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

EXAM 2 ANSWER KEY

Version A

I. Multiple choice

(1)d. (2)b. (3)b. (4)b. (5)c. (6)b. (7)b. (8)b. (9)c. (10)b. (11)b. (12)c. (13)b. (14)b. (15)c. (16)b.

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. 80 million.
  2. $19.
  3. $23.
  4. $75 million.
  5. 225 million.
  6. $320 million.
  7. $20 million.

(2) [Mandated benefits: 10 pts]

  1. Set demand equal to supply and solve to get E*=300, w*=$70.
  2. The mandate pushes the labor demand curve down by $9, because employers are only willing to pay the value of marginal product minus the cost of the free lunch.
    So w = 100 - (E/10) - 9 = 91 - (E/10).
  3. Set new demand equal to old supply to get E*=270, w*=$64.
  4. The mandate pushes the supply curve down by $6, what the free lunch is worth to workers, because workers are willing to accept a lower wage if they get a free lunch.
    So w = 10 + (E/5) - 6 = 4 + (E/5).
  5. Set new demand equal to new supply to get E*=290, w*=$62.

(3) [Gains from migration: 10 pts]

  1. WN = $14, WS = $8.
  2. Workers will migrate until wages are equal, so set WN = WS. Then substitute labor demand equations. Then substitute (120-EN) for ES, and solve to get EN = 80 million, ES = 40 million, and WN = WS = $12 thousand.
  3. Increase in efficiency
    = increase in value of output in North less decrease in value of output in South
    = [(14+12)/2 × (80-60) million] - [(12+8)/2 × (60-40) million] = $60 million.

(4) [Monopsony: 14 pts]

  1. Set supply equation w=VMP and solve to get EC=150. (Note incidentally that VMP = w = $17.)
  2. MLC = 2 + (2E/10) = 2 + (E/5).
  3. Set VMP=MLC and solve to get EM=100.
  4. Substitute EM=100 into labor supply equation to get wM=$12.
  5. The minimum wage ($15) is greater than the monopsonist employer's profit-maximizing wage, but less than the efficient wage ($17), so the outcome is on the supply curve. Substituting the minimum wage into the labor supply equation gives Emin=130.

(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 = 16 - 0.1 (100-ED).
    Solve to get ED=60, EC=20, 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) - (16 - 0.1 (100-ED)) = 0.2 ED.
    Solve to get ED=30, EC=50, WD=$17, WC=$11.

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

  1. VSL = Δ earnings / Δ risk = 943 / (1/10,000) = $9.8 million.
  2. Cost per statistical life saved = cost / reduction in death rate = $100,000 / (0.7 - 0.5) = $500 thousand.
  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" = 50,000 + (50,000/1.05) = $97,619.
  2. NPV "college" = -20,000 + (127,000/1.05) = $100,952.
  3. Chooses "college" because NPV is larger.
  4. Set 50,000 + 50,000/(1+r) = -20,000 + 127,000/(1+r) and solve to get r*=10 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."

III. Critical thinking

(1) Indifference curves connect combinations of the wage and the job characteristic that are equally attractive to workers. Workers' indifference curves must slope down here because workers like both wages and the job characteristic. Therefore, if the job characteristic is increased, the only way that the new combination can remain equally attractive is if the wage is decreased. (Full credit requires a sketch of a downward-sloping indifference curve.)

(2) The difference-in-differences estimate assumes that the trend in college enrollment for men would have been the same as the trend for women, if not for the ending of the military draft. It can be calculated two ways.
One way is to subtract the change in women over time from the change men over time: (47-55) - (50-49) = -9. So, the draft must have increased the number of men who entered college after high school in 1970 by 9 percentage points.
Another way is to subtract the gender difference in 1970 from the gender difference in 1976: (47-50) - (55-49) = -9. Again, the draft must have increased the number of men who entered college after high school in 1970 by 9 percentage points.

Version B

I. Multiple choice

(1)b. (2)d. (3)a. (4)d. (5)a. (6)c. (7)d. (8)c. (9)a. (10)d. (11)d. (12)c. (13)d. (14)a. (15)b. (16)c.

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. 60 million.
  2. $21.
  3. $17.
  4. $65 million.
  5. 195 million.
  6. $240 million.
  7. $20 million.

(2) [Mandated benefits: 10 pts]

  1. Set demand equal to supply and solve to get E*=200, w*=$60.
  2. The mandate pushes the demand curve down by $12, because employers are only willing to pay the value of marginal product minus the cost of the free lunch.
    So w = 80 - (E/10) - 12 = 68 - (E/10).
  3. Set new demand equal to old supply to get E*=160, w*=$52.
  4. The mandate pushes the supply curve down by $6, what the free lunch is worth to workers, because workers are willing to accept a lower wage if they get a free lunch.
    So w = 20 + (E/5) - 6 = 14 + (E/5).
  5. Set new demand equal to new supply to get E*=180, w*=$50.

(3) [Gains from migration: 10 pts]

  1. WN = $17, 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.
  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.

(4) [Monopsony: 14 pts]

  1. Set supply equation w=VMP and solve to get EC=120. (Note incidentally that VMP = w = $16.)
  2. MLC = 4 + (2E/10) = 4 + (E/5).
  3. Set VMP=MLC and solve to get EM=80.
  4. Substitute EM=80 into labor supply equation to get wM=$12.
  5. The minimum wage ($15) is greater than the monopsonist employer's profit-maximizing wage, but less than the efficient wage ($16), so the outcome is on the supply curve. Substituting the minimum wage into the labor supply equation gives Emin=110.

(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 = 16 - 0.1 (120-ED).
    Solve to get ED=80, EC=40, 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) - (16 - 0.1 (120-ED)) = 0.2 ED.
    Solve to get ED=40, EC=80, WD=$16, WC=$8.

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

  1. VSL = Δ earnings / Δ risk = 1025 / (1/10,000) = $10.25 million.
  2. Cost per statistical life saved = cost / reduction in death rate = $2,000,000 / (0.3 - 0.2) = $20 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" = -30,000 + (134,000/1.08) = $94,074.
  3. Chooses "no college" because NPV is larger.
  4. Set 50,000 + 50,000/(1+r) = -30,000 + 134,000/(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."

III. Critical thinking

Same as Version A.

[end of answer key]