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]
Third  Annual wage 
Share of earnings  Cumulative share 
Lowest  $30 thousand 
10 percent  10 percent 
Middle  $75 thousand 
25 percent  35 percent 
Highest  $195 thousand 
65 percent  100 percent 
 mean wage = $100 thousand.
 median wage = $75 thousand.
 shares and cumulative sharessee above.
 Lorenz curve passes through (33.3,10) and (66.7,35).
 Gini = 0.367.
(2) [Skillbiased technical change: 8 pts]
 relative wage will decrease.
 10 percent. (Substitute: 12 percent/x = 1.2 and solve for x.)
 demand must shift right to make relative wage increase.
 18 percent. (Substitute: 1.2 = (x12 percent)/5 percent, and solve for x.)
(3) [Intergenerational mobility: 4 pts]
 41st percentile. (Set x50 = 0.3(2050), and solve for x.)
 53rd percentile. (Set x50 = 0.3(6050), and solve for x.)
(4) [Migration decision: 4 pts]
 $1260 thousand.
 $840 thousand.
 $420 thousand.
(5) [Joint migration decision: 6 pts]
 NGM_{A} = $900,000  $800,000  $50,000 = $50,000.
NGM_{B} = $750,000  $800,000  $50,000 = $100,000.
Total NGM = $50,000, so NO they will not move.
 Party A is a tied stayer, because NGM_{A} is positive, yet Party A will stay.
 Party B is neither, because NGM_{B} is negative, so wants to stay.
(6) [Roy model: 6 pts]
 Workers move if the net gain from migration is positivethat is,
if w_{Y} > w_{X} + moving cost.
Substituting and solving for S gives 30 > S.
 Negatively selected, since workers from the low end of the distribution of S in country X will move.
(7) [Immigration cohorts: 4 pts]
 20 percent (comparing $48,000 and $40,000).
 $36,000 (computed as $30,000 × 1.20).
(8) [Oaxaca decomposition: 6 pts]
 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.
 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 (1613) = 0.45.
 The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes × blue workers' average schooling, or (1.00.9) + (0.150.10)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]
 The firm that does not discriminate hires only blue workers because they are cheaper. Set VMP = price × MP_{E} = $10 and solve to get E_{B} = 9. Substitute into production function to get q = 36 units. Compute profit as total revenue minus labor cost to get $90.
 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 × MP_{E} = $15 and solve to get E_{B} = 4. Substitute into production function to get q = 24 units. Compute profit as total revenue minus (true) labor cost to get $80.
 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 × MP_{E} = $30 and solve to get E_{G} = 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.
 MLC_{G} = 6 + (E_{G} /5).
MLC_{B} = 8 + (E_{B} /10).
 For each group, set VMP equal to MLC and solve for E.
This gives E_{G} = 70 and E_{B} = 120.
 Substitute employment into supply equations to get w_{G} = $13 and w_{B} = $14.
 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 E_{G} = 90 and E_{B} = 140.
III. Critical thinking
(1) If true, this would be an example of customerbased discrimination where the targets are women. Becker's model of customer preferencebased discrimination predicts that employers would respond by assigning women to jobs requiring less customer contact. Women would be assigned to backoffice jobs instead of sales jobsperhaps 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 preexisting health condition would be reluctant to move to a new employer if that new employer refused to cover the preexisting conditions. A move would effectively imply a reduction in total compensation for the worker. So requiring employers to cover preexisting 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]
Third  Annual wage 
Share of earnings  Cumulative share 
Lowest  $24 thousand 
10 percent  10 percent 
Middle  $72 thousand 
30 percent  40 percent 
Highest  $144 thousand 
60 percent  100 percent 
 mean wage = $80 thousand.
 median wage = $72 thousand.
 shares and cumulative sharessee above.
 Lorenz curve passes through (33.3,10) and (66.7,40).
 Gini = 0.333.
(2) [Skillbiased technical change: 8 pts]
 relative wage will decrease.
 5 percent. (Substitute: 8 percent/x = 1.6 and solve for x.)
 demand must shift right to make relative wage increase.
 24 percent. (Substitute: 1.6 = (x8 percent)/10 percent, and solve for x.)
(3) [Intergenerational mobility: 4 pts]
 42nd percentile. (Set x50 = 0.4(3050), and solve for x.)
 66th percentile. (Set x50 = 0.4(9050), and solve for x.)
(4) [Migration decision: 4 pts]
 $660 thousand.
 $440 thousand.
 $220 thousand.
(5) [Joint migration decision: 6 pts]
 NGM_{A} = $850,000  $800,000  $100,000 = $50,000.
NGM_{B} = $900,000  $700,000  $100,000 = $100,000.
Total NGM = $50,000, so YES they will move.
 Party A is a tied mover, because NGM_{A} is negative, yet Party A will move.
 Party B is neither, because NGM_{B} is positive, so wants to move.
(6) [Roy model: 6 pts]
 Workers move if the net gain from migration is positivethat is,
if w_{Y} > w_{X} + moving cost.
Substituting and solving for S gives S > 80.
 Positively selected, since workers from the high end of the distribution of S in country X will move.
(7) [Immigration cohorts: 4 pts]
 10 percent (comparing $25,000 and $27,500).
 $22,000 (computed as $20,000 × 1.10).
(8) [Oaxaca decomposition: 6 pts]
 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.
 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 (1514) = 0.12.
 The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes × blue workers' average schooling, or (1.00.9) + (0.120.10)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]
 The firm that does not discriminate hires only blue workers because they are cheaper. Set VMP = price × MP_{E} = $10 and solve to get E_{B} = 36. Substitute into production function to get q = 36 units. Compute profit as total revenue minus labor cost to get $360.
 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 × MP_{E} = $12 and solve to get E_{B} = 25. Substitute into production function to get q = 30 units. Compute profit as total revenue minus (true) labor cost to get $350.
 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 × MP_{E} = $20 and solve to get E_{G} = 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.
 MLC_{G} = 8 + (E_{G} /10).
MLC_{B} = 4 + (E_{B} /5).
 For each group, set VMP equal to MLC and solve for E.
This gives E_{G} = 120 and E_{B} = 80.
 Substitute employment into supply equations to get w_{G} = $14 and w_{B} = $12.
 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 E_{G} = 140 and E_{B} = 110.
III. Critical thinking
Same as Version A.
[end of answer key]