EXAM 2 ANSWER KEY
Version A
I. Multiple choice
(1)d. (2)c. (3)b. (4)b. (5)a. (6)c. (7)e. (8)d. (9)a. (10)e.
II. Problems
(1) [Payroll tax or subsidy: 14 pts] A payroll subsidy moves equilibrium to the employment level where supply is higher than demand by the rate of subsidy.
- 90 million.
- $12.
- $15.
- $85 million.
- $170 million.
- $270 million.
- $15 million.
(2) [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 -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.
(3) [Monopsony: 12 pts] Under monopsony, the wage is on the supply curve but not the demand curve.
- Set VMP = MLC and solve to get E = 180.
- Substitute E=180 into labor supply equation to get w = $13.
- Substitute w=$15 into labor supply equation to get E = 220. (Should check to see that labor supply curve is still below VMP curve at this value of E. Otherwise, the correct value of E should be found by substituting w=$15 into VMP curve.)
(4) [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 E_{E} = 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.
(5) [Compensating differential: 4 pts] Since all workers are assumed to have the same preferences in this problem, all jobs must offer the same utility in hedonic equilibrium.
- The low-noise job offers U = 15 - (4^{2}/2) = 7 utils. In equilibrium, the high-noise job must offer the same utility: 7 utils = w_{h} - (6^{2}/2). So w_{h} = $25.
- Compensating differential = $25 - $15 = $10.
(6) [Value of a statistical life: 4 pts]
VSL = Δ annual earnings / Δ annual risk
= [(22-20)×2000] / [0.0006-0.0001] = $8 million.
(7) [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."
(8) [Measuring return to schooling: 6 pts]
- 15 percent.
- If there is ability bias, the true rate of return is less than 15 percent. "Ability bias" means that more-able people are likely to attend school longer and do better in the labor market (even without more schooling). Hence the regression estimate of the coefficient of S picks up the effects of both schooling and ability.
(9) [Job market signaling: 4 pts]
To induce high-ability workers to obtain the certificate, w_{H} must be greater than w_{L} + $5000. To ensure that low-ability workers do not obtain the certificate, w_{H} must be less than w_{L} + $8000. Hence $30,000 < w_{H} < $33,000.
III. Critical thinking
- If training raises the worker's VMP at other employers too, then we have a case of general training. The worker's wage in the second year must equal the new VMP: $40,000. Otherwise the worker would leave for other employers. In that case, the wage in the first year must equal the first-year VMP minus the cost of the training: $25,000.
- If training raises the worker's VMP only at this employer, then we have a case of specific training, a shared investment whose value is lost if the employment relationship ends. So the second-year wage must discourage the worker from quitting and discourage the employer from firing the worker. To discourage the worker from quitting, the second-year wage must be must be greater than the worker's alternative wage at other employers ($30,000). To discourage the employer from firing the worker, the second-year wage must be less than the worker's new VMP ($40,000). A wage in this range ensures that both parties gain from continuing the employment relationship.
Version B
I. Multiple choice
(1)a. (2)d. (3)c. (4)c. (5)b. (6)b. (7)b. (8)c. (9)d. (10)e.
II. Problems
(1) [Payroll tax or subsidy: 14 pts] A payroll tax moves equilibrium to the employment level where demand is higher than supply by the tax rate.
- 80 million.
- $16.
- $13.
- $85 million.
- $170 million.
- $240 million.
- $15 million.
(2) [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) = 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.
(3) [Monopsony: 12 pts] Under monopsony, the wage is on the supply curve but not the demand curve.
- Set VMP = MLC and solve to get E = 240.
- Substitute E=240 into labor supply equation to get w = $14.
- Substitute w=$15 into labor supply equation to get E = 260. (Should check to see that labor supply curve is still below VMP curve at this value of E. Otherwise, the correct value of E should be found by substituting w=$15 into VMP curve.)
(4) [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 E_{E} = 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.
(5) [Compensating differential: 4 pts] Since all workers are assumed to have the same preferences in this problem, all jobs must offer the same utility in hedonic equilibrium.
- The low-noise job offers U = 15 - (1^{2}/2) = 14.5 utils. In equilibrium, the high-noise job must offer the same utility: 14.5 utils = w_{h} - (6^{2}/2). So w_{h} = $32.50.
- Compensating differential = $32.50 - $15 = $17.50.
(6) [Value of a statistical life: 4 pts]
VSL = Δ annual earnings / Δ annual risk
= [(16-15)×2000] / [0.0006-0.0002] = $5 million.
(7) [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."
(8) [Measuring return to schooling: 6 pts]
- 13 percent.
- If there is ability bias, the true rate of return is less than 13 percent. "Ability bias" means that more-able people are likely to attend school longer and do better in the labor market (even without more schooling). Hence the regression estimate of the coefficient of S picks up the effects of both schooling and ability.
(9) [Job market signaling: 4 pts]
To induce high-ability workers to obtain the certificate, w_{H} must be greater than w_{L} + $6000. To ensure that low-ability workers do not obtain the certificate, w_{H} must be less than w_{L} + $10,000. Hence $36,000 < w_{H} < $40,000.
III. Critical thinking
Same as Version A.
Version C
I. Multiple choice
(1)b. (2)b. (3)d. (4)d. (5)c. (6)b. (7)c. (8)e. (9)b. (10)e.
II. Problems
(1) [Payroll tax or subsidy: 14 pts] A payroll tax moves equilibrium to the employment level where demand is higher than supply by the tax rate.
- 90 million.
- $18.
- $15.
- $95 million.
- $190 million.
- $270 million.
- $15 million.
(2) [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.
(3) [Monopsony: 12 pts] Under monopsony, the wage is on the supply curve but not the demand curve.
- Set VMP = MLC and solve to get E = 120.
- Substitute E=120 into labor supply equation to get w = $12.
- Substitute w=$13 into labor supply equation to get E = 140. (Should check to see that labor supply curve is still below VMP curve at this value of E. Otherwise, the correct value of E should be found by substituting w=$15 into VMP curve.)
(4) [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 E_{E} = 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.
(5) [Compensating differential: 4 pts] Since all workers are assumed to have the same preferences in this problem, all jobs must offer the same utility in hedonic equilibrium.
- The low-noise job offers U = 15 - (2^{2}/2) = 13 utils. In equilibrium, the high-noise job must offer the same utility: 13 utils = w_{h} - (6^{2}/2). So w_{h} = $31.
- Compensating differential = $31 - $15 = $16.
(6) [Value of a statistical life: 4 pts]
VSL = Δ annual earnings / Δ annual risk
= [(19-15)×2000] / [0.0010-0.0002] = $10 million.
(7) [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."
(8) [Measuring return to schooling: 6 pts]
- 11 percent.
- If there is ability bias, the true rate of return is less than 11 percent. "Ability bias" means that more-able people are likely to attend school longer and do better in the labor market (even without more schooling). Hence the regression estimate of the coefficient of S picks up the effects of both schooling and ability.
(9) [Job market signaling: 4 pts]
To induce high-ability workers to obtain the certificate, w_{H} must be greater than w_{L} + $4000. To ensure that low-ability workers do not obtain the certificate, w_{H} must be less than w_{L} + $9000. Hence $34,000 < w_{H} < $39,000.
III. Critical thinking
Same as Version A.
[end of answer key]