ECON 115 - Labor Economics
Drake University, Spring 2017
William M. Boal

EXAM 2 ANSWER KEY

Version A

I. Multiple choice

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

II. Problems

(1) [Payroll tax or subsidy: 14 pts]

  1. 100 million.
  2. $14.
  3. 18.
  4. $95 million.
  5. $285 million.
  6. $400 million.
  7. $20 million.

(2) [Monopsony: 14 pts]

  1. MLC = -5 + 2 E/100.
  2. Set VMP=MLC and solve to get E=1500.
  3. Substitute E=1500 into labor supply equation to get w=$10.
  4. Substitute w=$12 into labor supply equation to get E = 1700. (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=$10 into VMP curve.)

(3) [Gains from migration: 12 pts]

  1. WN = $15, WS = $25.
  2. Set WN = WS, then substitute (60-EN) for ES, and solve to get EN = 20 thousand, ES = 40 thousand, and WN = WS = $20 thousand.
  3. Increase in efficiency = increase in value of output in South less decrease in value of output in North = [(25+20)/2 thousand × (40-10) thousand] - [(20+15)/2 thousand × (30-20) thousand] = $50 million.

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

  1. VSL = Δ earnings / Δ risk = 82 / (1/100,000) = $8.2 million.
  2. Cost per statistical life saved = cost / reduction in death rate = $500,000 / 0.2 = $2.5 million.
  3. Yes, the system should be required becasuse VSL > cost per statistical life saved.

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

  1. NPV "no college" = 160 + 440/1.10 = $560 thousand.
  2. NPV "college" = -50 + 660/1.10 = $550 thousand.
  3. Chooses "no college" because NPV is larger.

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

  1. If training is general, the worker must pay for training. Worker's wage in first year = VMP - training cost = $40,000 - $4,000 = $36,000.
  2. If training is general, the worker must be paid their new VMP in second year or the worker will leave for another employer. Worker's wage in second year = new VMP = $50,000.
  3. If training is specific, it human-capital value will disappear if the worker leaves the firm in the second year. To give the worker an incentive to stay and 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 and employer pays remainder, $4000-X. Workers wage in first year = $40,000 - X, where 0<X<$4000. This implies that wage in first year must be greater than $36,000 and less than $40,000.
  4. If the competitive wage is $40,000, then the average of the first and second year wages must be $40,000. Therefore, the wage in the second year will be $40,000 + X, which is greater than $40,000 and less than $44,000.

III. Critical thinking

  1. The data in the table show that the VSL, and hence the wage premium for high-risk jobs, has increased over time. The information given in the problem also states that the number of high-risk jobs has decreased. Only a leftward shift in supply is compatible with an increase in price and a decrease in quantity.
  2. Graph should show demand and supply for high-risk jobs (similar to figure 5-2 in the Borjas textbook, or to the graph in the slideshow on "Compensating Wage Differentials"). Graph should show a leftward shift in supply curve of employment in high-risk jobs, while demand curve remains fixed. Result should be an increase in the wage premium for high-risk jobs and a decrease in the quantity of workers in high-risk jobs.
  3. A possible explanation for the leftward shift in supply is that safety is a normal good. As people's incomes rise, they demand more of safety. Demanding more safety means being willing to pay more to avoid risk. Since U.S. incomes rose steadily from 1940 to 1980, this likely caused the rise in the VSL and the leftward shift in supply. (This is in fact the explanation that Costa and Kahn give for their results.)

Version B

I. Multiple choice

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

II. Problems

(1) [Payroll tax or subsidy: 14 pts]

  1. 80 million.
  2. $16.
  3. 12.
  4. $85 million.
  5. $255 million.
  6. $320 million.
  7. $20 million.

(2) [Monopsony: 14 pts]

  1. MLC = -10 + 2 E/50.
  2. Set VMP=MLC and solve to get E=750.
  3. Substitute E=750 into labor supply equation to get w=$5.
  4. Substitute w=$8 into labor supply equation to get E = 1700. (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=$8 into VMP curve.)

(3) [Gains from migration: 12 pts]

  1. WN = $40, WS = $10.
  2. Set WN = WS, then substitute (80-EN) for ES, and solve to get EN = 70 thousand, ES = 40 thousand, and WN = WS = $25 thousand.
  3. Increase in efficiency = increase in value of output in North less decrease in value of output in South = [(25+40)/2 thousand × (70-40) thousand] - [(25+10)/2 thousand × (40-10) thousand] = $450 million.

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

  1. VSL = Δ earnings / Δ risk = 48 / (1/100,000) = $4.8 million.
  2. Cost per statistical life saved = cost / reduction in death rate = $800,000 / 0.1 = $8.0 million.
  3. No, the system should not be required becasuse VSL < cost per statistical life saved.

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

  1. NPV "no college" = 200 + 440/1.10 = $600 thousand.
  2. NPV "college" = -50 + 770/1.10 = $650 thousand.
  3. Chooses "college" because NPV is larger.

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

  1. If training is general, the worker must pay for training. Worker's wage in first year = VMP - training cost = $30,000 - $6,000 = $24,000.
  2. If training is general, the worker must be paid their new VMP in second year, or the worker will leave for another employer. Worker's wage in second year = new VMP = $40,000.
  3. If training is specific, it human-capital value will disappear if the worker leaves the firm in the second year. To give the worker an incentive to stay and 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 and employer pays remainder, $6000-X. Workers wage in first year = $30,000 - X, where 0<X<$6000. This implies that wage in first year must be greater than $24,000 and less than $30,000.
  4. If the competitive wage is $30,000, then the average of the first and second year wages must be $30,000. Therefore, the wage in the second year will be $30,000 + X, which is greater than $30,000 and less than $36,000.

III. Critical thinking

Same as Version A.

[end of answer key]