ECON 115  Labor Economics
Drake University, Spring 2024
William M. Boal


FINAL EXAM ANSWER KEY
Version A
I. Multiple choice
(1)d. (2)d. (3)c. (4)a. (5)c. (6)d. (7)c. (8)a. (9)b. (10)c.
(11)c. (12)a. (13)d. (14)b.
II. Problems
(1) [Elasticity of labor demand: 8 pts]
 decrease.
 2 percent. Set 0.2 = percent change in jobs / 10 percent, and solve.
 increase.
 8 percent. Percent change in workers' income = percent change in jobs + percent change in wage.
(2) [Individual labor supplyincome and substitution effects: 22 pts]
Note that the "hypothetical budget line" is drawn tangent to the new indifference curve, but parallel to budget line #1.
 50 hours.
 $100. The graph shows that if Beth works zero hours, she can still enjoy $200 in consumption.
 $20 per hour. The wage is the negative of the slope of the budget line.
 $10 per hour. The wage is the negative of the slope of the budget line.
 Income effect: work more.
Reason: A decrease in the wage is like a decrease in nonlabor income in that the budget line is now closer to the origin. So the income effect is to "purchase" less leisure and less consumption. More precisely, the income effect is a movement between indifference curves and parallel budget lines, here from tangency with budget line #1 to tangency with the hypothetical budget line.
 15 hours.
 Substitution effect: work less.
Reason: A decrease in the wage is a decrease in the "price" of leisure compared to the price of consumption. So the substitution effect is to "purchase" more leisure and lessconsumption. More precisely, the substitution effect is a movement along a single indifference curve from tangency with hypothetical budget line to tangency with budget line #2.
 10 hours.
 Total effect: work more. Reason: total effect = substitution effect + income effect.
 +5 hours.
 (w,h) = ($20,25 hours), ($10,30 hours). This labor supply curve bends backwards.
(3) [SR labor demand: 9 pts]
 Value of marginal product = output price × MP_{E}
= 30 (K/E)^{1/2}.
 The firm maximizes profit by choosing E so that wage = VMP_{E},
or 20 = 30 (K/E)^{1/2}. Solve to get E* = 36.
 Using production function, q* = 2 (16×36)^{1/2} = 48 units of output.
 Profit = total revenue  total cost
= total revenue  cost of labor  cost of capital
= $1440  $720  $160
= $560.
(4) [Payroll tax or subsidy: 14 pts] To find equilibrium with a tax, find the employment level where demand is higher than supply by the amount of the tax.
 60 million.
 $21.
 $17.
 $65 million.
 195 million.
 $240 million.
 $20 million.
(5) [VSL, safety regulation: 12 pts]
 VSL = Δ earnings / Δ risk = 980 / (1/10,000)
= $9.8 million.
 Cost per statistical life saved = cost / reduction in death rate
= $100,000 / (0.7  0.5) = $500 thousand.
 Yes, the system should be required becasuse VSL > cost per statistical life saved.
(6) [Simple model of schooling decision: 10 pts]
 NPV "no college" = 50,000 + (50,000/1.08) = $96,296.
 NPV "college" = 30,000 + (134,000/1.08) = $94,074.
 Chooses "no college" because NPV is larger.
 Set 50,000 + 50,000/(1+r) = 30,000 + 134,000/(1+r) and solve to get
r*=5 percent.
 Chooses "college" because the benefits from "college" lie entirely in the future. As r decreases, then NPV of "college" rises more than NPV of "no college."
(7) [Skillbiased technical change: 8 pts]
 relative wage will decrease.
 5 percent. (Substitute: 7 percent/x = 1.4 and solve for x.)
 demand must shift right to make relative wage increase.
 21 percent. (Substitute: 1.4 = (x7 percent)/10 percent, and solve for x.)
(8) [Migration decision: 4 pts]
 $440 thousand.
 $550 thousand.
 $110 thousand.
(9) [Oaxaca decomposition: 6 pts]
 Raw log wage differential is found by substituting each group's average schooling into its own wage equation, to give 2.6  1.7 = 0.9.
 The log wage differential due to schooling equals the coefficient of schooling for green workers (who are assumed not subject to discrimination) times the difference in average schooling
= 0.10 (1410) = 0.9.
 The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes × blue workers' average schooling
= (1.20.9) + (0.100.08)10 = 0.5.
Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.
(10) [Monopsony wage discrimination: 12 pts]
This is similar to problem (4) on Exam 2, but with two groups of workers.
 MLC_{G} = 8 + (E_{G} /15).
MLC_{B} = 4 + (2 E_{B} /5).
 For each group, set VMP equal to MLC and solve for E.
This gives E_{G} = 180 and E_{B} = 40.
 Substitute employment into supply equations to get w_{G} = $14 and w_{B} = $12. Note that both groups are paid less than VMP due to monopsony power, but their wages are different because of the shapes of their respective labor supply curves.
 If the minimum wage is lower than the efficient (or competitive) wage, then employment is determined by the supply curve. Here the minimum wage = $15 < efficient wage = $20.
So substitute the minimum wage into the supply equation for each group and solve to get E_{G} = 210 and E_{B} = 55.
(10) [Monopoly unionism: 10 pts]
 E = 800.
 Labor demand curve has intercepts at W=$60 and E=1200.
 W=$30 and E=600.
 Plot outcome on demand curve at W=$30 and E=600.
 Efficiency loss = $1000, the area of the triangle bounded by the labor demand curve, the horizontal line at W_{C}, and a vertical line at E=600.
(12) [Piece rates and time rates: 10 pts]
 30 items, where MC=piece rate.
 $18, that is, 30 items times the piece rate.
 $9, the previous answer minus TC of packing 30 items per hour.
 $11, the hourly pay minus TC of packing 20 items per hour.
 Prefers Firm #2 because net benefit is higher.
(13) [Markov model: 10 pts]
 0.03.
 0.47.
 3 percent.
 47 percent.
 6 percent, found by setting inflows into unemployment (E × 0.03) equal to outflows from unemployment (U × 0.47), and solving for U/(E+U).
(14) [Job search: 10 pts]
 W = $12, where MC = MB.
 Yes, would accept because $15 is greater than reservation wage.
 MC would shift right (or down) because the marginal cost of further search would fall if the worker enjoys unemployment insurance (UI) benefits.
 The reservation wage would therefore increase because the worker could hold out for a higher wage offer.
 Time to find a new job would increase because the reservation wage would be higher.
III. Critical thinking
(1) A "tournament" pay scheme has both advantages and disadvantages.
 One advantage relative to straight hourly pay is that sales workers have an incentive to work harder. Unlike a simple piece rate, however, a "tournament" shelters workers from firmwide shifts in output due to factors that are beyond their control such as changes in the firm's advertising or pricing, competition from rival firms, and recessions.
 One disadvantage over straight hourly pay is that sales workers now face a disincentive to help each other. Since pay is determined by a worker's output relative to other workers, no one will want to help increase anyone else's output by, for example, sharing sales leads and contact information. Workers might even have an incentive to sabotage each other's work. Alternatively, workers might collude. Workers might all agree to reduce effort and share the bonuses.
In either case, output and profit are reduced.
(2) Theories of delayed compensation, specific onthejob training, and general onthejob training all predict that workers will enjoy higher wages, the longer they stay with their current employer. However, the reasons for this correlation are different for each theory.
 Both specific onthejob training and general onthejob training predict that workers' productivity will be higher, the longer they stay with their current employer because workers are acquiring more human capital over time. Specific onthejob training assumes this human capital is only productive at the current employer while general onthejob training assumes this human capital is productive at other employers, too.
 Both specific onthejob training and delayed compensation predict that workers' likelihood of quitting will be lower, the longer they stay with their current employer. Under both theories, workers are initially paid less than they would be paid at other employers, and then later are paid more than they would be paid at other employers.
Version B
I. Multiple choice
(1)e. (2)b. (3)b. (4)b. (5)a. (6)b. (7)c. (8)d. (9)c. (10)d.
(11)a. (12)d. (13)a. (14)a.
II. Problems
(1) [Elasticity of labor demand: 8 pts]
 decrease.
 3 percent. Set 0.3 = percent change in jobs / 10 percent, and solve.
 increase.
 7 percent. Percent change in workers' income = percent change in jobs + percent change in wage.
(2) [Individual labor supplyincome and substitution effects: 22 pts]
Note that the "hypothetical budget line" is drawn tangent to the new indifference curve, but parallel to budget line #1.
 50 hours.
 $200. The graph shows that if Beth works zero hours, she can still enjoy $200 in consumption.
 $10 per hour. The wage is the negative of the slope of the budget line.
 $20 per hour. The wage is the negative of the slope of the budget line.
 Income effect: work less.
Reason: An increase in the wage is like an increase in nonlabor income in that the budget line is now farther from the origin. So the income effect is to "purchase" more leisure and more consumption. More precisely, the income effect is a movement between indifference curves and parallel budget lines, here from tangency with budget line #1 to tangency with the hypothetical budget line.
 10 hours.
 Substitution effect: work more.
Reason: An increase in the wage is an increase in the "price" of leisure compared to the price of consumption. So the substitution effect is to "purchase" less leisure and more consumption. More precisely, the substitution effect is a movement along a single indifference curve from tangency with hypothetical budget line to tangency with budget line #2.
 +15 hours.
 Total effect: work more. Reason: total effect = substitution effect + income effect.
 +5 hours.
 (w,h) = ($10,30 hours), ($20,35 hours). This labor supply curve slopes up.
(3) [SR labor demand: 9 pts]
 Value of marginal product = output price × MP_{E}
= 10 (K/E)^{1/2}.
 The firm maximizes profit by choosing E so that wage = VMP_{E},
or 10 = 10 (K/E)^{1/2}. Solve to get E* = 25.
 Using production function, q* = 4 (25×25)^{1/2} = 100 units of output.
 Profit = total revenue  total cost
= total revenue  cost of labor  cost of capital
= $500  $125  $250
= $125.
(4) [Payroll tax or subsidy: 14 pts] To find equilibrium with a subsidy, find the place where supply is higher than demand by the amount of the subsidy.
 80 million.
 $19.
 $23.
 $75 million.
 225 million.
 $320 million.
 $20 million.
(5) [VSL, safety regulation: 12 pts]
 VSL = Δ earnings / Δ risk = 1025 / (1/10,000)
= $10.25 million.
 Cost per statistical life saved = cost / reduction in death rate
= $2,000,000 / (0.3  0.2) = $20 million.
 No, the system should not be required becasuse VSL < cost per statistical life saved.
(6) [Simple model of schooling decision: 10 pts]
 NPV "no college" = 50,000 + (50,000/1.05) = $97,619.
 NPV "college" = 20,000 + (127,000/1.05) = $100,952.
 Chooses "college" because NPV is larger.
 Set 50,000 + 50,000/(1+r) = 20,000 + 127,000/(1+r) and solve to get
r*=10 percent.
 Chooses "no college" because the benefits from "college" lie entirely in the future. As r increases, then NPV of "college" falls more than NPV of "no college."
(7) [Skillbiased technical change: 8 pts]
 relative wage will decrease.
 2.5 percent. (Substitute: 4 percent/x = 1.6 and solve for x.)
 demand must shift right to make relative wage increase.
 20 percent. (Substitute: 1.6 = (x4 percent)/10 percent, and solve for x.)
(8) [Migration decision: 4 pts]
 $630 thousand.
 $840 thousand.
 $210 thousand.
(9) [Oaxaca decomposition: 6 pts]
 Raw log wage differential is found by substituting each group's average schooling into its own wage equation, to give 2.4  1.9 = 0.5.
 The log wage differential due to schooling equals the coefficient of schooling for green workers (who are assumed not subject to discrimination) times the difference in average schooling
= 0.10 (1210) = 0.2.
 The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes × blue workers' average schooling
= (1.21.1) + (0.100.08)10 = 0.3.
Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.
(10) [Monopsony wage discrimination: 12 pts]
This is similar to problem (4) on Exam 2, but with two groups of workers.
 MLC_{G} = 2 + (E_{G} /5).
MLC_{B} = 8 + (E_{B} /10).
 For each group, set VMP equal to MLC and solve for E.
This gives E_{G} = 90 and E_{B} = 120.
 Substitute employment into supply equations to get w_{G} = $11 and w_{B} = $14. Note that both groups are paid less than VMP due to monopsony power, but their wages are different because of the shapes of their respective labor supply curves.
 If the minimum wage is lower than the efficient (or competitive) wage, then employment is determined by the supply curve. Here the minimum wage = $15 < efficient wage = $20.
So substitute the minimum wage into the supply equation for each group and solve to get E_{G} = 130 and E_{B} = 140.
(11) [Monopoly unionism: 10 pts]
 E = 800.
 Labor demand curve has intercepts at W=$60 and E=1200.
 W=$40 and E=400.
 Plot outcome on demand curve at W=$40 and E=400.
 Efficiency loss = $4000, the area of the triangle bounded by the labor demand curve, the horizontal line at W_{C}, and a vertical line at E=400.
(12) [Piece rates and time rates: 10 pts]
 25 items, where MC=piece rate.
 $25, that is, 25 items times the piece rate.
 $12.50, the previous answer minus TC of packing 25 items per hour.
 $7, the hourly pay minus TC of packing 20 items per hour.
 Prefers Firm #1 because net benefit is higher.
(13) [Markov model: 10 pts]
 0.98.
 0.52.
 2 percent.
 48 percent.
 4 percent, found by setting inflows into unemployment (E × 0.02) equal to outflows from unemployment (U × 0.48), and solving for U/(E+U).
(14) [Job search: 10 pts]
 W = $20, where MC = MB.
 No, would not accept because $15 is less than reservation wage.
 MC would shift up (or left) because the marginal cost of further search would increase if unemployment insurance (UI) benefits are decreased.
 The reservation wage would therefore decrease because MC would shift left.
 Time to find a new job would decrease because the reservation wage would be lower.
III. Critical thinking
Same as Version A.
[end of answer key]