ECON 115  Labor Economics
Drake University, Spring 2019
William M. Boal


EXAM 3 ANSWER KEY
Version A
I. Multiple choice
(1)d. (2)d. (3)b. (4)c. (5)b. (6)a. (7)c. (8)b. (9)c. (10)b.
(11)d.
II. Problems
(1) [Measuring inequality: 15 pts]

Third  Annual wage 
Share of earnings  Cumulative share 
Lowest  $10 thousand 
5 percent  5 percent 
Middle  $60 thousand 
30 percent  35 percent 
Highest  $130 thousand 
65 percent  100 percent 
 Lorenz curve passes through (33,5) and (67,35).
 Gini = 0.400.
 9010 wage gap = 1200 percent.
 9050 wage gap = 116.7 percent.
 5010 wage gap = 500 percent.
(2) [Shifts in relative supply and demand: 8 pts]
 decrease.
 1.425, because 1.6 = 2.28 / (percent change (W_{C}/W_{H}).
 Relative demand for skilled workers must have shifted to the right
even faster than relative supply did.
(3) [Joint migration decision: 8 pts]
 NGM_{A} = $1,000,000  $1,000,000  $50,000 = $50,000.
NGM_{B} = $1,200,000  $800,000  $50,000 = $350,000.
Total NGM = $300,000, so yes they will move to Los Angeles.
 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.
(4) [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 70 < S.
 Positively selected, since workers from the high end of the distribution of S in country X will move.
(5) [Immigration surplus: 8 pts]
 $40 thousand.
 $30 thousand.
 $800 billion.
 $100 billion.
(6) [Oaxaca decomposition: 6 pts]
 Raw log wage differential is found by substituting each group's average schooling into its own wage equation, to give 2.9  2.3 = 0.60.
 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 (1.10.9) + (0.120.10)14 = 0.48. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.
(7) [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 = 180 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 = 150 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} = $15 and solve to get E_{G} = 16. Substitute into production function to get q = 120 units. Compute profit as total revenue minus labor cost to get $240.
(8) [Monopsony wage discrimination: 12 pts]
This is similar to problem (2) on Exam 2, but with two groups of workers.
 MLC_{G} = 3 + (E_{G} /50).
MLC_{B} = 1 + (E_{G} /25).
 For each group, set VMP equal to MLC and solve for E.
This gives E_{G} = 1100 and E_{B} = 600.
 Substitute into supply equations to get w_{G} = $14 and w_{B} = $13.
 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 = $25.
So substitute the minimum wage into the supply equation for each group and solve to get E_{G} = 1200 and E_{B} = 700.
III. Critical thinking
(1) 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 heart 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 violinist can be a "superstar" because a violinist can reach a mass audience through recordings and broadcasting.
(2) We cannot conclude from the information given that immigrants double their earnings in 20 years because of possible cohort effects. To estimate the return to labormarket experience, we must follow the same cohort over time. Immigrants who have been here 10 years are likely different from immigrants who have been here 30 yearsthey come from different countries and likely had different amounts of human capital when they arrived. So to estimate the returns to experience, we must compare immigrants in the latest Census who have been here 30 years with immigrants in the Census 20 years earlier who had been here 10 years.
Version B
I. Multiple choice
(1)c. (2)d. (3)c. (4)a. (5)a. (6)c. (7)a. (8)a. (9)a. (10)d.
(11)a.
II. Problems
(1) [Measuring inequality: 15 pts]

Third  Annual wage 
Share of earnings  Cumulative share 
Lowest  $20 thousand 
10 percent  10 percent 
Middle  $40 thousand 
20 percent  30 percent 
Highest  $140 thousand 
70 percent  100 percent 
 Lorenz curve passes through (33,10) and (67,30).
 Gini = 0.400.
 9010 wage gap = 600 percent.
 9050 wage gap = 250 percent.
 5010 wage gap = 100 percent.
(2) [Shifts in relative supply and demand: 8 pts]
 decrease.
 1.176, because 1.7 = 2.00 / (percent change (W_{C}/W_{H}).
 Relative demand for skilled workers must have shifted to the right
even faster than relative supply did.
(3) [Joint migration decision: 8 pts]
 NGM_{A} = $1,000,000  $900,000  $50,000 = $50,000.
NGM_{B} = $750,000  $800,000  $50,000 = $100,000.
Total NGM = $50,000, so no they will not move to Los Angeles.
 Party A is a tied stayer, because NGM_{A} is positive, yet Party A will not move.
 Party B is neither, because NGM_{B} is negative, so does not want to move.
(4) [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 10 > S.
 Negatively selected, since workers from the low end of the distribution of S in country X will move.
(5) [Immigration surplus: 8 pts]
 $50 thousand.
 $30 thousand.
 $1200 billion.
 $400 billion.
(6) [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 = 0.90.
 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 (1410) = 0.4.
 The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes × blue workers' average schooling, or (1.20.9) + (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.
(7) [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 = 180 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+0.5) = $15, still cheaper than green workers. Set VMP = price × MP_{E} = $15 and solve to get E_{B} = 16. Substitute into production function to get q = 120 units. Compute profit as total revenue minus (true) labor cost to get $320.
 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 = 90 units. Compute profit as total revenue minus labor cost to get $180.
(8) [Monopsony wage discrimination: 12 pts]
This is similar to problem (2) on Exam 2, but with two groups of workers.
 MLC_{G} = 4 + (E_{G} /25).
MLC_{B} = 2 + (E_{G} /15).
 For each group, set VMP equal to MLC and solve for E.
This gives E_{G} = 350 and E_{B} = 240.
 Substitute into supply equations to get w_{G} = $11 and w_{B} = $10.
 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 = $18.
So substitute the minimum wage into the supply equation for each group and solve to get E_{G} = 400 and E_{B} = 300.
III. Critical thinking
Same as Version A.
[end of answer key]