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


EXAM 3 ANSWER KEY
Version A
I. Multiple choice
(1)a. (2)b. (3)b. (4)b. (5)b. (6)b. (7)c. (8)a. (9)b. (10)c.
(11)d. (12)a.
II. Problems
(1) [Measuring inequality: 14 pts]
Quintile  Income share  Cumulative share 
Lowest quintile  3 %  3 % 
Second quintile  8 %  11 % 
Third quintile  14 %  25 % 
Fourth quintile  23 %  48 % 
Fifth quintile  52 %  100 % 
 Gini = area between Lorenz curve and diagonal line, divided by (1/2)
= 0.226/0.5 = 0.452.
(2) [Skillbiased technical change: 8 pts]
 relative wage will decrease.
 5 percent. (Substitute: 7 percent/x = 1.4 and solve for x.)
 demand must shift right to make relative wage increase.
 21 percent. (Substitute: 1.4 = (x7 percent)/10 percent, and solve for x.)
(3) [Intergenerational mobility: 4 pts]
 47st percentile. (Set x50 = 0.3(4050), and solve for x.)
 59th percentile. (Set x50 = 0.3(8050), and solve for x.)
(4) [Migration decision: 4 pts]
 $630 thousand.
 $840 thousand.
 $210 thousand.
(5) [Joint migration decision: 6 pts]
 NGM_{A} = $1000 thousand  $600 thousand  $50 thousand = $350 thousand.
NGM_{B} = $700 thousand  $800 thousand  $50 thousand = $150 thousand.
Total NGM = $350 thousand + $150 thousand = +$200 thousand, so YES they will move.
 Party A is neither, because NGM_{A} is positive, so wants to move.
 Party B is a tied mover, because NGM_{B} is negative, yet Party B will move.
(6) [Roy model: 6 pts]
 Workers move if the net gain from migration is positive, that is, if
w_{Y}  w_{X}  moving cost > zero.
Substituting and solving for S gives S < 10.
 Negatively selected, since workers from the low end of the distribution of S in country X will move.
(7) [Immigration cohorts: 4 pts]
 10 percent, comparing $44,000 and $40,000.
 $33,000, computed as $30,000 × 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 2.6  1.7 = 0.9.
 The log wage differential due to schooling equals the coefficient of schooling for green workers (who are assumed not subject to discrimination) times the difference in average schooling
= 0.10 (1410) = 0.9.
 The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes × blue workers' average schooling
= (1.20.9) + (0.100.08)10 = 0.5.
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 = 72 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 = 60 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+1.5) = $25, 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 = 36 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} = 2 + (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} = 90 and E_{B} = 120.
 Substitute employment into supply equations to get w_{G} = $11 and w_{B} = $14. Note that both groups are paid less than VMP due to monopsony power, but their wages are different because of the shapes of their respective labor supply curves.
 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} = 130 and E_{B} = 140.
III. Critical thinking
(1) Superstars. According to Sherwin Rosen (1981), "superstars" are people who are slightly more able than their rivals, but manage to convert this slight difference into a huge difference in earnings by using technology to reach a mass audience (through publishing, electronic media, etc.)
 A brain surgeon cannot be a "superstar" because a surgeon cannot use technology to reach a mass audience. A surgeon can only operate on one patient at a time.
 A pianist can be a "superstar" because a pianist can reach a mass audience through recordings, broadcasting, streaming, etc.
(2) Discrimination and profit
 Becker's theory of preferencebased employer discrimination predicts that employers with a positive discrimination coefficient will hire too few workers than the profitmaximizing number, and perhaps hire more expensive workers than necessary. An employer with no preference for discrimination, by contrast, will make profitmaximizing choices and enjoyer higher profit.
 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 profitmaximizing 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 preferencebased 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)c. (2)d. (3)c. (4)a. (5)a. (6)a. (7)c. (8)d. (9)d. (10)e. (11)a. (12)c.
II. Problems
(1) [Measuring inequality: 14 pts]
Quintile  Income share  Cumulative share 
Lowest quintile  3 %  3 % 
Second quintile  9 %  12 % 
Third quintile  15 %  27 % 
Fourth quintile  23 %  50 % 
Fifth quintile  50 %  100 % 
 Gini = area between Lorenz curve and diagonal line, divided by (1/2)
= 0.216/0.5 = 0.432.
(2) [Skillbiased technical change: 8 pts]
 relative wage will decrease.
 2.5 percent. (Substitute: 4 percent/x = 1.6 and solve for x.)
 demand must shift right to make relative wage increase.
 20 percent. (Substitute: 1.6 = (x4 percent)/10 percent, and solve for x.)
(3) [Intergenerational mobility: 4 pts]
 58th percentile. (Set x50 = 0.4(7050), and solve for x.)
 34th percentile. (Set x50 = 0.4(1050), and solve for x.)
(4) [Migration decision: 4 pts]
 $440 thousand.
 $550 thousand.
 $110 thousand.
(5) [Joint migration decision: 6 pts]
 NGM_{A} = $600 thousand  $800 thousand  $50 thousand = $250 thousand.
NGM_{B} = $1000 thousand  $800 thousand  $50 thousand = $150 thousand.
Total NGM = $250 thousand + $150 thousand = $100 thousand, so NO they will not move.
 Party A is neither, because NGM_{A} is negative, so does not want to move.
 Party B is a tied stayer, because NGM_{B} is positive, yet Party B will stay.
(6) [Roy model: 6 pts]
 Workers move if the net gain from migration is positive, that is, if
w_{Y}  w_{X}  moving cost > zero.
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]
 20 percent, comparing $36,000 and $30,000.
 $24,000, computed as $20,000 × 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 2.4  1.9 = 0.5.
 The log wage differential due to schooling equals the coefficient of schooling for green workers (who are assumed not subject to discrimination) times the difference in average schooling
= 0.10 (1210) = 0.2.
 The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes × blue workers' average schooling
= (1.21.1) + (0.100.08)10 = 0.3.
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} = 81.
Substitute into production function to get q = 54 units.
Compute profit as total revenue minus labor cost to get $810.
 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} = 36.
Substitute into production function to get q = 36 units.
Compute profit as total revenue minus true labor cost to get $720.
 This firm hires only green workers because it perceives blue workers' wage as 10 (1+1) = $20, more expensive than green workers.
Set VMP = price × MP_{E} = $18 and solve to get E_{G} = 25.
Substitute into production function to get q = 30 units.
Compute profit as total revenue minus labor cost to get $450.
(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} /15).
MLC_{B} = 4 + (2 E_{B} /5).
 For each group, set VMP equal to MLC and solve for E.
This gives E_{G} = 180 and E_{B} = 40.
 Substitute employment into supply equations to get w_{G} = $14 and w_{B} = $12. Note that both groups are paid less than VMP due to monopsony power, but their wages are different because of the shapes of their respective labor supply curves.
 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} = 210 and E_{B} = 55.
III. Critical thinking
Same as Version A.
[end of answer key]