discrimination may occur during the process of choosing an occupation (i.e., occupational crowding). As students, for example, girls may be encouraged to take a different set of courses than boys. Later, discrimination may preclude women from being hired into the higher paying occupations. Put differently, accepting the statistics at face value requires there to be wage discrimination but no employment discrimination and no discrimination in the schooling process. (b) Explain why discrimination may explain less than 8 cents of the 20 cent differential.

The labor supply curve of women and men could be different, because they have different preferences when it comes to leisure and consumption. Thus, wage differences might come about to account for gender-based preferences and not discrimination. Put differently, other factors chosen by the employee, such as hours worked or work experience, have yet to be controlled for and could explain at least some of the remaining 8 cent differential.

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9-11. Consider a town with 10 percent blacks (and the remainder is white). Because blacks are more likely to work the night shifts, 20 percent of all cars driven at night are driven by blacks. One out of every twenty people driving at night is drunk, regardless of race.

Persons who are not drunk never swerve their cars, but 10 percent of all drunk drivers, regardless of race, swerve their cars. On a typical night, 5,000 cars are observed by the police force. (a) What percent of blacks driving at night are driving drunk? What percent of whites driving at night are driving drunk?

The percent of drivers who are drunk is identical across races – 5 percent of all drivers regardless of race are drunk. (b) Of the 5,000 cars observed, how many are driven by blacks? How many of these cars are driven by a drunk? Of the 5,000 cars observed at night, how many are driven by whites? How many of these cars are driven by a drunk? What percent of nighttime drunk drivers are black?

Of the 5,000 cars driven at night, 20 percent (or 1,000) are driven by blacks. As one out of every twenty people are drunk, there are 50 black drunk drivers. Similarly, 4,000 of the cars are driven by whites, and there are 200 drunk white drivers. Thus 20 percent (50 out of 250) of the drunk drivers are black, just like 20 percent of all drivers are black. (c) The police chief believes the drunk-driving problem is mainly due to black drunk drivers. He orders his policemen to pull over all swerving cars and one in every two nonswerving cars that is driven by a black person. The driver of a non-swerving car is then given a breathalyzer test that is 100 percent accurate in diagnosing drunk driving. Under this enforcement scheme, what percent of people arrested for drunk driving will be black?

One-tenth of white drunk drivers will be arrested as they were swerving. This totals 20 drivers.

Likewise, one-tenth of black drunk drivers will be arrested as they were seen swerving. This totals 5 drivers.

Of the remaining 4,975 drivers, 995 are black with 45 being drunk. As one in every two blacks is pulled over on suspicion, 22.5 additional blacks will be arrested for drunk driving on average as they will fail the breathalyzer test. Therefore, at the end of the night, 47.5 people will be arrested for drunk driving, 27.5 of which are black. Therefore, even though only 20 percent of all drunks are black, 58 percent (27.5 ÷ 47.5) of drunks arrested are black.

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9-12. Suppose 100 men and 100 women graduate from high school. After high school, each can work in a low-skill job and earn $200,000 over his or her lifetime, or each can pay $50,000 and go to college. College graduates are given a test. If someone passes the test, he or she is hired for a high-skill job paying lifetime earnings of $300,000. Any college graduate who fails the test, however, is relegated to a low-skill job. Academic performance in high school gives each person some idea of how he or she will do on the test if they go to college. In particular, each person’s GPA, call it x, is an “ability score” ranging from 0.01 to 1.00. With probability x, the person will pass the test if he or she attends college. Upon graduating high school, there is one man with x = .01, one with x = .02, and so on up to x = 1.00. Likewise, there is one woman with x = .01, one with x = .02, and so on up to x = 1.00. (a) Persons attend college only if the expected lifetime payoff from attending college is higher than that of not attending college. Which men and which women will attend college?

What is the expected pass rate of men who take the test? What is the expected pass rate of women who take the test?

Both groups are identical, so the answers are identical. The expected value requirement for attending college is: $300,000 x + $200,000 (1 – x) – $50,000 > $200,000 $100,000 x > $50,000 x > 0.50.

Thus, the 50 men and 50 women with x = .51 to x = 1.00 all go to college and take the test. The number of test takers expected to pass is then the sum of expected pass rates: .51 + .52 + … + 1.00 = 37.75. Thus, 75.5 percent (37.75 of the 50) of men and 75.5 percent of the women who take the test are expected to pass the test. (b) Suppose policymakers feel not enough women are attending college, so they take actions that reduce the cost of college for women to $10,000. Which women will now attend college?

What is the expected pass rate of women who take the test?

The expected value requirement for attending college for women has changed to: $300,000 x + $200,000 (1 – x) – $10,000 > $200,000 $100,000 x > $10,000 x > 0.10.

Thus, the 90 women with x = .11 to x = 1.00 attend college and take the test. The number of female test takers expected to pass is the sum of expected pass rates: .11 + .12 + … + 1.00 = 49.95. Thus, 55.5 percent (49.95 of the 90) of the women who take the test are expected to pass the test.

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9-13. Suppose the discrimination coefficient increases as the firm employs more black workers. In particular, the discrimination coefficient is d = 0.01EB where EB is the number of blacks hired by the firm so that each employer facing competitive wages of wW for whites and wB for blacks acts as if she faces competitive wages of wW for whites and wB(1+d) for blacks. Lastly, assume that the firm must employ 200 workers. Define the wage ratio to be wW / wB. Solve for the number of blacks hired as a function of the wage ratio. Graph the number of blacks hired (x-axis) against the wage ratio (y-axis).

The firm hires whichever worker is perceived to be cheaper on the margin. Put differently, the firm adjusts (if it can) its hiring decisions so that the cost of the marginal white worker equals the cost of the marginal black person. Therefore, on the margin, we will have (if not at a corner solution): wW = (1 + d)·wB = (1 + 0.01EB)·wB wW / wB = 1 + 0.01EB EB = 100·( wW / wB) – 100 Notice that if the black wage exceeds the white wage that EB, according to the above, is negative.

Similarly, EB exceeds 200 if the wage ratio exceeds 3. Thus, the demand equation for black workers: EB = 100·( wW / wB) – 100, is correct unless the firm wants to hire no black workers (if the black wage exceeds the white wage) or if the demand equation would imply hiring more than 200 black workers. Thus, the most precise demand function for black workers is:     w   E B* = min max 0,100 W − 100,200 . wB      

Labor demand for blacks, which is increasing in the wage ratio as the black wage is in the denominator, is graphed below.

Wage Ratio: wW / wB

Labor Demand for Blacks 3

2

1

0

100

200

EB = Number of Blacks Hired

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9-14. Consider a data set with the following descriptive statistics.

Table 1. Descriptive Statistics.

Ln(wages) Black Age Work experience Schooling % female occupation

Mean 3.562 0.231 42.2 18.1 13.9 18.2

Men Min 1.389 0 19 0 9 2.3

Max 5.013 1 68 42 21 95.4

Mean 3.198 0.191 39.2 16.1 14.1 62.3

Women Min 1.213 0 19 0 9 6.7

Max 4.875 1 63 35 21 98.5

Wage is the worker’s hourly wage; Black takes on a value of 1 if the worker is Black and a value of 0 otherwise; work experience is actual years of work experience, schooling is measured in years; and % female occupation is the percent of all employees in the worker’s occupation who are female. The following table reports the regression results from a logwage regression.

Table 2. Regression Results.

Men Constant 2.314 Black -0.198 Age 0.054 Years of work experience 0.042 Years of schooling 0.085 Percent female in occupation -0.0012

Women 2.556 -0.154 0.037 0.059 0.083 0.0024

Decompose the raw difference in average wages using the Oaxaca-Blinder decomposition.

Specifically, decompose the raw difference into the portion due to differences in personal characteristics (schooling, race, age, and experience), the portion due to occupation, and the portion left unexplained possibly due to gender discrimination.

The raw wage gap is w = wM − wF = 3.562 − 3.198 = 0.364.

Next, for the five variables in the regression we have: Race: Age: Work Exp: School: Occupation:

βM = -0.198 and x M − x F = 0.231 − 0.191 = 0.04  −0.198(0.04) = −0.008. βM = 0.054 and x M − x F = 42.2 − 39.2 = 3.0  3(0.054) = 0.162. βM = 0.042 and x M − x F = 18.1 − 16.1 = 2.0  2(0.042) = 0.084. βM = 0.085 and x M − x F = 13.9 − 14.1 = −0.20  −0.2(0.085) = −0.017. βM = -0.121 and x M − x F = 18.2 − 62.3 = −44.1  −0.0012(−44.1) = 0.053.

Thus, personal characteristics (race, age, work experience, and schooling) explain –0.008 + 0.162 + 0.084 – 0.017 = 0.221 of the 0.364 wage gap. Occupation explains 0.053 of the 0.364 wage gap. This leaves 0.364 – 0.053 – 0.221 = 0.09 of the wage gap left unexplained, possibly due to gender discrimination.

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9-15. In 2006, Evo Morales assumed the presidency in Bolivia, a South American country in which official commerce is done in Spanish. Morales was the first Bolivian president of indigenous decent. As president, he quickly instituted reforms that were designed to reduce discrimination against indigenous populations with the aim of eventually reducing inequality. Suppose discrimination before Morales took two forms–discrimination in education by not providing state funds to educate all children (and particularly not educating indigenous children in Spanish), and discrimination in the job market by firms not willing to hire indigenous workers. (a) In terms of education, which policy would be better at combating discrimination and inequality: (1) providing state funds to educate all people in their native languages, or (2) providing state funds for a public education system that requires all people to learn Spanish and a second, indigenous language? Why? The second policy is better to fight the inequality resulting from discrimination in education. Of course spending money on educating indigenous populations is important (policy 1), but as commerce takes place in Spanish, it is also important to educate indigenous populations in a way that allows them to fully participate in society. This requires educating everyone in Spanish. As a side note, Morales’s policy (#2 above) goes one step further in trying to end cultural discrimination by requiring everyone to learn Spanish and at least one indigenous language. The hope is that this will further erode cultural differences (or at least cultural biases) across subpopulations in Bolivia. (b) In terms of the job market, which policy would be best at combating discrimination and inequality: (1) increasing the minimum wage, (2) requiring all firms with at least 50 workers to hire some indigenous workers, or (3) improving the legal system to protect economic rights and activities? Why? In a competitive or free or capitalistic economy, it is likely most beneficial to do #3. Raising the minimum wage doesn’t help indigenous workers if they cannot find jobs or cannot land wellpaying jobs. And though #2 is in the right direction, what is defined as “indigenous” is a bit unclear, and so such a regulation likely has no real effect on firms. However, if #3 comes about, then indigenous workers know there will be economic rewards for working hard and becoming educated. Providing such incentives would likely eventually lead to less inequality.

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CHAPTER 10 10-1. Suppose the firm’s labor demand curve is given by: w = 20 - 0.01E, where w is the hourly wage and E is the level of employment. Suppose also that the union’s utility function is given by U = w  E. It is easy to show that the marginal utility of the wage for the union is E and the marginal utility of employment is w. What wage would a monopoly union demand? How many workers will be employed under the union contract?

Utility maximization requires the absolute value of the slope of the indifference curve equal the absolute value of the slope of the labor demand curve. In this case, the absolute value of the slope of the indifference curve is MU E w . = MU w E

The absolute value of the slope of the labor demand function is 0.01. Thus, utility maximization requires that

w = 0.01 .

E Substituting for w with the labor demand function, the employment level that maximizes utility solves

20 − 0.01E = 0.01 , E 20 – 0.01E = 0.01E 20 = 0.02E E = 1,000 workers.

The highest wage at which the firm is willing to hire 1,000 workers is 20 – 0.01(1000) = $10.

Thus, the monopoly union requires the firm to employ 1,000 workers, each at $10 per hour.

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10-2. Suppose the union in problem 1 has a different utility function. In particular, its utility function is given by: U = (w - w*)  E where w* is the competitive wage. The marginal utility of a wage increase is still E, but the marginal utility of employment is now w – w*. Suppose the competitive wage is $8 per hour.

What wage would a monopoly union demand? How many workers will be employed under the union contract? Contrast your answers to those in problem 1. Can you explain why they are different?

Again equate the absolute value of the slope of the indifference curve to the absolute value of the slope of the labor demand curve:

MU E w − w* = = 0.01 .

MU w E Setting w* = $8 and using the labor demand equation yields:

20 − 0.01E − 8 = 0.01 , E 12 – 0.01E = 0.01E 12 = 0.02E E = 600 workers.

The highest wage at which the firm is willing to hire 600 workers is 20 – 0.01(600) = $14. Thus, the monopoly union requires the firm to employ 600 workers, each at $14 per hour.

In problem 1, the union maximized the total wage bill. In problem 2 the utility function depends on the difference between the union wage and the competitive wage. That is, the union maximizes its rent. Since the alternative employment option pays $8, the union is willing to suffer a cut in employment in order to obtain a greater rent of $6 per hour ($8 up to $14).

10-3. Figure 10-2 demonstrates some of the tradeoffs involved when deciding to join a union. Suppose in addition to higher wages the union negotiates a 10 percent employer contribution to a defined contribution pension plan. Provide a graph similar to Figure 10-2 that incorporates this retirement benefit into the decision of whether to join a union. Show on your graph how additional fringe benefits such as a retirement plan may cause the worker to be more inclined to join the union.

Negotiating a 10% employer contribution to a defined contribution pension plan is almost the same as negotiating an additional 10% increase in the wage. Thus, the budget line (BT) in Figure 10-2 will rotate out. As long as the firm does not respond by cutting hours too much (such as to h0 in Figure 10-2), workers will have more incentive to join the union as they will receive higher hourly compensation (though possibly asked to work fewer hours).

C

2

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B

P1

U1

h1 h2

T

The graph above is a simplified version of Figure 10-2 from the text. The negotiated contribution rotates the budget line from BT to CT. As long as the firm does not reduce hours from h1 to less than h2, the worker is better off.

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10-4. Consider a two-sector economy with homogeneous labor and jobs in both sectors. Two million workers supply their labor perfectly inelastically. Labor demand in both sectors can be written as: E1 = 1,800,000 – 100,000w1 and E2 = 1,800,000 – 100,000w2. (a) If both sectors are competitive, what is the market-clearly wage and how many workers are employed in both sectors?

As labor demand is identical in both sectors and labor is homogeneous, 1 million workers will work in both sectors. Using this for E in the labor demand equations, we find that 1,000,000 = 1,800,000 – 100,000w 100,000w = 800,000 w* = $8 per hour. (b) Suppose a labor union forms in sector 1. The union negotiates a wage of $12 per hour, and firms choose how much labor to employ. Anyone not employed in sector 1 is relegated to sector 2. How many workers will be employed in sector 1 (unionized)? How many workers will be employed in sector 2, and what wage will they receive?

At a wage of $12 per hour, the unionized sector (sector 1) will employ: E1 = 1,800,000 – 100,000w1 E1 = 1,800,000 – 100,000 × 12 E1 = 1,800,000 – 1,200,000 E1* = 600,000 workers.

This forces 2 million – 0.6 million = 1.4 million workers into the non-unionized sector (sector 2).

With this many workers relegated to sector 2, wages are: 1,400,000 = 1,800,000 – 100,000w 100,000w = 400,000 w* = $4 per hour.

Therefore, 600,000 workers are employed at $12 per hour in the unionized sector while 1,400,000 workers are employed at $4 per hour in the non-unionized sector. (c) What is the union-wage gap in part (b)? What would the union-wage effect be if one controlled for the spillover effect?

Using the answers to part (b), the union-wage effect is ($12 – $4) / $4 = 200% (or it could be expressed as $8 = $12 – $4 per hour as well).

The spillover effect refers to the infusion of workers into sector 2 because the union formed and the unionized firms restricted labor. If we compare the union wage of $12 to the competitive wage of $8 per hour that would have come about without a union (part a), the union-wage effect is ($12 – $8) / $8 = 50% (or it could be expressed as $4 = $12 – $8 per hour as well).

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10-5. Consider a firm that faces a constant per unit price of $1,200 for its output. The firm hires workers, E, from a union at a daily wage of w, to produce output, q, where q = 2E½.

Given the production function, the marginal product of labor is 1/E½. There are 225 workers in the union. Any union worker who does not work for the firm can find a nonunion job paying $96 per day. (a) What is the firm’s labor demand function?

The problem stipulates that the price of output is constant at $1,200. This means that the firm also faces constant marginal revenue at $1,200. That is, p = MR = $1,200. The labor demand function, or the value of marginal product of labor, is VMPE = MR × MPE = 1200 / E ½. (b) If the firm is allowed to specify w and the union is then allowed to provide as many workers as it wants (up to 225) at the daily wage of w, what wage will the firm set? How many workers will the union provide? How much output will be produced? How much profit will the firm earn? What is the total income of the 225 union workers?

If the firm offers w < $96, no workers will be provided. This would leave the firm with no output and no profit. The workers would all receive $96 per day, making their total daily income $21,600.

If the firm offers a wage of w > $96, all 225 workers will be provided. These 225 workers would produce q = 2 × sqrt(E) = 2 × sqrt(225) = 30 units of output. The firm would then earn a profit of 30($1,200) – 225w. Profit, therefore, is maximized when w is minimized subject to the constraint.

If the union would supply all 225 workers at a wage of $96, for example, the firm would offer w = $96 and earn a daily profit of $14,400. The total daily income of the 225 workers would remain at $21,600. (If the firm needs to offer strictly more than $96 per day to attract workers, it would offer a daily wage of $96.01. All 225 workers would work for the firm, making 30 units of output. The firm’s daily profit would be $14,397.75. And the total daily income of the 225 workers would be $21,602.25.)

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10-6. Consider the same set-up as in problem 10-5, but now the union is allowed to specify any wage, w, and the firm is then allowed to hire as many workers as it wants (up to 225) at the daily wage of w. What wage will the union set in order to maximize the total income of all 225 workers? How many workers will the firm hire? How much output will be produced? How much profit will the firm earn? What is the total income of the 225 union workers?

To solve this with Excel, the spreadsheet looks like the following, where the union specifies the wage, labor demand comes from part (a), and everything else follows naturally: Union Labor Labor Daily wage Demand Costs Output Price Revenue Profit Income $96 156.25 $15,000.00 25.00 $1,200 $30,000.00 $15,000.00 $21,600.00 $97 153.04 $14,845.36 24.74 $1,200 $29,690.72 $14,845.36 $21,753.04 $98 149.94 $14,693.88 24.49 $1,200 $29,387.76 $14,693.88 $21,899.88 $99 146.92 $14,545.45 24.24 $1,200 $29,090.91 $14,545.45 $22,040.77 $100 144.00 $14,400.00 24.00 $1,200 $28,800.00 $14,400.00 $22,176.00 … … … … … … … … $190 39.89 $7,578.95 12.63 $1,200 $15,157.89 $7,578.95 $25,349.58 $191 39.47 $7,539.27 12.57 $1,200 $15,078.53 $7,539.27 $25,349.90 $192 39.06 $7,500.00 12.50 $1,200 $15,000.00 $7,500.00 $25,350.00 $193 38.66 $7,461.14 12.44 $1,200 $14,922.28 $7,461.14 $25,349.90 $194 38.26 $7,422.68 12.37 $1,200 $14,845.36 $7,422.68 $25,349.60 $195 37.87 $7,384.62 12.31 $1,200 $14,769.23 $7,384.62 $25,349.11 Thus, the union sets a daily wage of $192. The firm responds by hiring 39.06 workers, who produce 12.5 units of output. The firm earns a daily profit of $7,500, while the 225 workers, 39.06 of whom are in the union and 185.94 of whom are not in the union, earn a total of $25,350 each day.

The calculus solution is: given any wage, the firm will employ (1200/w)2 workers. This is derived by setting the value of marginal product equal to the wage and solving for employment:

.

As the union’s objective is to maximize total income, it chooses w to maximize the income of the workers employed by the union plus the income of the workers not employed by the union.

Therefore, we have: 2 2  138,240,000  1,200   1,200   1,440,000  Max w . + 21,600 −  + 96 225 −   =   w  w   w   w2 

The first order condition, therefore is

− 1,440,000 w

2

+

276,480,000 w3

= 0 which solves as w = $192.

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10-7. Suppose the union’s resistance curve is summarized by the following data. The union’s initial wage demand is $10 per hour. If a strike occurs, the wage demands change as follows: Length of Strike: 1 month 2 months 3 months 4 months 5 or more months

Hourly Wage Demanded 9 8 7 6 5

Consider the following changes to the union resistance curve and state whether the proposed change makes a strike more likely to occur, and whether, if a strike occurs, it is a longer strike. (a) The drop in the wage demand from $10 to $5 per hour occurs within the span of 2 months, as opposed to 5 months.

If the union is willing to drop its demands very fast, the firm will find it profitable to delay agreement until the wage demand drops to $5. A strike, therefore, is more likely to occur. If $5 is the lowest wage the union is willing to accept, the strike is much more likely to last 2 months now than the probability it would have lasted 5 months under the original resistance curve. (b) The union is willing to moderate its wage demands further after the strike has lasted for 6 months. In particular, the wage demand keeps dropping to $4 in the 6th month, $3 in the 7th month, etc.

If the union is willing to accept even lower wages in the future, some firms will find it optimal to wait the union out. Thus, strikes will be more likely and last longer. (c) The union’s initial wage demand is $20 per hour, which then drops to $9 after the strike lasts one month, $8 after 2 months, and so on.

Conditioning on a strike occurring, the length of strike will be unchanged as the resistance curve after the initial demand stays the same. The probability of a strike ever occurring increases, however, when the initial demand increases but everything else remains the same.

10-8. At the competitive wage of $20 per hour, firms A and B both hire 5,000 workers (each working 2,000 hours per year). The elasticity of demand is -2.5 and -0.75 at firms A and B respectively. Workers at both firms then unionize and negotiate a 12 percent wage increase. (a) What is the employment effect at firm A? How has total worker income changed?

At firm A, ηA = %ΔEA ÷ %ΔwA = -2.5. When wages increase 12%, therefore, employment falls by 30%. The firm will start to employ 70% of 5000 × 2000 = 7 million work-hours per year, possibly by hiring 3,500 workers for 2,000 hours each. Total income was 10 million work-hours times the wage of $20 per hour for a total of $200 million. Total income will now be 7 million work-hours times the new wage of $22.40 (a 12 percent increase above $20), for a total income of $156.8 million plus any income earned by the workers who no longer work at firm A because of the reduction in labor used.

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(b) What is the employment effect at firm B? How has total worker income changed?

At firm B, ηB = %ΔEB ÷ %ΔwB = -0.75. When wages increase 12%, therefore, employment falls by 9%. The firm will start to employ 91% of 5000 × 2000 = 9.1 million work-hours per year, possibly by hiring 4,550 workers for 2,000 hours each. Total income was 10m work-hours times the wage of $20 per hour, for a total of $200 million. Total income will now be 9.1 million workhours times the new wage of $22.40 (a 12 percent increase above $20), for a total income of $203.84 million plus any income earned by the workers who no longer work at firm B because of the reduction in labor used. (c) How much would the workers at each firm be willing to pay in annual union dues to achieve the 12 percent gain in wages?

To answer this question, assume that reductions in employment come from reducing the number of workers hired, and not by reducing the number of hours worked by each worker. So, for firm A, assume the number of workers falls to 3,500 but hours remain at 2,000. Similarly, for firm B, assume the number of workers falls to 4,550 but hours remain at 2,000. In this case, income has increased from 2,000 x $20 = $40,000 per year per worker to 2,000 x $22.40 = $44,800 per year for each worker continuing to have a job. So, workers at either firm, as long as they retain their job, are willing to pay up to $4,800 annually in union dues.

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10-9. Several states recently passed laws restricting bargaining rights for public employees.

Most notably the changes tended to restrict the union’s right to negotiate over fringe benefits such as health care and retirement benefits. What problems were these legislative changes trying to address? Even assuming such a law survives a constitutional challenge (which some did not), why might restricting bargaining rights not fully address the problems lawmakers were aiming to solve?

Following the Great Recession, many private employee labor contracts and conditions were changed. Fewer fringe benefits were being paid—employees were asked to pay more of their health insurance costs, and contributions to and benefits paid from retirement plans fell (especially to and from defined benefit plans). Salary increases were marginal from 2007 – 2010.

And so on. It’s harder to have such shifts in the public sector in part because public organizations are not arranged nor operate the same way as private firms. Public sector unions had also negotiated terrific healthcare and retirement benefits in the decades leading up to the Great Recession. The defined benefit retirement plans for public sector workers in many states became vastly insolvent as benefits steadily increased at the same time state budgets became strapped due to lower state tax revenues. Thus, the states that passed these laws did so because, in their mind, the compensation package previously offered to public sector unions was out of line with the private sector marketplace, and so out of line that the current state of things threatened state solvency.

There are at least two reasons to think that these laws may not be as successful in lowering the state burden in terms of public sector employee’s as advertised. First, the unions are still allowed to bargain over salaries. As money (and compensation) is fungible, the union may demand that cost-savings on healthcare or retirement be offset with higher direct salaries. Second, the unions still have the right to strike and have significant political power. Thus, even though their bargaining rights may be hypothetically restricted, it remains unclear if the state would actually take hard stands during negotiations.

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10-10. Suppose the economy consists of a union and a non-union sector. The labor demand curve in each sector is given by L = 1,000,000 – 20w. The total (economy-wide) supply of labor is 1,000,000, and it does not depend upon the wage. All workers are equally skilled and equally suited for work in either sector. A monopoly union sets the wage at $30,000 in the union sector. What is the union wage gap? What is the effect of the union on the wage in the non-union sector?

In a competitive economy, both sectors would hire half of the workers as labor is supplied inelastically. Therefore, to solve for the competitive wage, solve 500,000 = 1,000,000 – 20w → wComp = $25,000.

If the union wage is set at $30,000, the union sector employs L = 1,000,000 – 20(30,000) = 400,000 union workers.

The remaining 600,000 must be employed in the non-union sector, which will happen if the wage in the non-union sector is (1,000,000 – 600,000)/20 = $20,000.

Hence, the wage gap between the union and the non-union sectors equals: Union Wage Gap: $30,000 – $20,000 = $10,000.

Thus, the union wage gap represents 50% of the non-union wage as $10,000 ÷ $20,000 = 50%.

The effect of the union wage gap is that more people now work in the non-union sector, which depresses wages there. In particular, although the union only negotiated a pay raise of $5,000 above the competitive wage, the wage gap is $10,000 as the workers who no longer work in the union sector compete wages down in the non-union sector.

10-11. In Figure 10-6, the contract curve is PZ. (a) Does point P represent the firm or the workers having all of the bargaining power?

Does point Z represent the firm or the workers having all of the bargaining power?

Explain.

The firm’s isoprofit curves improve as it hires the same number of workers at a lower wage, which means improvements are achieved by moving down (to the south). So, from the firm’s perspective, π* > πM > πZ.. From the union’s point of view, indifference curves increase to the northeast (as more people are hired at the same wage or when the same number of people are hired at a higher wage). Thus, from the union’s perspective, U* < UM < UR < UZ. Thus, point P represents the firm having all of the bargaining power, and point Z represents the union having all of the bargaining power.

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(b) Suppose the union has the power to be a monopoly union in setting wages if it chooses, but it doesn’t have the power to force a wage and an employment level on the firm. On what portion of the contract curve PZ would you expect the bargained wage-employment contract to occur?

The union sets the wage, but not the employment level. Thus, for any wage set by the union, the firm “sees” a horizontal line at w and maximizes its profit by choosing an employment level that gives the firm a position on its highest possible isoprofit line. Thus, the firm will choose a point on the line described by PM. Knowing this, the best the union can do is to set wage wM as the firm will then choose EM (not drawn in Figure 10-6, but associated with point M) which puts the outcome at point M and gives the union UM. At any other wage, the firm chooses a different employment level according to PM, all of which are associated with indifference curve levels lower than UM.

10-12. Consider the following data on union versus non-union wage and fringe benefit compensation.

Union Workers Non-Union Workers

Average Hourly Wage $21.91 $17.66

Average Hourly Fringe Benefit $13.69 $6.85

Total Hourly Compensation $35.60 $24.51

Calculate the union effect for hourly wages, hourly fringe benefits, and total hourly compensation. What might you infer from the various union-negotiated effects?

The union wage effect is ($21.91 – $17.66) ÷ $17.66 = 24%.

The union effect on total benefits is ($13.69 – $6.85) ÷ $6.85 = 99.9%.

The union effect on total compensation is ($35.60 – $24.51) ÷ $24.51 = 45.2%.

There are several conclusions to draw from this data. First, the union wage effect is substantial regardless if one is looking at wages, fringe benefits, or total compensation. Of these, the most important is likely fringe benefits, and the average worker is earning 45.2% more per hour in total compensation compared to non-union workers. Also, though, the data suggest that unions are relatively more successful at negotiating fringe benefits than they are at negotiating wage increases as the average unionized worker receives almost twice (100%) the value of fringe benefits compared to the average non-unionized worker while they “only” receive 24% more in wages.

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10-13. Use a graph similar to Figure 10-10 to demonstrate the likely bargaining outcomes of three industries, all with identical union resistance curves. (a) Firm A has been losing money recently as wages and fringe benefits have risen from 63 to 89 percent of all costs in just the last three years. (b) Most of firm B’s revenues come from supplying a product to three customers who use the product in their manufacturing of computers using a just-in-time inventory system. (c) Firm C is a local government that finds itself negotiating with its unionized employees.

Government officials are pleased with the employees’ productivity, but they also face local pressure to keep taxes low.

Firm A is likely to have very long and shallow isoprofit lines as it perceives that it cannot afford more pay increases.

Firm B is vulnerable to union demands, because it will lose much of its revenue if it experiences a disruption in its production process as most of its output is sold to three firms that all use a justin-time inventory process. Thus, Firm B likely has very steeply sloped isoprofit lines.

Firm C probably doesn’t care if it gives higher wages and benefits, as it can simply raise taxes to cover the costs. However, elected officials also feel pressure to keep taxes low and to at least look tough in negotiations with public employee unions. Thus, firm C is probably between firm A and firm B in terms of the steepness of its isoprofit lines. In particular, firm C is probably willing to bear short strikes but not long ones.

Each of these resistance curves are plotted in the following graph. The graph shows that firm A is the most willing to endure a long strike and the least likely to agree to a high wage demand, while firm B is the least willing to endure a long strike and the most likely to agree to a high wage demand. Firm C is somewhere between the two on both issues.

Dollars B

C

Union Resistance Curve

A πB

πC

πA Duration of Strike

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10-14. Major League Baseball players are not eligible for arbitration or free-agency until they have been in the league for several years. During these “restricted” years, a player can only negotiate with his current team. Consider a small-market team that happens to own the rights to last year’s Rookie-of-the-Year. This player is currently under contract for $500,000 for the next 3 years. Because his current team is in a small market, the player’s value to his current team is $6 million per year (now and in the future). When the player becomes eligible for free-agency, he will likely command $10 million per year for 7 years in free-agency from competing large-market teams. In the questions below, assume the player wants to maximize his lifetime earnings. (a) What is the worst 10-year contract extension from the player’s point of view that the player would accept from his current team?

If the player decides to play out his current contract and then signs with a large-market team, he will earn 3 × $500,000 + 7 × $10,000,000 = $71.5 million. Thus, the worst 10-year contract extension from the player’s point of view that he would accept is $7.15 million dollars per year for 10 years. (b) What is the best 10-year contract extension from the player’s point of view that his current team would offer him?

The best contract extension his current firm is willing to offer is $6 million per year for the next 10 years. (c) Would you expect this player to sign a contract extension or to play out his contract and enter free-agency three years from now?

Given these numbers, if the player wants to maximize his earnings over the next 10 years (and assuming away discounting as the problem has done), the player will play out his current contract and then enter free-agency in order to sign with a large-market team.

10-15. Recently the National Football League Players Association (NFLPA), which is the union for the players in the National Football League (NFL), and the team owners (the NFL) experienced a labor impasse in the form of a lockout. For the record, each year about 150 players (called rookies) enter the NFL and 150 veteran players exit the league (via retirement or not making a team roster). While renegotiating the most recent labor settlement, the union took several stances. Explain why a union of players would advocate against: (a) Expanding the number of games played.

Games played is analogous to hours worked. As NFL players are paid a salary, increasing the number of games played is effectively lowering each player’s hourly wage. A player who earns $1,440,000 per year, for example, is paid $90,000 per game. If the season were expanded to 18 games, the same player is now paid $80,000 per game.

On this issue, the NFLPA publically argued that 18 games would cause substantially more physical damage to players over their playing careers (and felt for their lifetime) than does a 16 game schedule.

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(b) Expanding the size of team rosters.

One way a union negotiates higher wages for its members is to restrict entry into jobs. When rosters expand, more players are in the union, each competing for money paid by firms. At the extreme, with a team salary cap of $100,000,000 per year, a 53-man roster allows for an average salary of $1.886 million whereas a 57-man roster only allows for an average salary of $1.754 million. (c) A team salary cap.

In all professional sports leagues, the players union objects to salary caps because salary caps are simply a way by which the owners regulate one another. In a purely competitive environment, the players believe that owners would spend more money on salaries.

For the record, salary caps now exist to some degree, in the NFL (football), NBA (basketball), and NHL (hockey). Although baseball doesn’t have an official salary cap, it does have a luxury tax that penalizes clubs from spending too much more than average. (It also penalizes clubs for spending too little.) (d) A rookie salary cap.

One of the strangest result of the NFL lockout, according to the media, was that the NFLPA was against a rookie salary cap. The argument (from the media) went: current players should support a rookie salary cap so that the real, on-the-field performers receive a greater share of the salaries.

(JaMarcus Russell, the #1 overall pick in 2007 by the Oakland Raiders, was paid almost $40 million, played very little, played poorly when he did play, and was released in 2010.) A rookie salary cap would prevent such atrocities, and instead reward the players who have longer, more productive careers.

So why did the NFLPA not support a rookie salary cap?

The answer for economists is that the NFLPA understands that teams conduct marginal benefit– marginal cost analyses. If rookie salaries are kept artificially low, teams will have more incentive to employ rookies rather than, say, 4-year veterans. And although the NFLPA includes all of the NFL superstars, most of its members are 3- to 7-year veterans who are hoping to stay in the league for a few more years. These players know that if teams are given the opportunity of hiring a rookie for $50,000 or the marginally better but much more expensive 5-year veteran for $1,000,000, the team will go with the rookie. Therefore, in order to protect the jobs and salaries of a large part of the rank and file membership, the NFLPA advocated against a rookie salary cap.

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CHAPTER 11 11-1. Suppose there are 100 workers in an economy with two firms. All workers are worth $35 per hour to firm A but differ in their productivity at firm B. Worker 1 has a value of marginal product of $1 per hour at firm B; worker 2 has a value of marginal product of $2 per hour at firm B, and so on. Firm A pays its workers a time-rate of $35 per hour, while firm B pays its workers a piece rate. How will the workers sort themselves across firms?

Suppose a decrease in demand for both firms’ output reduces the value of every worker to either firm by half. How will workers now sort themselves across firms?

Workers 1 to 34 work for firm A as a time rate of $35 is more than their value to firm B, while workers 36 to 100 work for firm B. Worker 35 is indifferent. More productive workers, therefore, flock to the piece rate firm. After the price of output falls, firm A values all workers at $17.50 per hour, while worker 1’s value at firm B falls to 50 cents, worker 2’s value falls to $1 at firm B, etc.

The question is what happens to the wage. Presumably wage also falls, to $17.50 per hour in firm A. If it falls by half, then the sorting of workers to the two firms remains unchanged.

11-2. Taxicab companies in the United States typically own a large number of cabs and licenses; taxicab drivers then pay a daily fee to the taxicab company to lease a cab for the day. In return, the drivers keep all of their fares (so that, in essence, they receive a 100 percent commission on their sales). Why do you think this type of compensation system developed in the taxicab industry?

Imagine what would happen if the cab company paid a 50 percent commission on fares. The cab drivers would have an incentive to misinform the company about the amount of fares they generated in order to pocket most of the receipts. Because cab companies find it almost impossible to monitor their workers, they have developed a compensation scheme that leaves the monitoring to the drivers. By charging drivers a rental fee and letting the drivers keep all the fares, each driver has an incentive to not shirk on the job.

11-3. A firm hires two workers to assemble bicycles. The firm values each assembly at $12.

Charlie’s marginal cost of allocating effort to the production process is 4N, where N is the number of bicycles assembled per hour. Donna’s marginal cost is 6N. (a) If the firm pays piece rates, what will be each worker’s hourly wage?

As the firm values each assembly at $12, it will pay $12 for 1 assembly, $24 for 2 assemblies, etc. when offering piece rates. As Charlie’s marginal cost of the first assembly is $4, the second is $8, the third is $12, and the fourth is $16; Charlie assembles 3 bicycles each hour and is paid an hourly wage of $36. As Donna’s marginal cost of the first assembly is $6, the second is $12, and the third is $18; Donna assembles 2 bicycles each hour and is paid an hourly wage of $24. (b) Suppose the firm pays a time rate of $15 per hour and fires any worker who does not assemble at least 1.5 bicycles per hour. How many bicycles will each worker assemble in an 8 hour day?

As working is painful to workers, each will work as hard as necessary to prevent being fired, but that is all. Thus, each worker assembles 1.5 bicycles each hour, for a total of 12 bicycles in an eight hour day.

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11-4. All workers start working for a particular firm when they are 21 years old. The value of each worker’s marginal product is $18 per hour. In order to prevent shirking on the job, a delayed-compensation scheme is imposed. In particular, the wage level at every level of seniority is determined by: Wage = $10 + (.4  Years in the firm).

Suppose also that the discount rate is zero for all workers. What will be the mandatory retirement age under the compensation scheme? (Hint: Use a spreadsheet.)

To simplify the problem, suppose the workers work 1 hour per year. (The answer would be the same regardless of how many hours are worked, as long as the number of hours worked does not change over time). Some of the relevant quantities required to determine the optimal length of the contract are:

Age 21 22 23 24 : 40 41 42 43 : 60 61 62

Years on the Job 1 2 3 4 : 20 21 22 23 : 40 41 42

VMP $18 $18 $18 $18 : $18 $18 $18 $18 : $18 $18 $18

Accumulated VMP $18 $36 $54 $72 : $360 $378 $396 $414 : $720 $738 $756

Contract Wage $10.00 $10.40 $10.80 $11.20 : $17.60 $18.00 $18.40 $18.80 : $25.60 $26.00 $26.40

Accumulated Contract Wage $10.00 $20.40 $31.20 $42.40 : $276.00 $294.00 $312.40 $331.20 : $712.00 $738.00 $764.40

The VMP is constant at $18 per year. The accumulated VMP gives the total product the worker has contributed to the firm up to that point in the contract. The wage in the contract follows from the equation, and the accumulated wage is the total wage payments received by the worker up to that point. Until the 20th year in the firm, the worker receives a wage lower than her VMP; after the 21st year the worker’s wage exceeds the VMP. The contract will be terminated when the total accumulated VMP equals the total accumulated wage under the delayed compensation contract, which occurs on the worker’s 41st year on the job. So the optimal retirement age is age 61.

Allowing the worker to retire after this age would be a bad deal for the firm as total lifetime wage payments exceed total lifetime value to the firm after 41 years of service.

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11-5. Suppose a firm’s technology requires it to hire 100 workers regardless of the wage level or market demand conditions. The firm, however, has found that worker productivity is greatly affected by its wage. The historical relationship between the wage level and the firm’s output is given by: Units of Wage Rate Output $8.00 65 $10.00 80 $11.25 90 $12.00 97 $12.50 102 What wage level should a profit-maximizing firm choose?

The data in the problem can be used to calculate the elasticity of the change in output with respect to the change in the wage. The efficiency wage is determined by the condition that this elasticity must equal 1. This elasticity is 1 when the firm raises the wage from $10 to $11.25 an hour: (90-80)/80  (11.25-10)/10 = 1.

11-6. Consider three firms identical in all aspects except their monitoring efficiency, which cannot be changed. Even though the cost of monitoring is the same across the three firms, shirkers at Firm A are identified almost for certain; shirkers at Firm B have a slightly greater chance of not being found out; and shirkers at Firm C have the greatest chance of not being identified as a shirker. If all three firms pay efficiency wages to keep their workers from shirking, which firm will pay the greatest efficiency wage? Which firm will pay the smallest efficiency wage?

In this example, there is no connection between the cost of monitoring and the efficiency of monitoring, as it is assumed that monitoring efficiency cannot be changed. Moreover, the value of unemployment is the same for workers regardless of their employer. Focusing just on the probability of being caught shirking, therefore, workers in Firm A have the least incentive to shirk (as they are most likely to get caught) while workers in Firm C have the greatest incentive to shirk (as they are least likely to get caught). The idea of efficiency wages is to use wages to buy-off the incentive to shirk. Therefore, Firm A will pay the lowest efficiency wage, while Firm C will pay the greatest efficiency wage.

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11-7. Consider three firms identical in all aspects (including the probability with which they discover a shirker), except that monitoring costs vary across the firms. Monitoring workers is very expensive at Firm A, less expensive at Firm B, and cheapest at Firm C. If all three firms pay efficiency wages to keep their workers from shirking, which firm will pay the greatest efficiency wage? Which firm will pay the smallest efficiency wage?

In this example, there is no connection between the cost of monitoring and the efficiency of monitoring. The efficiency wage, therefore, is determined by the incentives of the workers, not the costs of the firms. (The decision of whether to monitor workers, of course, will depend on the cost of monitoring.) Thus, all three firms will offer the same efficiency wage.

11-8. A firm can hire as much labor as it wants at $5 per hour. In return, each worker produces 10 units of output per hour. The firm can sell up to 2,500 units of output each day at $2 per unit, but it cannot sell any more than 2,500 units of output in a day. The firm has no other costs besides labor. (a) How many hours of labor does the firm purchase and how much profit does it earn each day?

As each hour of labor costs $5 but provides 10 units of output that are sold at $2 each for an hourly revenue of $20 and an hourly profit of $15, the firm hires as many workers as necessary to sell all 2,500 units that it can sell each day. Therefore, the firm hires 250 hours of labor each day and earns profit of 2,500 × $2 – 250 × $5 = $3,750 of daily profit. (b) The firm can choose to pay an efficiency wage. In particular, the firm can choose to pay $6, $7, $8, $9, or $10 per hour, and in exchange, each worker will produce 18, 23, 27, 28, or 29 units of output per hour respectively. What hourly wage should the firm offer to maximize profits?

One way to answer the problem is find the wage level at which the elasticity of output with respect to the wage equals (or is the closest) to 1. Below are the elasticities: Wage = $6: Wage = $7: Wage = $8: Wage = $9: Wage = $10:

(18 – 10)/10 ÷ (6 – 5)/5 = 4.0 (23 – 18)/18 ÷ (7 – 6)/6 = 1.67 (27 – 23)/23 ÷ (8 – 7)/7 = 1.22 (28 – 27)/27 ÷ (9 – 8)/8 = 0.30 (29 – 28)/28 ÷ (10 – 9)/9 = 0.32

Therefore, the optimal efficiency wage is $8 per hour.

This problem can also be done with the same technique as in part (a) and simply calculate all of the profits: Wage = $6: Wage = $7: Wage = $8: Wage = $9: Wage = $10:

E = 2,500 / 18 = 139 E = 2,500 / 23 = 109 E = 2,500 / 27 = 93 E = 2,500 / 28 = 89 E = 2,500 / 29 = 86

→ → → → →

π = 2,500 × $2 – 139 × $6 ≈ $4,167. π = 2,500 × $2 – 109 × $7 ≈ $4,239. π = 2,500 × $2 – 93 × $8 ≈ $4,259. π = 2,500 × $2 – 89 × $9 ≈ $4,196. π = 2,500 × $2 – 86 × $10 ≈ $4,138.

Therefore, this method also results in the optimal efficiency wage being $8 per hour.

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11-9. Consider a firm that offers the following employee benefit. When a worker turns 60 years-old she is given a one-time opportunity to quit her job, and in return the firm will pay her a bonus of 1.5 times her annual salary and pay her health insurance premiums until she is eligible for Medicare. (a) What problem is the firm trying to solve by offering this benefit?

In general, wages (and salaries) increase with age. Thus, even when someone becomes eligible to receive “full” social security benefits and go on Medicare, several people choose to continue to work. Again, they are choosing to work when they are probably very well paid and possibly less valuable to the firm than they were in previous years. The firm, therefore, is trying to entice workers to retire and not continue to work once retirement becomes a possibility. This is a problem these days as federal law prohibits most firms from enforcing a mandatory retirement age. (b) Why is the health insurance premium portion of the benefit important in the United States?

The health insurance premium is important in the United States, because healthcare is not provided by the government for everyone in the United States. Most people receive their healthcare through their employer. Thus, if one is not eligible to receive Medicare until he or she turns 65 years-old, for example, the cost of retiring before age 65 is larger than just the cost of foregoing earnings, it’s also foregoing health care insurance premiums. (c) For what industries might one expect such opportunities to be presented to workers?

These types of retirement incentives are most likely to arise in industries or occupations in which (1) older workers are paid a lot more than younger (new) workers and/or (2) older workers are not as productive as younger workers.

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11-10. (a) Why would a firm ever choose to offer profit-sharing to its employees in place of paying piece rates?

Piece rates can be very difficult to pay in some situations. For example, in a situation in which a group of workers is responsible for producing the good, determining who made what may be impossible. Consider Southwest Airlines, which is known to have a profit sharing program that is well-liked by its employees. To pay a flight attendant a piece rate, the airline would have to survey passengers as they depart the plane, and then, from the passengers’ opinions, pay the appropriate piece rates. Clearly this is untenable. Profit sharing, on the other hand, is a convenient way to approximate the piece rate system. Since all workers are covered by profit sharing at Southwest Airlines, all workers have a continuous incentive to do their job very well. They also have the added incentive to make sure that their co-workers also do their jobs well. (b) Describe the free riding problem in a profit-sharing compensation scheme. How might the workers of a firm “solve” the free riding problem?

When all workers are covered by a profit sharing plan, an individual worker has the incentive to shirk his responsibilities as his direct effect on profits is likely small. If all workers do this, however, the total profit created by the firm will be much smaller than it would be if workers were paid a piece rate.

One way to “solve” the free rider problem is with social pressure. If the atmosphere of the workers is that everyone works and shirkers will be punished somehow – socially, annual reviews, being fired, etc. – then the incentive to shirk is diminished. Thus, a profit-sharing scheme works best when many workers must interact with each other (such as the flight attendants, pilots, luggage movers, and ticket associates at Southwest Airlines).

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11-11. (a) How does the offering of stock options to CEOs attempt to align CEO incentives with share holder incentives?

The idea of stock options is that the CEO will get paid more (via the option to purchase shares of the firm’s stock below market value) if the share price increases during his or her tenure with the firm. Thus, as share holders want the firm to maximize the share price; by offering the CEO stock options, the CEO has a greater incentive to take actions that accomplish this. (b) Enron was a company that was ruined in part because of the stock options offered to upper management. Explain.

Although offering stock options can align CEO incentives with share holder incentives, what really happens is that the stock options provide an incentive to the CEO to maximize the short-run share price by any means possible. At Enron (and WorldCom and others), this led unethical CEOs to maximize the share price by improper accounting methods. Thus, the share price rose, but not for fundamentally strong reasons. The CEOs then cashed in their stock options before the market discovered the problem. In the long-run, share-holder value was not maximized, though CEO wealth may be. (c) In addition to accounting reforms, how might stock options be changed to try to prevent situations like what happened at Enron from occurring in the future?

One possible solution to the problem in (b) is to issue stock options that cannot be cashed in until the CEO has been gone from the company for some time (two, five, or even ten years). Such options would supposedly cause the CEO to make the best long-run decisions for the firm.

11-12. (a) Personal injury lawyers typically do not charge a client unless they obtain a monetary award on their client’s behalf. Why? One reason is that many litigants with worthwhile lawsuits could not afford to pay lawyer expenses if they would lose. Even though they may have a good case, they are not certain to win.

And so without this type of arrangement, these litigants may not choose to go forward with the lawsuit.

Another reason is incentives. By having the lawyers receive payment only when an award is received, the incentives of the lawyer are better aligned with the objective of the litigant. In essence, this is a profit-sharing payment scheme. (b) What would happen to the number of lawsuits if lawyers had to charge an hourly rate win or lose and could not charge a fixed percentage of the award?

By all accounts, this would greatly reduce the number of lawsuits as litigants would not go forward with frivolous lawsuits. The problem, of course, is that some potential litigants would not pursue legitimate lawsuits either, because they are risk averse and would be afraid of losing and being stuck with huge lawyer fees.

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11-13. Consider the following four tasks (all of which require significant time and/or effort): (1) Trekking through a forest carrying a trowel and 40 saplings, and every quarter of a mile kneeling to the ground, digging a hole, and planting a sapling; (2) using a pick axe to extract 100 pounds of ore from the ground; (3) a team of 200 shoveling snow from the 85,000 seats in a stadium before a January football game; and (4) advising a college senior in her senior thesis which, by protocol, requires weekly 90-minute meetings plus an additional 2 hours each week of reading and preparation. Describe in detail why an employer may or may not want to pay employees by the piece to accomplish these tasts? What are some conclusions for when paying by the piece is most useful?

The problem with paying by the piece for task (1) is monitoring. It is very costly (or impossible) to monitor people walking through the forest and planting saplings. If paid by the piece, one could imagine someone taking their 40 saplings, walking one mile out of site, throwing the samplings into a ravine, and returning 8 hours later claiming to have planted all 40.

Task (2) is very easily paid a piece rate as the worker needs to actually undertake the effort to mine 100 pounds of ore.

The problem with paying by the piece for task (3) is that the work is done by a team. In the end, the entire team has cleared all of the snow in the stadium, so maybe a team-reward or profitsharing scheme could be employed, but it would likely be difficult to know exactly how much snow was cleared by each person.

The problem with task (4) is quality control. If the professor agrees to advise a senior thesis, the Dean of the Faculty will only know if the student received credit for the work, but that credit is assigned by the professor. Unless the Dean is willing to read all of the senior theses that received credit to evaluate their quality, the university may not be able to judge very well which professors spent 90 minutes each week with the student plus a couple more hours each week in preparation versus which professors met only once a month for 30 minutes each time.

The lesson is that piece rates are best used when work is individualized and can be easily monitored and measured with the worker having little or no control over the quality of the work.

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11-14. Economists and psychologist have long wondered how worker effort relates to wages.

Specifically, the question is whether worker effort responds to increased wages alone or whether effort also responds to relative wages. (a) Design a classroom experiment that would allow you to quantify the relationship between effort, reward, and relative reward.

The reward is going to be M&Ms. At the start of the experiment, each student is secretly given an identity (maybe an ID number) and a wage. For each unit of “output” produced, student i is paid wi M&Ms. Each student is then given a sheet of paper that shows all of the wages being paid (e.g., wages range from w = 1 to w = 5), but students don’t know who is earning which wage. Alternatively, you might put students in groups of five and tell them their own wage and what the average wage is in their group of 5.

Each student is then given 200 single-digit addition problems and 1 minute to answer as many of the questions as they can. Each student, of course, must put their ID number on their answers in order to be paid later. (Note, the experimenter must be able to align wage rates with output, not only to collect data but to also pay the students after the experiment.) (b) Explain how the data you collect can be used to identify both relationships. What do you think you would find?

Consider a class with 20 students. Divide the group into 4 groups of 5 each. In one group, the wage rates are 1, 2, 3, 4, and 5 with an average of 3. In the next group, the wage rates are 3, 4, 5, 6, and 7 with an average of 5. And so on, with averages of 7 and 9 in the last two groups respectively. Everyone is then given 200 easy math problems and 1 minute to do as many of them as they like. As the experimenter, I need to know each person’s wage and each person’s answers. After class, I can then score the answers, determine each students “pay,” and pay them at the next class. For each student, then, I know their total output, wage, and their wage relative to their group’s average. My guess is that there will be a positive relationship between wage and output, but maybe not. I don’t know if relative wage will matter or not. The answer might also depend on the reward. Though it may not pass a human subjects committee, if the reward was extra credit, there might not be any wage or relative wage effect.

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11-15. Some compensation schemes include a signing bonus while others include the potential to receive annual year-end bonuses. (a) From the firm’s perspective, what are the benefits of offering a signing bonus? What are the benefits of offering a year-end bonus?

Offering a signing bonus is a means by which firms compete for talent. A signing bonus may be used to signify value or to allow a potential worker to pay for transferring jobs. It is also a means by which firms might be able to keep annual salaries relatively equal while still paying the most valuable workers more.

Year-end bonuses can be rewards for merit or can be akin to offering profit sharing to workers if bonuses are tied to firm performance. Thus, in lieu of offering only a commission or only a piece-rate scheme, year-end bonuses allow the firm to dangle the idea of profit sharing, not shirking, etc. in front of its workers all year long. (b) If a firm pays its sales staff a piece rate and a year-end bonus, why will it be the case that the rate of pay per piece is less than the market value? Why will the sales staff willingly accept such an arrangement?

Suppose each unit of output (or piece) is worth $11 to the firm. At the end of the year, the firm may have a policy that it awards 10% bonuses to people who “had a good year.” In this case, the firm would pay a piece rate of $10 per piece and then top this off with a 10% (or $1 per piece) year-end bonus. Clearly the firm must pay a rate per piece throughout the year that is lower than market value in order to afford the year-end bonus. As long as the firm is known to not renege on its promise of a bonus, the workers should be fine with this. (If the firm was a frequent renege, workers would learn this and stop valuing the bonus scheme.) (c) How does the existence of year-end bonuses support the bonding critique?

A year-end bonus is essentially a bond. The worker knows that if she performs as expected, she will receive the bonus. If she shirks on the job, however, or doesn’t meet performance targets or if she leaves the firm mid-year, she will forego the bonus. That is, she foregoes the bond that she placed on the job.

To further illustrate this point, Wall Street firms are famous for offering year-end bonus packages. As a result, (1) many workers who want to change jobs simply do not in months 8 – 12 as they know they would be leaving considerable monies on the table, (2) workers who do change jobs mid-year are offered considerable signing bonuses to make up for the year-end bonus that is being foregone, and (3) most of the turnover between jobs happens in months 1 – 3, shortly after year-end bonuses have been announced.

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CHAPTER 12 12-1. Suppose 25,000 persons become unemployed. You are given the following data about the length of unemployment spells in the economy: Duration of Spell (in months) 1 2 3 4 5 6

Exit Rate 0.60 0.20 0.20 0.20 0.20 1.00

where the exit rate for month t gives the fraction of unemployed persons who have been unemployed t months and who “escape” unemployment at the end of the month. (a) How many unemployment-months will the 25,000 unemployed workers experience?

The data can be used in the problem to calculate the number of workers who have 1 month of unemployment, the number who have 2 months of unemployment, and so on, and how many months of unemployment are associated with workers who get a job after a given duration.

Duration (Months) 1 2 3 4 5 6

Exit Rate 0.60 0.20 0.20 0.20 0.20 1.00

# Unemp: Start of Month 25,000 10,000 8,000 6,400 5,120 4,096

# of Exiters 15,000 2,000 1,600 1,280 1,024 4,096

# of Stayers 10,000 8,000 6,400 5,120 4,096 0

# Months For Duration 15,000 4,000 4,800 5,120 5,120 24,576

The 25,000 workers will experience 58,616 months of unemployment, 2.34 months per worker. (b) What fraction of persons who are unemployed are “long-term unemployed” in that their unemployment spells will last 5 or more months?

Only 5,120 (1,024 + 4,096) of the 25,000 workers (20.5 percent) are in spells lasting 5 or more months. (c) What fraction of unemployment months can be attributed to persons who are long-term unemployed?

Although only 20.5 percent of workers are unemployed for 5 or more months, they account for 29,696 (5,120 + 24,576) of the 58,616 (50.7 percent) months of unemployment.

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12-2. According the U.S. labor statistics, roughly 5.8 million people were unemployed in 2006. Of these, 2.1 million were unemployed for less than 5 weeks, 1.7 million were unemployed for 5 to 14 weeks, 900,000 were unemployed for 15 to 26 weeks, and 1.1 million were unemployed for 27 or more weeks. Assume that the average spell of unemployment is 2.5 weeks for anyone unemployed for less than 5 weeks. Similarly, assume the average spell is 10 weeks, 20 weeks, and 35 weeks for the remaining categories. How many weeks did the average unemployed worker remain unemployed? What percent of total months of unemployment are attributable to the workers that remained unemployed for at least 15 weeks?

The total number of weeks of unemployment is calculated as: 2.1 × 2.5 weeks + 1.7 × 10 weeks + 0.9 × 20 weeks + 1.1 × 35 weeks ≈ 81.65 million weeks.

The second two groups comprise the unemployed workers who remained unemployed for at least 15 weeks. These two groups account for 0.9 × 20 weeks + 1.1 × 35 weeks ≈ 56.5 million weeks of unemployment. Looked at differently, these two group comprising the long-term unemployed accounted for 56.5 ÷ 81.65 = 69.2% of all weeks of unemployment.

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12-3. The previous question concerned the unemployment rate and the distribution of weeks of unemployment immediately prior to the Great Recession. Looking at the Great Recession, the data show roughly 12.7 million people were unemployed in 2009. Of these, 2.7 million were unemployed for less than 5 weeks, 3.3 million were unemployed for 5 to 14 weeks, 2.5 million were unemployed for 15 to 26 weeks, and 4.2 million were unemployed for 27 or more weeks. Generally, how did the unemployment picture change with the Great Recession?

First, let’s repeat the analysis from 12-2 but for 2009.

The total number of weeks of unemployment is calculated as: 2.7 × 2.5 weeks + 3.3 × 10 weeks + 2.5 × 20 weeks + 4.2 × 35 weeks ≈ 236.75 million weeks.

The long-term unemployed comprised 2.5 × 20 weeks + 4.2 × 35 weeks ≈ 197 million weeks of unemployment, or 197 ÷ 236.75 = 83.2% of all weeks of unemployment.

Generally, there are two extremely important take-away points regarding unemployment during the Great Recession: (1) The sheer number of unemployed people increased dramatically, by more than double. (2) The number of long spells of unemployment also increased markedly.

Although the percent of unemployment weeks “only” increased from about 69% before the Great Recession to over 83% during the Great Recession, the number of such weeks ballooned from about 47 million before the Great Recession to over 197 million during the Great Recession.

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12-4. Suppose the marginal revenue from search is MR = 50 – 1.5w, where w is the wage offer at hand. The marginal cost of search is MC = 5 + w. (a) Why is the marginal revenue from search a negative function of the wage offer at hand?

If the offer-at-hand is relatively low, it pays to keep on searching as the next offer is likely higher than the offer-at-hand. If the offer-at-hand is very high, however, it does not pay to keep on searching since it is unlikely that the next search will generate a higher wage offer. (b) Can you give an economic interpretation of the intercept in the marginal cost equation; in other words, what does it mean to say that the intercept equals $5? Similarly, what does it mean to say that the slope in the marginal cost equation equals one dollar?

The $5 indicates the out-of-pocket search costs. Even if the offer-at-hand is zero (so that there is no opportunity cost to search), it still costs money to get to the firm and learn about the details of the potential job offer. The slope equals $1, because the costs of search also vary directly with the opportunity cost of search which is the wage offer at hand. If the wage offer at hand is $10, the opportunity cost from one more search equal $10; if the wage offer at hand is $11, the opportunity cost would be $11, and so on. (c) What is the worker’s asking wage? Will a worker accept a job offer of $15?

The asking wage is obtained by equating the marginal revenue of search to the marginal cost of search, or 50 – 1.5w = 5 + w. Solving for w implies that the asking wage is $18. The worker, therefore, would not accept a job offer of $15. (d) Suppose Unemployment Insurance benefits are reduced, causing the marginal cost of search to increase to MC = 20 + w. What is the new asking wage? Will the worker accept a job offer of $15?

If we equate the new marginal cost equation to the marginal revenue equation we find that the asking wage drops to $12. The worker will now accept a wage offer of $15.

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12-5. A labor market has 50,000 people in the labor force. Each month, a fraction p of employed workers become unemployed (0 < p < 1) and a fraction q of unemployed workers become employed (0 < q < 1). (a) What is the steady-state unemployment rate?

The steady-state unemployment rate is p / (p + q). (b) Under the steady-state, how many of the 50,000 in the labor force are employed and how many are employed each month? How many of the unemployed become employed each month?

As the unemployment rate is p / (p + q), the employment rate is 1 – p / (p + q) = q / (p + q).

Therefore, we have that: Number Employed Each Month = 50,000 × q / (p + q).

Number Unemployed Each Month = 50,000 × p / (p + q).

As q fraction of the unemployed become employed each month, the total number of people flowing from unemployment to employment (which equals the total number of people flowing from employment to unemployment each month) is: Monthly flow to and from unemployment = 50,000 × p × q / (p + q). (c) Suppose p = 0.08 and q = 0.32. What is the steady-state unemployement rate and how many workers move from employment to unemployment each month?

This question can be answered using the parameter values and the equations above: The steady-state unemployment rate

= p / (p + q) = 0.08 / (0.08 + 0.32) = 20%.

Monthly flow to and from unemployment = 50,000 × p × q / (p + q) = 50,000 × 0.08 × 0.32 / (0.08 + 0.32) = 3,200.

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12-6. Compare two unemployed workers; one is 25 years-old while the other is 55 years-old.

Both workers have similar skills and face the same wage offer distribution. Suppose that both workers also incur similar search costs. Which worker will have a higher asking wage?

Why? Can search theory explain why the unemployment rate of young workers differs from that of older workers?

The marginal revenue of search depends on the length of the payoff period. Younger workers have the most to gain from obtaining higher paying jobs, since they can then collect the returns from their search investment over a longer expected work-life. As a result, it pays for younger workers to set their asking wage at a relatively high level. This implies that younger workers will tend to have higher unemployment rates and longer spells of unemployment than older workers.

12-7. Suppose the government proposes to increase the level of UI benefits for unemployed workers. A particular industry is now paying efficiency wages to its workers in order to discourage them from shirking. What is the effect of the proposed legislation on the wage and on the unemployment rate for workers in that industry? (Hint: this is best shown with a graph similar to Figure 12-13.)

The introduction of UI benefits shifts the no-shirking supply curve upwards (from NS to NS ), because a higher wage would have to be paid in order to attract the same number of workers who do not shirk. As a result, the new equilibrium (point Q ) entails a higher efficiency wage and leads to a larger number of unemployed workers (i.e., lower total employment).

Dollars

S Q NS

Q

NS

P D Employment E

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12-8. During the debate over a federal spending bill, Senator A proposed changing the schedule for paying out unemployment benefits to be one where benefits were doubled, but offered for half the current duration (so that UI benefits would expire after 13 weeks). In contrast, Senator B proposed cutting UI benefits in half but to pay benefits for twice as long (so that UI benefits would not expire until after 52 weeks). Comparing to the status quo of offering UI benefits for 26 weeks, contrast both plans along the following dimensions: overall unemployment rate, average duration of unemployment spells, and the distribution of wages accepted by workers coming out of a spell of unemployment.

The answers to this problem are somewhat complicated, because both plans provide a new benefit and a new cost. Plan A’s new benefit is doubled benefits while its new cost is benefits for a shorter period of time. Plan B’s new benefit is benefits for twice as long while its new cost is that it offers half the benefit of the status quo. Moreover, the results of the plans likely depend on the point of time in the unemployment spell under consideration.

Overall Unemployment Rate: As Plan A offers twice the benefit, people may find that they change jobs more frequently if they are fairly certain of finding new employment. In the United States, most unemployed workers find new employment within 13 weeks, so plan A may encourage the (short-term) unemployment rate to increase. In contrast, plan B may encourage the (short-term) unemployment rate to fall as people receive less benefit when unemployed.

Average Duration of Unemployment Spells: At the start of an unemployment spell, Plan A may encourage longer spells as the benefit to unemployment remains high. As the 13th week approaches, however, Plan A will likely encourage ending an unemployment spell as benefits will expire sooner. Thus, there will likely be longer short spells but fewer long spells under Plan A. Plan B is exactly the opposite. At the start of an unemployment spell, plan B will likely encourage ending the spell as the benefit to continuing is lower than the status quo. As the 26th week approaches, however, Plan B will encourage a longer spell as benefits (though at a lower level) will continue for another 26 weeks.

Distribution of Accepted Wages: The distribution of accepted wages follows the distribution of unemployment spells. Under Plan A, the accepted wage will be higher than the accepted wage under the status quo early in the unemployment spell, but will be lower later in the unemployment spell. Similarly, the distribution of accepted wages under Plan B will be lower than the accepted wage under the status quo early in the unemployment spell but higher later in the unemployment spell.

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12-9. Consider a small island economy in which almost all jobs are in the tourism industry.

A law is passed mandating that all workers in the tourism industry be paid the same national hourly wage, even though workers differ in their skills and effort. In fact, some workers simply cannot produce enough output to be worth the national wage. (a) How will a worker’s optimal job search strategy differ from that discussed in the text?

What is the essential difference between this example and the general case discussed in the text?

The worker’s optimal job search strategy will differ from that discussed in the text in that all jobs are associated with the same wage, so turning down job offers and extending one’s search in hopes of finding a higher wage are in vain. The only reason to not accept a job offer is if firms differ in their working conditions. But in general, people will search for any offer, and accept it. (b) Despite the law, workers become more productive with experience. How might firms compete over workers when all workers must be paid the same wage?

Firms will compete over workers by offering different job amenities, such as better working hours, better working conditions, subsidizing an employee cafeteria, offering a lighter work load, granting more vacation days, etc.

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12-10. During the Great Recession, many news stories focused on a rising number of discouraged workers. The implication of many of these stories is that the unemployment situation was worse than indicated by the unemployment rate because of the existence of these discouraged workers. (a) What are some of the reasons typically given for not including discouraged workers in the unemployment rate calculation?

The standard argument for not including discouraged workers in the unemployment rate calculation is that these people may, for a variety of reasons, be choosing to no longer seek work.

Mainly, they may be taking advantage of a low-wage state of the economy to consume more leisure or to take care of family members. Some discouraged workers may also return to school. (b) Show mathematically that if discouraged workers are treated as unemployed that the unemployment rate would increase.

Let E be the number of employed people, U be the number of unemployed people, and D be the number of discouraged workers. When discouraged workers are not included in the unemployment rate, the unemployment rate is calculated as U / (U+ E). When discouraged workers are included in the unemployment rate, the unemployment rate is calculated as (U + D) / (E + U + D). As D was added to both the numerator and the denominator, and as D is positive, the unemployment rate must be higher when discouraged workers are included in the calculation. (c) Show mathematically that the unemployment rate as defined by the Bureau of Labor Statistics would be lower if data on the underground economy was more available.

Let E be the number of employed people as reported to the BLS, UNU be the number of unemployed people who do not work in the underground economy, and UU be the number of people who are reported as unemployed by the BLS who actually have jobs in the underground economy. Because the BLS does not know that UU people are actually, employed, the unemployment rate is calculated as (UNU + UU) / (E + UNU + UU). Had the BLS known, however, of the people working in the underground economy, the unemployment rate would be calculated as (UNU) / (E + UNU + UU), which is clearly less than the actual unemployment rate.

12-11. Reread “Theory At Work: Cash Bonuses and Unmployment” from the text and answer the following questions. (a) What is the general research question? What is the difference between the control group and the treatment group?

The general question is whether people receiving UI benefits (for up to 26 weeks) will exit unemployment sooner (and thereby possibly save the state money) if they are given a financial incentive to do so. The control group are unemployed workers who are on UI and under the regular UI rules. The treatment group are unemployed workers who are on UI and have been told they will receive a cash payout if they accept a job within a certain amount of time (11 weeks in Illinois and 6 weeks in Pennsylvania) and keep the job for at least four months. (b) Why is it an important result that accepted wages were essentially the same between the control group and the treatment group?

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It is important that the wages eventually earned by the treatment group were essentially the same as the wages eventually earned by the control group, because this supplies policy-makers with evidence that the treatment group are not taking “bad” jobs just to get the cash incentive. Rather, if wages and duration of employment at the new job look the same for both groups, then the cash incentive really can be viewed as encouraging unemployed workers to act more quickly to leave unemployment and forego UI benefits. (c) What if anything might this research imply about whether discouraged workers should be included in an unemployment rate calculation?

The general take-away from the research “might” be extendable to discouraged workers. Of course, discouraged workers are not receiving UI benefits. But if discouraged workers remain out of the labor force simply because they are taking more leisure during a time of low wages, then they certainly should not be included in unemployment rate calculations (which they are not).

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12-12.

(a) The table below provides 2006 unemployment rates for whites, blacks, and Hispanics in the United States separately for those with a high school degree (and no more schooling) and those with a college degree. Describe how educational status is related to unemployment rates for each of these groups. For which racial groups is a college education an equalizer in terms of unemployment rates compared to whites?

Whites Blacks Hispanics

2006 Unemployment Rate High School College Degree Degree 3.7 2.0 8.0 2.8 4.1 2.2

The table shows that unemployment falls for all races as education increases. It further shows that discrepancies in unemployment rates across racial groups are much more of a problem at lower levels of education. (b) Consider Figure 12-2. Looking at the years of the Great Recession, did unemployment increase for all education groups? Which group was most affected?

According to Figure 12-2, the unemployment rate increased sharply for all education groups during the Great Recession. Most observers would say that High School Dropouts were the most (adversely affected), though it does depend a little on how one measures the effect. College Graduates saw their unemployment rate increase by 3 percentage points, but this was almost a 150% increase as it went from 2% to about 5%. High School graduates saw their unemployment rate increase by about 6 percentage points, going from about 4% to over 10%. This group, too, therefore, experienced about a 150% increase in the unemployment rate. Most observers would say that High School Dropouts were the most affected because their unemployment rate increased by about 8 percentage points—increasing from about 7% to about 15%. In comparison, however, this was about a 115% increase in the rate.

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12-13. Suppose the current UI system pays $500 per week for up to 15 weeks. The government considers changing to an UI system that requires someone to be unemployed for five weeks before receiving any benefits. After five weeks, the person receives a lumpsum payment of $2,500. He then receives no benefits for another five weeks. If he is still unemployed then, he receives a second lump-sum payment of $2,500. He again receives no benefits for another five weeks. If he is still unemployed then, he receives a third and final lump-sum payment of $2,500. Provide a graph similar to Figure 12-11 showing how the probability of finding a job over time is likely to be different under the status quo and the proposed scheme.

The new UI plan provides an incentive to be unemployed after 5, 10, and 15 weeks. It provides less (actually no) incentive to be unemployed during the other weeks other than for banking time to qualify for payments later. This idea is embedded in the following graph.

Probability of finding a new job

0

5

10 Weeks of Unemployment

15

12-14. Unemployment Insurance automatically stimulates the economy during an economic contraction, which is good from the workers’ point of view. From the firm’s point of view, however, the UI system can be overbearing on business during prolonged contractions. (a) What is it about the UI system that generates these opposing views?

UI payments (made by firms) depend on the firm’s record of layoffs. The more layoffs in a firm’s recent past, the greater the firm’s UI payments will be. Thus, if a firm has had recent layoffs during a recession, it will have to pay more in taxes to the government. Worse, however, is that firms may be more reluctant during contractions, compared to when the economic outlook is good, to hire workers who may increase its profits if the economy continues to recover but would lower profits if the economy got even worse. The problem is that the firm doesn’t want to hire workers only to fire them if the economy doesn’t continue to improve as this places a further burden on the firm whose UI obligations will increase following the firing. (b) How could the UI system be changed to also assist firms during economic contractions while not removing the benefits available to laid-off workers?

UI payments could be linked to a longer firm history of layoffs. Firms could also be given credit for new workers hired during a recession.

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12-15. Consider the standard job search model as described in the text. (a) Why are the asking wage and expected unemployment duration positively related?

Expected unemployment duration is positively related to the asking wage, because the higher is the asking wage, the less likely it is to be offered a job that one accepts (because the wage associated with the offer exceeds the asking wage). (b) Can the standard job search model explain why unemployment duration is longer, on average, for secondary workers when compared to primary workers? Discuss.

Yes. The asking wage is likely lower for primary workers than it is for secondary workers. By definition, secondary workers have other options – stay at home, go back to school, lounge around, volunteer, etc. As secondary workers do not need a job, they have the luxury of setting a high asking wage. Alternatively, primary workers need to have a job to support the household.

Thus, although primary workers would like a well-paying job, they may find themselves setting a low asking wage because the household needs money coming in. If this description is true, the data should show that primary workers experience shorter spells of unemployment, on average, than secondary workers (assuming secondary workers are classified as being unemployed). (c) In the context of the standard search model, explain how the economy-wide average asking wage and unemployment duration are affected by an expanded underground (cash) economy. What is the effect on the equilibrium unemployment rate?

The underground economy provides an income to people who otherwise appear to be unemployed (or at least jobless). This outside option of working in the underground economy raises the asking wage just as increased unemployment benefits increase the asking wage, and therefore the existence of an expanded underground economy, via higher asking wages, will increase the average unemployment duration. Assuming people who operate in the underground economy are not employed elsewhere and report to the government as being unemployed, then an expanded underground economy raises the equilibrium unemployment rate.

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