FINAL EXAM ANSWER KEY
Version A
I. Multiple choice
(1)a. (2)d. (3)b. (4)b. (5)c. (6)e. (7)b. (8)a. (9)b. (10)b.
(11)b. (12)b. (13)a. (14)d. (15)b. (16)c. (17)a. (18)b.
II. Problems
(1) [Individual labor supply - income and substitution effects: 22 pts]
- 60 hours.
- $200.
- $5 per hour.
- $20 per hour.
- income effect: work less.
- -20 hours.
- substitution effect: work more.
- +10 hours.
- total effect: work less.
- -10 hours.
- (w,h) = ($5,40 hours), ($20,30 hours).
(2) [Value of a statistical life: 4 pts]
VSL = Δ annual earnings / Δ annual risk
= [(19-15)×2000] / [0.0010-0.0002] = $10 million.
(3) [LR labor demand - scale and substitution effects: 16 pts]
- Slope of any isocost line = -w/r, where r = price of capital.
The slope of isocost line #1 is -2/5.
We are given that r = $20, so w = $8 on isocost line #1.
- Similarly, the slope of isocost line #2 is - 6/5, so w = $24 on isocost line #2.
- substitution effect: use less labor.
- 40 units of labor.
- scale effect: use less labor.
- 30 units of labor.
- total effect: use less labor.
- 70 units of labor.
(4) [Mandated benefits: 12 pts] A mandated benefit shifts the labor demand curve down by the cost of the benefit to employers, but it may shift the labor supply curve down also if the benefit is valued by workers.
- Set -50 + (E/5) = 400 - (E/10) and solve to get E=1500, w = $250.
- Set -50 + (E/5) = 400 - (E/10) - 9 and solve to get E = 1470, w = $244.
- Set -50 + (E/5) - 6 = 400 - (E/10) - 9 and solve to get E = 1490, w = $242.
(5) [Gains from migration: 12 pts] If migration is costless, then in the long run, wages are equal in the two markets.
- W_{E} = $45 thousand, W_{W} = $15 thousand.
- Set W_{E} = W_{W}, then substitute (100-E_{E}) for E_{W}, and solve to get EE = 80 thousand, E_{W} = 20 thousand, and W_{E} = W_{W} = $30 thousand.
- Increase in efficiency = increase in value of output in East minus decrease in value of output in West
= (45+30)/2 thousand × 30 thousand - (30+15)/2 thousand × 30 thousand = $450 million.
(6) [Simple model of schooling decision: 10 pts] Worker chooses option with greatest NPV.
- NPV "no college" = $664,286.
- NPV "college" = $670,000.
- Chooses "college" because NPV is larger.
- Set 150 + 540/(1+r) = -50 + 756/(1+r) and solve to get r* = 8 percent.
- If r > r*, chooses "no college."
(7) [Measuring inequality: 16 pts]
- Let N be the population. Then 80 percent of the population has a total of 0.8 × N × $25000 = $20000 N earnings, while 20 percent of the population has a total of 0.2 × N × $150000 = $30000 N earnings. Total earnings are therefore $50000 N. The share of the bottom 80 percent is (20000 N) / (50000 N) = 40 percent. The Lorenz curve therefore is straight with a kinkpoint at (80 percent of population, 40 percent of earnings).
- Gini = 0.40 .
- 90-50 wage gap = (150000 - 25000) / 25000 = 500 percent.
- 50-10 wage gap = (25000 - 25000) / 25000 = 0 percent.
- 90-10 wage gap = (150000 - 25000) / 25000 = 500 percent.
(8) [Roy model: 6 pts]
- Workers move if the net gain from migration is positive--that is, if w_{Y} - moving cost > w_{X}. Substituting and solving for S gives S > 70.
- Positively selected, since workers from the high end of the distribution of S will move.
(9) [Monopsony wage discrimination: 12 pts] Recall that a monopsonist chooses the employment level by setting VMP=MLC. The monopsony wage is then found by substituting this employment level into the labor supply equation.
- For each group, set VMP equal to MLC and solve for E. This gives E_{G} = 1500 and E_{B} = 950.
- Substitute into supply equations to get w_{G} = $12.50 and w_{B} = $10.50.
- Substitute the minimum wage into the supply equation for each group to get E_{G} = 2000 and E_{B} = 1400.
(10) [Welfare effects of monopoly unionism: 4 pts]
- Substitute the union wage into the VMP (or labor demand) equation to get E = 75,000.
- The efficiency cost is the deadweight loss, the area of a triangle bounded by the VMP curve, the labor supply curve, and the vertical line at the union employment level found in part (a). Note that in this problem, the labor supply curve is a horizontal line at the competitive wage. The area of this triangle is $12.5 million.
(11) [Markov model: 11 pts] Recall that horizontal rows of the transition matrix must some to one because everyone goes somewhere.
- 0.04 .
- 0.46 .
- 0.04 .
- 0.46 .
- Flows into unemployment must equal flows out of unemployment: 0.04 E = 0.46 U. Solving for the unemployment rate U/(E+U) gives 0.08 or 8 percent.
(12) [Efficient bargaining: 9 pts] Efficient combinations of wage and employment lie on tangencies between the union's indifference curves and the firm's iso-profit curves.
- Union chooses wage at tangency between labor demand curve and the highest indifference curve that the union can reach: $30. Employer chooses employment level corresponding to that wage on its labor demand curve: 40.
- Wage = $25, employment = 80.
- Wage = $20, employment = 80.
- Both of the above combinations, plus wage = $30, employment = 90.
(13) [Piece rates and time rates: 16 pts]
- Set Abby's MC = piece rate and solve to get N=100. Pay = N × piece rate = $10.
- Set Ben's MC = piece rate and solve to get N=50. Pay = N × piece rate = $5.
- Abby's preference appears uncertain because Firm 1 pays more but also requires more effort. (However, summing the marginal costs of the additional envelopes shows that the additional effort at Firm 1 costs Abby $3.75, so Abby would in fact prefer Firm 2.)
- Ben definitely prefers firm 2 because it pays better but requires the same effort as Firm 1.
(14) [Search: 10 pts]
- Set MC = MB to find reservation wage = $19.
- Yes, accept this job because wage > reservation wage.
- If unemployment insurance benefits were increased, then the marginal cost of search would shift down because the opportunity cost of search would decrease.
- The reservation wage would increase because the MC curve has shifted down.
- Average time to find a new job would increase because the reservation wage has increased.
III. Critical thinking
- The theory of specific human capital predicts that workers with greater seniority earn higher wages. Specific human capital is training, or other skills that are only useful at this employer. Because specific human capital is worthless if the worker leaves the company, wages are structured to give both the worker and the company an incentive to stay together: each pays part of the cost and enjoys part of the return. So according to the "specific human capital" explanation, each worker's wage rises with that same worker's seniority, though not as much as VMP rises.
- The theory of matching also predicts that workers with greater seniority earn higher wages, but not because an individual worker's wage grows as they stay with the same employer. This theory argues that a good worker-employer match results in higher pay and a lower probability that the worker will leave the company. On the other hand, a poor match results in lower pay and a higher probability that the worker will leave. So at any point in time, workers with higher pay are also likely to have been with the company longer, though no individual worker's pay changes over time as that worker gains seniority.
- The theory of deferred compensation also predicts that workers with greater seniority earn higher wages. To deter shirking (and possibly to reduce turnover) employers "back-load" wages. New employees are paid less than the value of the marginal product, which is the wage they could earn elsewhere. Workers that do not shirk eventually are paid more than the value of their marginal product. Any workers that are found shirking are fired and therefore lose the opportunity for high pay later in their careers. This "back-loaded" wage structure gives workers an incentive to work hard even if they are not constantly supervised.
Version B
I. Multiple choice
(1)c. (2)a. (3)d. (4)c. (5)e. (6)e. (7)b. (8)c. (9)d. (10)b.
(11)c. (12)c. (13)b. (14)e. (15)c. (16)d. (17)b. (18)c.
II. Problems
(1) [Individual labor supply - income and substitution effects: 22 pts]
- 50 weeks.
- $5000.
- $400 per week.
- $2000 per week.
- income effect: work less.
- -10 weeks.
- substitution effect: work more.
- +20 weeks.
- total effect: work more.
- +10 weeks.
- (w,h) = ($400, 25 weeks), ($2000, 35 weeks).
(2) [Value of a statistical life: 4 pts]
VSL = Δ annual earnings / Δ annual risk
= [(22-20)×2000] / [0.0006-0.0001] = $8 million.
(3) [LR labor demand - scale and substitution effects: 16 pts]
- Slope of any isocost line = -w/r, where r = price of capital.
The slope of isocost line #1 is -3/2.
We are given that r = $20, so w = $30 on isocost line #1.
- Similarly, the slope of isocost line #2 is - 1/2, so w = $10 on isocost line #2.
- substitution effect: use more labor.
- 30 units of labor.
- scale effect: use more labor.
- 20 units of labor.
- total effect: use more labor.
- 50 units of labor.
(4) [Mandated benefits: 6 pts] A mandated benefit shifts the labor demand curve down by the cost of the benefit to employers, but it may shift the labor supply curve down also if the benefit is valued by workers.
- Set -50 + (E/5) = 250 - (E/10) and solve to get E=1000, w = $150.
- Set -50 + (E/5) = 250 - (E/10) - 9 and solve to get E = 970, w = $144.
- Set -50 + (E/5) - 6 = 250 - (E/10) - 9 and solve to get E = 990, w = $142.
(5) [Gains from migration: 12 pts] If migration is costless, then in the long run, wages are equal in the two markets.
- W_{E} = $15 thousand, W_{W} = $55 thousand.
- Set W_{E} = W_{W}, then substitute (100-E_{E}) for E_{W}, and solve to get EE = 10 thousand, E_{W} = 90 thousand, and W_{E} = W_{W} = $35 thousand.
- Increase in efficiency = increase in value of output in West minus decrease in value of output in East
= (55+35)/2 thousand × 40 thousand - (35+15)/2 thousand × 40 thousand = $800 million.
(6) [Simple model of schooling decision: 10 pts] Worker chooses option with greatest NPV.
- NPV "no college" = $631,818.
- NPV "college" = $624,545.
- Chooses "no college" because NPV is larger.
- Set 150 + 530/(1+r) = -50 + 742/(1+r) and solve to get r* = 6 percent.
- If r < r*, chooses "college."
(7) [Measuring inequality: 16 pts]
- Let N be the population. Then 70 percent of the population has a total of 0.7 × N × $20000 = $14000 N earnings, while 30 percent of the population has a total of 0.3 × N × $120000 = $36000 N earnings. Total earnings are therefore $50000 N. The share of the bottom 70 percent is (14000 N) / (50000 N) = 28 percent. The Lorenz curve therefore is straight with a kinkpoint at (70 percent of population, 28 percent of earnings).
- Gini = 0.42 .
- 90-50 wage gap = (120000 - 20000) / 20000 = 500 percent.
- 50-10 wage gap = (20000 - 20000) / 20000 = 0 percent.
- 90-10 wage gap = (120000 - 20000) / 20000 = 500 percent.
(8) [Roy model: 6 pts]
- Workers move if the net gain from migration is positive--that is, if w_{Y} - moving cost > w_{X}. Substituting and solving for S gives 30 > S.
- Negatively selected, since workers from the low end of the distribution of S will move.
(9) [Monopsony wage discrimination: 12 pts] Recall that a monopsonist chooses the employment level by setting VMP=MLC. The monopsony wage is then found by substituting this employment level into the labor supply equation.
- For each group, set VMP equal to MLC and solve for E. This gives E_{G} = 700 and E_{B} = 550.
- Substitute into supply equations to get w_{G} = $8.50 and w_{B} = $6.50.
- Substitute the minimum wage into the supply equation for each group to get E_{G} = 1000 and E_{B} = 900.
(10) [Welfare effects of monopoly unionism: 4 pts]
- Substitute the union wage into the VMP (or labor demand) equation to get E = 150,000.
- The efficiency cost is the deadweight loss, the area of a triangle bounded by the VMP curve, the labor supply curve, and the vertical line at the union employment level found in part (a). Note that in this problem, the labor supply curve is a horizontal line at the competitive wage. The area of this triangle is $100 million.
(11) [Markov model: 11 pts] Recall that horizontal rows of the transition matrix must some to one because everyone goes somewhere.
- 0.97 .
- 0.53 .
- 0.03 .
- 0.47 .
- Flows into unemployment must equal flows out of unemployment: 0.03 E = 0.47 U. Solving for the unemployment rate U/(E+U) gives 0.06 or 6 percent.
(12) [Efficient bargaining: 9 pts] Efficient combinations of wage and employment lie on tangencies between the union's indifference curves and the firm's iso-profit curves.
- Union chooses wage at tangency between labor demand curve and the highest indifference curve that the union can reach: $25. Employer chooses employment level corresponding to that wage on its labor demand curve: 60.
- Wage = $20, employment = 120.
- Wage = $15, employment = 110.
- Both of the above combinations, plus wage = $30, employment = 130.
(13) [Piece rates and time rates: 16 pts]
- Set Abby's MC = piece rate and solve to get N=150. Pay = N × piece rate = $22.50.
- Set Ben's MC = piece rate and solve to get N=75. Pay = N × piece rate = $11.25.
- Abby's preference appears uncertain because Firm 1 pays more but also requires more effort. (However, summing the marginal costs of the additional envelopes shows that the additional effort at Firm 1 costs Abby only $8.44, so Abby would in fact prefer Firm 1.)
- Ben definitely prefers firm 2 because it pays better but requires the same effort as Firm 1.
(14) [Search: 10 pts]
- Set MC = MB to find reservation wage = $9.
- Yes, accept this job because wage > reservation wage.
- If unemployment insurance benefits were decreased, then the marginal cost of search would shift up because the opportunity cost of search would increase.
- The reservation wage would decrease because the MC curve has shifted up.
- Average time to find a new job would decrease because the reservation wage has decreased.
III. Critical thinking
Same as Version A.
Version C
I. Multiple choice
(1)a. (2)b. (3)c. (4)d. (5)b. (6)e. (7)a. (8)d. (9)c. (10)c.
(11)c. (12)d. (13)c. (14)a. (15)d. (16)a. (17)c. (18)d.
II. Problems
(1) [Individual labor supply - income and substitution effects: 22 pts]
- 80 hours.
- $100.
- $30 per hour.
- $10 per hour.
- income effect: work more.
- +15 hours.
- substitution effect: work less.
- -25 hours.
- total effect: work less.
- -10 hours.
- (w,h) = ($30, 50 hours), ($10, 40 hours).
(2) [Value of a statistical life: 4 pts]
VSL = Δ annual earnings / Δ annual risk
= [(16-15)×2000] / [0.0006-0.0002] = $5 million.
(3) [LR labor demand - scale and substitution effects: 16 pts]
- Slope of any isocost line = -w/r, where r = price of capital.
The slope of isocost line #1 is -1/2.
We are given that r = $20, so w = $10 on isocost line #1.
- Similarly, the slope of isocost line #2 is -2, so w = $40 on isocost line #2.
- substitution effect: use less labor.
- -20 units of labor.
- scale effect: use less labor.
- -40 units of labor.
- total effect: use less labor.
- -60 units of labor.
(4) [Mandated benefits: 12 pts] A mandated benefit shifts the labor demand curve down by the cost of the benefit to employers, but it may shift the labor supply curve down also if the benefit is valued by workers.
- Set -200 + (E/5) = 400 - (E/10) and solve to get E=2000, w = $200.
- Set -200 + (E/5) = 400 - (E/10) - 9 and solve to get E = 1970, w = $194.
- Set -200 + (E/5) - 6 = 400 - (E/10) - 9 and solve to get E = 1990, w = $192.
(5) [Gains from migration: 12 pts] If migration is costless, then in the long run, wages are equal in the two markets.
- W_{E} = $25 thousand, W_{W} = $35 thousand.
- Set W_{E} = W_{W}, then substitute (100-E_{E}) for E_{W}, and solve to get EE = 40 thousand, E_{W} = 60 thousand, and W_{E} = W_{W} = $30 thousand.
- Increase in efficiency = increase in value of output in East minus decrease in value of output in West
= (35+30)/2 thousand × 10 thousand - (25+30)/2 thousand × 10 thousand = $50 million.
(6) [Simple model of schooling decision: 10 pts] Worker chooses option with greatest NPV.
- NPV "no college" = $627,273.
- NPV "college" = $618,182.
- Chooses "no college" because NPV is larger.
- Set 150 + 525/(1+r) = -50 + 735/(1+r) and solve to get r* = 5 percent.
- If r < r*, chooses "college."
(7) [Measuring inequality: 16 pts]
- Let N be the population. Then 60 percent of the population has a total of 0.6 × N × $10000 = $6000 N earnings, while 40 percent of the population has a total of 0.4 × N × $110000 = $44000 N earnings. Total earnings are therefore $50000 N. The share of the bottom 60 percent is (6000 N) / (50000 N) = 12 percent. The Lorenz curve therefore is straight with a kinkpoint at (60 percent of population, 12 percent of earnings).
- Gini = 0.48 .
- 90-50 wage gap = (110000 - 10000) / 10000 = 1000 percent.
- 50-10 wage gap = (10000 - 10000) / 10000 = 0 percent.
- 90-10 wage gap = (110000 - 10000) / 10000 = 1000 percent.
(8) [Roy model: 6 pts]
- Workers move if the net gain from migration is positive--that is, if w_{Y} - moving cost > w_{X}. Substituting and solving for S gives S > 80.
- Positively selected, since workers from the high end of the distribution of S will move.
(9) [Monopsony wage discrimination: 12 pts] Recall that a monopsonist chooses the employment level by setting VMP=MLC. The monopsony wage is then found by substituting this employment level into the labor supply equation.
- For each group, set VMP equal to MLC and solve for E. This gives E_{G} = 2000 and E_{B} = 1200.
- Substitute into supply equations to get w_{G} = $15 and w_{B} = $13.
- Substitute the minimum wage into the supply equation for each group to get E_{G} = 3000 and E_{B} = 1900.
(10) [Welfare effects of monopoly unionism: 4 pts]
- Substitute the union wage into the VMP (or labor demand) equation to get E = 35,000.
- The efficiency cost is the deadweight loss, the area of a triangle bounded by the VMP curve, the labor supply curve, and the vertical line at the union employment level found in part (a). Note that in this problem, the labor supply curve is a horizontal line at the competitive wage. The area of this triangle is $25 million.
(11) [Markov model: 11 pts] Recall that horizontal rows of the transition matrix must some to one because everyone goes somewhere.
- 0.98 .
- 0.62 .
- 0.02 .
- 0.38 .
- Flows into unemployment must equal flows out of unemployment: 0.02 E = 0.38 U. Solving for the unemployment rate U/(E+U) gives 0.05 or 5 percent.
(12) [Efficient bargaining: 9 pts] Efficient combinations of wage and employment lie on tangencies between the union's indifference curves and the firm's iso-profit curves.
- Union chooses wage at tangency between labor demand curve and the highest indifference curve that the union can reach: $35. Employer chooses employment level corresponding to that wage on its labor demand curve: 50.
- Wage = $30, employment = 100.
- Wage = $25, employment = 90.
- Both of the above combinations, plus wage = $35, employment = 110.
(13) [Piece rates and time rates: 16 pts]
- Set Abby's MC = piece rate and solve to get N=200. Pay = N × piece rate = $20.
- Set Ben's MC = piece rate and solve to get N=100. Pay = N × piece rate = $10.
- Abby's preference appears uncertain because Firm 1 pays more but also requires more effort. (However, summing the marginal costs of the additional envelopes shows that the additional effort at Firm 1 only costs Abby $7.50, so Abby would in fact prefer Firm 1.)
- Ben definitely prefers firm 2 because it pays better but requires the same effort as Firm 1.
(14) [Search: 10 pts]
- Set MC = MB to find reservation wage = $17.
- No, do not accept this job because wage < reservation wage.
- If unemployment insurance benefits were decreased, then the marginal cost of search would shift up because the opportunity cost of search would increase.
- The reservation wage would decrease because the MC curve has shifted up.
- Average time to find a new job would decrease because the reservation wage has decreased.
III. Critical thinking
Same as Version A.
[end of answer key]