ECON 115 - Labor Economics
Drake University, Spring 2018
William M. Boal

EXAM 3 ANSWER KEY

Version A

I. Multiple choice

(1)c. (2)b. (3)d. (4)b. (5)a. (6)d. (7)b. (8)c. (9)d. (10)c. (11)b. (12)c. (13)a. (14)b. (15)c. (16)c. (17)a.

II. Problems

(1) [Measuring inequality: 15 pts]

  1. ThirdAnnual wage Share of earningsCumulative share
    Lowest$10 thousand 5 percent5 percent
    Middle$40 thousand 20 percent25 percent
    Highest$150 thousand 75 percent100 percent
  2. Lorenz curve passes through (33,5) and (67,25).
  3. Gini = 0.467.
  4. 90-10 wage gap = 1400 percent.
  5. 90-50 wage gap = 275 percent.
  6. 50-10 wage gap = 300 percent.

(2) [Migration decision: 8 pts]

  1. Net gain from migration = PDV of earnings in Denver - PDV of earnings in Des Moines - moving cost.
    PDV of eanings in Denver = 60000 + 60000/1.1 + 60000/1.12.
    Similarly, PDV of eanings in Des Moines = 50000 + 50000/1.1 + 50000/1.12.
    Moving cost is given as $30,000. So net gain is -$2645. Since net gain is negative, she will not move.
  2. Highest cost of moving that she will incur and still move to Denver
    = PDV of earnings in Denver - PDV of earnings in Des Moines = $27,355.

(3) [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 10 > S.
  2. Negatively selected, since workers from the low end of the distribution of S in country X will move.

(4) [Immigration cohorts: 8 pts]

  1. Should not compare earnings of new immigrants in 2000 with immigrants who have been in U.S. for ten years in 2000, because these are different people. Must compare new immigrants in 2000 with immigrants who have been in U.S. for ten years in 2010.
    Percent change in earnings = (36,000-32,000)/32,000 = 12.5 percent.
  2. Applying this growth rate to earnings of new immigrants in 2010, 20,000 × (1+0.125) = $22,500.

(5) [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 2.4 - 1.9 = 0.50.
  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 = 0.10 (12-10) = 0.20.
  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 (1.2-1.1) + (0.10-0.08)10 = 0.30. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

(6) [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 = 72 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 = 60 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+1.5) = $25, more expensive than green workers. Set VMP = price × MPE = $20 and solve to get EG = 9. Substitute into production function to get q = 36 units. Compute profit as total revenue minus labor cost to get $180.

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

  1. MLCG = 7 + (EG /10). MLCB = 1 + (EG /5).
  2. For each group, set VMP equal to MLC and solve for E. This gives EG = 80 and EB = 70.
  3. Substitute into supply equations to get wG = $11 and wB = $8.
  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 = $12 < efficient wage = $15. So substitute the minimum wage into the supply equation for each group and solve to get EG = 100 and EB = 110.

III. Critical thinking

(1) Wages and seniority

  1. "Specific human capital" is education, training, or other skills that are only useful at this employer. Because specific human capital is worthless if the worker leaves the company, wages are structured to give both the worker and the company an incentive to stay together: each pays part of the cost and enjoys part of the return. So according to the "specific human capital" explanation, each worker's wage rises with that same worker's seniority, though not as much as VMP rises.
  2. The "matching" explanation argues that a good worker-company match results in higher pay and a lower probability that the worker will leave the company. On the other hand, a poor match results in lower pay and a higher probability that the worker will leave. So at any point in time, workers with higher pay are also likely to have been with the company longer, though no individual worker's pay changes over time as that worker gains seniority.
  3. To determine which explanation is correct, it would be useful to collect data on each worker's starting wage with the company, and perhaps their wages over time. If workers with more seniority have experienced substantial wage growth, then the "specific human capital" explanation seems more likely. If not, then the "matching" explanation seems more likely.

(2) Discrimination and profit

  1. Becker's theory of preference-based employer discrimination predicts that employers with a positive discrimination coefficient will hire too few workers than the profit-maximizing number, and perhaps hire more expensive workers than necessary. An employer with no preference for discrimination, by contrast, will make profit-maximizing choices and enjoyer higher profit.
  2. The theory of monopsony wage discrimination predicts that a discriminating employer will set different wages for different groups of workers, according to VMP = MLC for each group. A monopsonist employer facing similar labor supply curves, but who does not set different wages, will enjoy lower profit.
    Alternate answer: The theory of statistical discrimination predicts that an employer with little information about job applicants' individual characteristics, but accurate information about group averages, will find it profit-maximizing to hire and set wages according to those group averages. An employer with the same information who does not discriminate will enjoy lower profit. (An employer who has complete information on individual characteristics, by contrast, will hire and set wages individually and enjoy even higher profit.)
    Alternate answer: Becker's theory of preference-based employee discrimination assumes that one group of workers (call them green workers) must be given a compensating wage differential for working alongside another group of workers (call them blue workers). Employers who discriminate, hiring only one group (blue or green), can avoid paying this compensating wage differential. Employers who try to hire both green and blue workers must pay the differential to green workers and therefore enjoy lower profit.

Version B

I. Multiple choice

(1)a. (2)d. (3)b. (4)e. (5)d. (6)a. (7)c. (8)a. (9)a. (10)d. (11)a. (12)c. (13)d. (14)d. (15)c. (16)a. (17)b.

II. Problems

(1) [Measuring inequality: 15 pts]

  1. ThirdAnnual wage Share of earningsCumulative share
    Lowest$20 thousand 10 percent10 percent
    Middle$80 thousand 40 percent50 percent
    Highest$100 thousand 50 percent100 percent
  2. Lorenz curve passes through (33,10) and (67,50).
  3. Gini = 0.267.
  4. 90-10 wage gap = 400 percent.
  5. 90-50 wage gap = 25 percent.
  6. 50-10 wage gap = 300 percent.

(2) [Migration decision: 8 pts]

  1. Net gain from migration = PDV of earnings in Denver - PDV of earnings in Des Moines - moving cost.
    PDV of eanings in Denver = 65000 + 65000/1.1 + 65000/1.12.
    Similarly, PDV of eanings in Des Moines = 50000 + 50000/1.1 + 50000/1.12.
    Moving cost is given as $40,000. So net gain is +$1033. Since net gain is positive, she will move.
  2. Highest cost of moving that she will incur and still move to Denver
    = PDV of earnings in Denver - PDV of earnings in Des Moines = $41,033.

(3) [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.

(4) [Immigration cohorts: 8 pts]

  1. Should not compare earnings of new immigrants in 2000 with immigrants who have been in U.S. for ten years in 2000, because these are different people. Must compare new immigrants in 2000 with immigrants who have been in U.S. for ten years in 2010.
    Percent change in earnings = (42,000-40,000)/40,000 = 5.0 percent.
  2. Applying this growth rate to earnings of new immigrants in 2010, 20,000 × (1+0.05) = $21,000.

(5) [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 2.5 - 1.8 = 0.70.
  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 = 0.10 (13-10) = 0.30.
  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 (1.2-1.0) + (0.10-0.08)10 = 0.40. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

(6) [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 = 81. Substitute into production function to get q = 54 units. Compute profit as total revenue minus labor cost to get $810.
  2. This firm hires only green workers because it perceives blue workers' wage as 10 (1+1.0) = $20, more expensive than green workers. Set VMP = price × MPE = $18 and solve to get EG = 25. Substitute into production function to get q = 30 units. Compute profit as total revenue minus labor cost to get $540.

  3. 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 = 36. Substitute into production function to get q = 36 units. Compute profit as total revenue minus (true) labor cost to get $720.

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

  1. MLCG = 5 + (EG /10). MLCB = 3 + (EG /5).
  2. For each group, set VMP equal to MLC and solve for E. This gives EG = 100 and EB = 60.
  3. Substitute into supply equations to get wG = $10 and wB = $9.
  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 = $12 < efficient wage = $15. So substitute the minimum wage into the supply equation for each group and solve to get EG = 140 and EB = 90.

III. Critical thinking

Same as Version A.

[end of answer key]