ECON 115 - Labor Economics
Drake University, Spring 2022
William M. Boal

EXAM 2 ANSWER KEY

Version A

I. Multiple choice

(1)d. (2)b. (3)a. (4)c. (5)d. (6)b. (7)b. (8)c. (9)c. (10)b. (11)d. (12)c. (13)c. (14)b. (15)b.

II. Problems

(1) [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.

  1. 50 million.
  2. $19.
  3. $15.
  4. $55 million.
  5. 165 million.
  6. $200 million.
  7. $20 million.

(2) [Gains from migration: 10 pts]

  1. WN = $24 thousand, WS = $18 thousand.
  2. Workers will migrate until wages are equal, so set WN = WS. Then substitute labor demand equations, and solve to get EN = 80 million, ES = 40 million, and WN = WS = $22 thousand.
  3. Increase in efficiency
    = increase in value of output in North less decrease in value of output in South
    = [(24+22)/2 thousand × (80-60) million] - [(22+18)/2 thousand × (60-40) million] = $60 billion.

(3) [Cobweb model: 8 pts]

  1. E = 2000.
  2. W = $90.
  3. E = 8000.
  4. W = $60.
  5. E = 5000.
  6. W = $75.
  7. E = 6000 (at intersection of LR supply and new demand).
  8. W = $70.

(4) [Monopsony: 14 pts]

  1. Set supply equation w=VMP and solve to get E=120. (Note incidentally that VMP = w = $18.)
  2. MLC = 6 + 2E/10.
  3. Set VMP=MLC and solve to get E=80.
  4. Substitute E=80 into labor supply equation to get w=$14.
  5. The minimum wage ($15) is greater than the monopsonist employer's profit-maximizing wage, but less than the efficient wage ($18), so the outcome is on the supply curve. Substituting the minimum wage into the labor supply equation gives E=90.

(5) [Compensating differential with heterogeneous preferences: 8 pts]

  1. If workers do not care in which industry they work, then competition will force the wages to be equal:
    WC = WD
    20 - 0.1 ED = 14 - 0.1 (100-ED).
    Solve to get ED=80, EC=20, WD=WC=$12.
  2. If workers required a compensating differential to work in the Dirty industry, then we have:
    WD - WC = 0.2 ED
    (20 -0.1 ED) - (14 - 0.1 (100-ED)) = 0.2 ED.
    Solve to get ED=40, EC=60, WD=$16, WC=$8.

(6) [VSL, safety regulation: 12 pts]

  1. VSL = Δ earnings / Δ risk = 943 / (1/10,000) = $10.35 million.
  2. Cost per statistical life saved = cost / reduction in death rate = $100,000 / (0.9 - 0.5) = $0.25 million.
  3. Yes, the system should be required becasuse VSL > cost per statistical life saved.

(7) [Simple model of schooling decision: 10 pts]

  1. NPV "no college" = 40,000 + (40,000/1.04) = $78,462.
  2. NPV "college" = -10,000 + (94,000/1.04) = $80,385.
  3. Chooses "college" because NPV is larger.
  4. Set 40,000 + 40,000/(1+r) = -10,000 + 94,000/(1+r) and solve to get r*=8 percent.
  5. 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."

(8) [Who pays for OJT: 16 pts]

  1. A constant $40,000 wage will not work because the training is general, so the worker's productivity rises at other employers too. Since worker's VMP elsewhere rises to $45,000 in the second year as a result of training, many other employers are willing to pay the worker a wage of $45,000 and the worker will leave for a better job. So the employer will lose the $5000 in training cost.
  2. In equilibrium, the worker will be paid $35,000 in the first year and $45,000 in the second year. In other words, the worker "pays" for general training.
  3. The above wage scheme will not work if training is specific to a particular employer because the value of the investment will disappear if the worker leaves the firm in the second year. To give the worker an incentive to stay and to give the employer an incentive not to fire the worker in the second year, both parties must share the returns from training. If they share the returns, competition in the labor market forces the parties also to share the costs of training. Suppose worker pays X in training cost, where X is greater than zero but less than $5000. Then the wage in the first year is $40,000-X. But if the competitive wage is $40,000, then the average of the first and second year wages must also be $40,000. This implies that the wage in the second year must be $40,000+X.
  4. For example, the wage in the first year might be $37,000 and in the second year $43,000.

III. Critical thinking

(1) This fact does not contradict the theory of compensating differentials. That theory predicts that wages and benefits will be negatively correlated ceteris paribus. But all workers are not equally productive. Lawyers and executives command both higher wages and more attractive benefits because they are more productive than store clerks and laborers. To test the theory of compensating differentials, one must compare equally-productive workers.

(2) An increase in the wage differential for high-risk jobs and a decrease in the fraction of high-risk jobs in the economy together could only be caused by a leftward shift in supply. A rightward shift in supply would cause a decrease in the the wage differential and an increase in high-risk employment. A shift in demand (left or right) would cause both a wage change and an employment change in the same direction. [Full credit requires a graph showing a stable demand curve and a leftward shift in the supply curve.]

Version B

I. Multiple choice

(1)b. (2)a. (3)c. (4)b. (5)c. (6)c. (7)a. (8)d. (9)b. (10)a. (11)b. (12)a. (13)d. (14)c. (15)a.

II. Problems

(1) [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.

  1. 70 million.
  2. $17.
  3. $21.
  4. $65 million.
  5. 195 million.
  6. $280 million.
  7. $20 million.

(2) [Gains from migration: 10 pts]

  1. WN = $17 thousand, WS = $14 thousand.
  2. Workers will migrate until wages are equal, so set WN = WS. Then substitute labor demand equations, and solve to get EN = 40 million, ES = 20 million, and WN = WS = $16 thousand.
  3. Increase in efficiency
    = increase in value of output in North less decrease in value of output in South
    = [(17+16)/2 thousand × (40-30) million] - [(14+16)/2 thousand × (30-20) million] = $15 billion.

(3) [Cobweb model: 8 pts]

  1. E = 3000.
  2. W = $100.
  3. E = 9000.
  4. W = $70.
  5. E = 6000.
  6. W = $85.
  7. E = 7000 (at intersection of LR supply and new demand).
  8. W = $80.

(4) [Monopsony: 14 pts]

  1. Set supply equation w=VMP and solve to get E=90. (Note incidentally that VMP = w = $11.)
  2. MLC = 2 + 2E/10.
  3. Set VMP=MLC and solve to get E=60.
  4. Substitute E=60 into labor supply equation to get w=$8.
  5. The minimum wage ($10) is greater than the monopsonist employer's profit-maximizing wage, but less than the efficient wage ($11), so the outcome is on the supply curve. Substituting the minimum wage into the labor supply equation gives E=80.

(5) [Compensating differential with heterogeneous preferences: 8 pts]

  1. If workers do not care in which industry they work, then competition will force the wages to be equal:
    WC = WD
    20 - 0.1 ED = 18 - 0.1 (100-ED).
    Solve to get ED=60, EC=40, WD=WC=$14.
  2. If workers required a compensating differential to work in the Dirty industry, then we have:
    WD - WC = 0.2 ED
    (20 -0.1 ED) - (18 - 0.1 (100-ED)) = 0.2 ED.
    Solve to get ED=30, EC=70, WD=$17, WC=$11.

(6) [VSL, safety regulation: 12 pts]

  1. VSL = Δ earnings / Δ risk = 844 / (1/10,000) = $8.44 million.
  2. Cost per statistical life saved = cost / reduction in death rate = $2,500,000 / (0.8 - 0.7) = $25 million.
  3. No, the system should not be required becasuse VSL < cost per statistical life saved.

(7) [Simple model of schooling decision: 10 pts]

  1. NPV "no college" = 50,000 + (50,000/1.08) = $96,296.
  2. NPV "college" = -10,000 + (113,000/1.08) = $94,630.
  3. Chooses "no college" because NPV is larger.
  4. Set 50,000 + 50,000/(1+r) = -10,000 + 113,000/(1+r) and solve to get r*=5 percent.
  5. 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."

(8) [Who pays for OJT: 16 pts]

  1. A constant $50,000 wage will not work because the training is general, so the worker's productivity rises at other employers too. Since worker's VMP elsewhere rises to $55,000 in the second year as a result of training, many other employers are willing to pay the worker a wage of $55,000 and the worker will leave for a better job. So the employer will lose the $5000 in training cost.
  2. In equilibrium, the worker will be paid $45,000 in the first year and $55,000 in the second year. In other words, the worker "pays" for general training.
  3. The above wage scheme will not work if training is specific to a particular employer because the value of the investment will disappear if the worker leaves the firm in the second year. To give the worker an incentive to stay and to give the employer an incentive not to fire the worker in the second year, both parties must share the returns from training. If they share the returns, competition in the labor market forces the parties also to share the costs of training. Suppose worker pays X in training cost, where X is greater than zero but less than $5000. Then the wage in the first year is $50,000-X. But if the competitive wage is $50,000, then the average of the first and second year wages must also be $50,000. This implies that the wage in the second year must be $50,000+X.
  4. For example, the wage in the first year might be $48,000 and in the second year $52,000.

III. Critical thinking

Same as Version A.

[end of answer key]