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

EXAM 3 ANSWER KEY

Version A

I. Multiple choice

(1)d. (2)b. (3)c. (4)a. (5)c. (6)a. (7)c. (8)a.

II. Problems

(1) [Measuring inequality: 15 pts]
ThirdAnnual wage Share of earningsCumulative share
Lowest$30 thousand 10 percent10 percent
Middle$75 thousand 25 percent35 percent
Highest$195 thousand 65 percent100 percent

  1. mean wage = $100 thousand.
  2. median wage = $75 thousand.
  3. shares and cumulative shares--see above.
  4. Lorenz curve passes through (33.3,10) and (66.7,35).
  5. Gini = 0.367.

(2) [Skill-biased technical change: 8 pts]

  1. relative wage will decrease.
  2. 10 percent. (Substitute: 12 percent/x = 1.2 and solve for x.)
  3. demand must shift right to make relative wage increase.
  4. 18 percent. (Substitute: 1.2 = (x-12 percent)/5 percent, and solve for x.)

(3) [Intergenerational mobility: 4 pts]

  1. 41st percentile. (Set x-50 = 0.3(20-50), and solve for x.)
  2. 53rd percentile. (Set x-50 = 0.3(60-50), and solve for x.)

(4) [Migration decision: 4 pts]

  1. $1260 thousand.
  2. $840 thousand.
  3. $420 thousand.

(5) [Joint migration decision: 6 pts]

  1. NGMA = $900,000 - $800,000 - $50,000 = $50,000.
    NGMB = $750,000 - $800,000 - $50,000 = -$100,000.
    Total NGM = -$50,000, so NO they will not move.
  2. Party A is a tied stayer, because NGMA is positive, yet Party A will stay.
  3. Party B is neither, because NGMB is negative, so wants to stay.

(6) [Roy model: 6 pts]

  1. Workers move if the net gain from migration is positive--that is, if wY > wX + moving cost. Substituting and solving for S gives 30 > S.
  2. Negatively selected, since workers from the low end of the distribution of S in country X will move.

(7) [Immigration cohorts: 4 pts]

  1. 20 percent (comparing $48,000 and $40,000).
  2. $36,000 (computed as $30,000 × 1.20).

(8) [Oaxaca decomposition: 6 pts]

  1. Raw log wage differential is found by substituting each group's average schooling into its own wage equation, to give 3.4 - 2.2 = 1.2.
  2. The log wage differential due to schooling equals the coefficient of schooling for green workers (who are not subject to discrimination) times the difference in average schooling = 0.15 (16-13) = 0.45.
  3. The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes × blue workers' average schooling, or (1.0-0.9) + (0.15-0.10)13 = 0.75. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

(9) [Employer preference discrimination: 18 pts]

  1. The firm that does not discriminate hires only blue workers because they are cheaper. Set VMP = price × MPE = $10 and solve to get EB = 9. Substitute into production function to get q = 36 units. Compute profit as total revenue minus labor cost to get $90.
  2. This firm hires only blue workers because it perceives their wage as 10 (1+0.5) = $15, still cheaper than green workers. Set VMP = price × MPE = $15 and solve to get EB = 4. Substitute into production function to get q = 24 units. Compute profit as total revenue minus (true) labor cost to get $80.
  3. This firm hires only green workers because it perceives blue workers' wage as 10 (1+2.5) = $35, more expensive than green workers. Set VMP = price × MPE = $30 and solve to get EG = 1. Substitute into production function to get q = 12 units. Compute profit as total revenue minus labor cost to get $30.

(10) [Monopsony wage discrimination: 12 pts] This is similar to problem (4) on Exam 2, but with two groups of workers.

  1. MLCG = 6 + (EG /5). MLCB = 8 + (EB /10).
  2. For each group, set VMP equal to MLC and solve for E. This gives EG = 70 and EB = 120.
  3. Substitute employment into supply equations to get wG = $13 and wB = $14.
  4. If the minimum wage is lower than the efficient (or competitive) wage, then employment is determined by the supply curve. Here the minimum wage = $15 < efficient wage = $20. So substitute the minimum wage into the supply equation for each group and solve to get EG = 90 and EB = 140.

III. Critical thinking

(1) If true, this would be an example of customer-based discrimination where the targets are women. Becker's model of customer preference-based discrimination predicts that employers would respond by assigning women to jobs requiring less customer contact. Women would be assigned to back-office jobs instead of sales jobs--perhaps working as clerks or accountants. If there were enough men to fill the sales jobs, there would be no difference in wages, according to Becker's model. If there were not enough men to fill the sales jobs, then some women would be assigned to sales jobs but at lower pay in equilibrium.

(2) The Affordable Care Act likely increased worker turnover. A worker with a pre-existing health condition would be reluctant to move to a new employer if that new employer refused to cover the pre-existing conditions. A move would effectively imply a reduction in total compensation for the worker. So requiring employers to cover pre-existing health conditions likely increased worker mobility and turnover.

Version B

I. Multiple choice

(1)d. (2)c. (3)a. (4)b. (5)c. (6)c. (7)a. (8)b.

II. Problems

(1) [Measuring inequality: 15 pts]
ThirdAnnual wage Share of earningsCumulative share
Lowest$24 thousand 10 percent10 percent
Middle$72 thousand 30 percent40 percent
Highest$144 thousand 60 percent100 percent

  1. mean wage = $80 thousand.
  2. median wage = $72 thousand.
  3. shares and cumulative shares--see above.
  4. Lorenz curve passes through (33.3,10) and (66.7,40).
  5. Gini = 0.333.

(2) [Skill-biased technical change: 8 pts]

  1. relative wage will decrease.
  2. 5 percent. (Substitute: 8 percent/x = 1.6 and solve for x.)
  3. demand must shift right to make relative wage increase.
  4. 24 percent. (Substitute: 1.6 = (x-8 percent)/10 percent, and solve for x.)

(3) [Intergenerational mobility: 4 pts]

  1. 42nd percentile. (Set x-50 = 0.4(30-50), and solve for x.)
  2. 66th percentile. (Set x-50 = 0.4(90-50), and solve for x.)

(4) [Migration decision: 4 pts]

  1. $660 thousand.
  2. $440 thousand.
  3. $220 thousand.

(5) [Joint migration decision: 6 pts]

  1. NGMA = $850,000 - $800,000 - $100,000 = -$50,000.
    NGMB = $900,000 - $700,000 - $100,000 = $100,000.
    Total NGM = $50,000, so YES they will move.
  2. Party A is a tied mover, because NGMA is negative, yet Party A will move.
  3. Party B is neither, because NGMB is positive, so wants to move.

(6) [Roy model: 6 pts]

  1. Workers move if the net gain from migration is positive--that is, if wY > wX + moving cost. Substituting and solving for S gives S > 80.
  2. Positively selected, since workers from the high end of the distribution of S in country X will move.

(7) [Immigration cohorts: 4 pts]

  1. 10 percent (comparing $25,000 and $27,500).
  2. $22,000 (computed as $20,000 × 1.10).

(8) [Oaxaca decomposition: 6 pts]

  1. Raw log wage differential is found by substituting each group's average schooling into its own wage equation, to give 2.8 - 2.3 = 0.5.
  2. The log wage differential due to schooling equals the coefficient of schooling for green workers (who are not subject to discrimination) times the difference in average schooling = 0.12 (15-14) = 0.12.
  3. The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes × blue workers' average schooling, or (1.0-0.9) + (0.12-0.10)14 = 0.38. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

(9) [Employer preference discrimination: 18 pts]

  1. The firm that does not discriminate hires only blue workers because they are cheaper. Set VMP = price × MPE = $10 and solve to get EB = 36. Substitute into production function to get q = 36 units. Compute profit as total revenue minus labor cost to get $360.
  2. This firm hires only blue workers because it perceives their wage as 10 (1+0.2) = $12, still cheaper than green workers. Set VMP = price × MPE = $12 and solve to get EB = 25. Substitute into production function to get q = 30 units. Compute profit as total revenue minus (true) labor cost to get $350.
  3. This firm hires only green workers because it perceives blue workers' wage as 10 (1+2.0) = $30, more expensive than green workers. Set VMP = price × MPE = $20 and solve to get EG = 9. Substitute into production function to get q = 18 units. Compute profit as total revenue minus labor cost to get $180.

(10) [Monopsony wage discrimination: 12 pts] This is similar to problem (4) on Exam 2, but with two groups of workers.

  1. MLCG = 8 + (EG /10). MLCB = 4 + (EB /5).
  2. For each group, set VMP equal to MLC and solve for E. This gives EG = 120 and EB = 80.
  3. Substitute employment into supply equations to get wG = $14 and wB = $12.
  4. If the minimum wage is lower than the efficient (or competitive) wage, then employment is determined by the supply curve. Here the minimum wage = $15 < efficient wage = $20. So substitute the minimum wage into the supply equation for each group and solve to get EG = 140 and EB = 110.

III. Critical thinking

Same as Version A.

[end of answer key]