EXAM 3 ANSWER KEY
Version A
I. Multiple choice
(1)a. (2)b. (3)b. (4)b. (5)b. (6)b. (7)c. (8)c.
II. Problems
(1) [Measuring inequality: 16 pts]
- Let N be the population. Then 80 percent of the population has a total of 0.8 × N × $25000 = $20000 N earnings, while 20 percent of the population has a total of 0.2 × N × $150000 = $30000 N earnings. Total earnings are therefore $50000 N. The share of the bottom 80 percent is (20000 N) / (50000 N) = 40 percent. The Lorenz curve therefore is straight with a kinkpoint at (80 percent of population, 40 percent of earnings).
- Gini = 0.40 .
- 90-50 wage gap = (150000 - 25000) / 25000 = 500 percent.
- 50-10 wage gap = (25000 - 25000) / 25000 = 0 percent.
- 90-10 wage gap = (150000 - 25000) / 25000 = 500 percent.
(2) [Joint migration decision: 6 pts]
- Net gain from migration = $300000, positive, so they will move.
- George's individual net gain is also positive, so he is neither a tied stayer nor a tied mover.
- Laura's individual net gain is negative, so she is a tied mover.
(3) [Immigration--cohort effects: 12 pts]
- To compute the growth of immigrants' earnings, we must use the earnings of immigrants in the same cohort in different censuses: new immigrants in 2000 and the same immigrants here 10 years in 2010. These immigrants moved up the earnings distribution from 10 percent less than all native-born workers, to 5 percent less, a gain of 5 percentage points. Meanwhile individual native-born workers enjoyed a gain of 10 percentage points. So immigrants enjoyed slower earnings growth.
- New immigrants in 2010 have earnings 30 percent below that of native-born workers. If they gain 5 percentage points, the same as the previous cohort, their earnings will be 25 percent below that of native-born workers in 2020.
(4) [Roy model: 6 pts]
- Workers move if the net gain from migration is positive--that is, if w_{Y} - moving cost > w_{X}. Substituting and solving for S gives 30 > S.
- Negatively selected, since workers from the low end of the distribution of S will move.
(5) [Oaxaca decomposition: 12 pts]
- Raw log wage differential is found by substituting each group's average schooling into its own wage equation, to give 3.1 - 2.2 = 0.9.
- 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 (14-13) = 0.15.
- The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes times 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.
(6) [Employer discrimination: 18 pts]
- The firm that does not discriminate hires only blue workers because they are cheaper. Set VMP = price × MP_{E} = $8 and solve to get E_{B} = 25. Substitute into production function to get q = 40 units. Compute profit as total revenue minus labor cost to get $200.
- This firm also hires only blue workers because it perceives their wage as 8 (1+0.25) = $10, still cheaper than green workers. Set VMP = price × MP_{E} = $10 and solve to get E_{B} = 16. Substitute into production function to get q = 32 units. Compute profit as total revenue minus (true) labor cost to get $192.
- This firm hires only green workers because it perceives blue workers' wage as 8 (1+2.0) = $24, more expensive than green workers. Set VMP = price × MP_{E} = $20 and solve to get E_{G} = 4. Substitute into production function to get q = 16 units. Compute profit as total revenue minus labor cost to get $80.
(7) [Monopsony wage discrimination: 12 pts] This is similar to problem (3) on Exam 2, with two groups of workers.
- For each group, set VMP equal to MLC and solve for E. This gives E_{G} = 2000 and E_{B} = 1200.
- Substitute into supply equations to get w_{G} = $15 and w_{B} = $13.
- Substitute the minimum wage into the supply equation for each group to get E_{G} = 3000 and E_{B} = 1900.
III. Critical thinking
- 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.
- 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.
- To determine which explanation is correct, it would be useful to collect data on each worker's starting wage with the company. 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.
Version B
I. Multiple choice
(1)b. (2)d. (3)b. (4)c. (5)c. (6)a. (7)d. (8)b.
II. Problems
(1) [Measuring inequality: 16 pts]
- Let N be the population. Then 90 percent of the population has a total of 0.9 × N × $20000 = $18000 N earnings, while 10 percent of the population has a total of 0.1 × N × $320000 = $32000 N earnings. Total earnings are therefore $50000 N. The share of the bottom 90 percent is (18000 N) / (50000 N) = 36 percent. The Lorenz curve therefore is straight with a kinkpoint at (90 percent of population, 36 percent of earnings).
- Gini =0.54 .
- 90-50 wage gap: This question is a bit unclear. Does the 90th percentile enjoy earnings of $20000 or $320000? If the former, then the 90-50 wage gap is (320000 - 20000) / 20000 = 1500 percent. If the latter, 0 percent.
- 50-10 wage gap = (20000 - 20000) / 20000 = 0 percent.
- 90-10 wage gap: Again this question is a bit unclear. Does the 90th percentile enjoy earnings of $20000 or $320000? If the former, then the 90-10 wage gap is (320000 - 20000) / 20000 = 1500 percent. If the latter, 0 percent.
(2) [Joint migration decision: 6 pts]
- Net gain from migration = $100000, positive, so they will move.
- George's individual net gain is negative, so he is a tied mover.
- Laura's individual net gain is positive, so she is neither a tied stayer nor a tied mover.
(3) [Immigration--cohort effects: 12 pts]
- To compute the growth of immigrants' earnings, we must use the earnings of immigrants in the same cohort in different censuses: new immigrants in 2000 and the same immigrants here 10 years in 2010. These immigrants moved up the earnings distribution from 10 percent less than all native-born workers, to about the same as native-born workers, a gain of 10 percentage points. Meanwhile individual native-born workers also enjoyed a gain of 10 percentage points. So immigrants enjoyed the same earnings growth.
- New immigrants in 2010 have earnings 25 percent below that of native-born workers. If they gain 10 percentage points, the same as the previous cohort, their earnings will be 15 percent below that of native-born workers in 2020.
(4) [Roy model: 6 pts]
- Workers move if the net gain from migration is positive--that is, if w_{Y} - moving cost > w_{X}. Substituting and solving for S gives S > 80.
- Positively selected, since workers from the high end of the distribution of S will move.
(5) [Oaxaca decomposition: 12 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 not subject to discrimination) times the difference in average schooling = 0.1 (12-10) = 0.2.
- The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes times blue workers' average schooling, or (1.2-1.1) + (0.1-0.08)10 = 0.3. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.
(6) [Employer 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 also 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.
(7) [Monopsony wage discrimination: 12 pts] This is similar to problem (3) on Exam 2, with two groups of workers.
- For each group, set VMP equal to MLC and solve for E. This gives E_{G} = 1500 and E_{B} = 950.
- Substitute into supply equations to get w_{G} = $12.50 and w_{B} = $10.50.
- Substitute the minimum wage into the supply equation for each group to get E_{G} = 2000 and E_{B} = 1400.
III. Critical thinking
Same as Version A.
Version C
I. Multiple choice
(1)c. (2)d. (3)a. (4)a. (5)d. (6)b. (7)a. (8)d.
II. Problems
(1) [Measuring inequality: 16 pts]
- Let N be the population. Then 60 percent of the population has a total of 0.6 × N × $10000 = $6000 N earnings, while 40 percent of the population has a total of 0.4 × N × $110000 = $44000 N earnings. Total earnings are therefore $50000 N. The share of the bottom 60 percent is (6000 N) / (50000 N) = 12 percent. The Lorenz curve therefore is straight with a kinkpoint at (60 percent of population, 12 percent of earnings).
- Gini = 0.48 .
- 90-50 wage gap = (110000 - 10000) / 10000 = 1000 percent.
- 50-10 wage gap = (10000 - 10000) / 10000 = 0 percent.
- 90-10 wage gap = (110000 - 10000) / 10000 = 1000 percent.
(2) [Joint migration decision: 6 pts]
- Net gain from migration = -$100000, negative, so they will not move.
- George's individual net gain is positive, so he is a tied stayer.
- Laura's individual net gain is negative, so she is neither a tied stayer nor a tied mover.
(3) [Immigration--cohort effects: 12 pts]
- To compute the growth of immigrants' earnings, we must use the earnings of immigrants in the same cohort in different censuses: new immigrants in 2000 and the same immigrants here 10 years in 2010. These immigrants moved up the earnings distribution from 20 percent less than all native-born workers, to 15 percent less, a gain of 5 percentage points. Meanwhile individual native-born workers enjoyed a gain of 10 percentage points. So immigrants enjoyed slower earnings growth.
- New immigrants in 2010 have earnings 40 percent below that of native-born workers. If they gain 5 percentage points, the same as the previous cohort, their earnings will be 35 percent below that of native-born workers in 2020.
(4) [Roy model: 6 pts]
- Workers move if the net gain from migration is positive--that is, if w_{Y} - moving cost > w_{X}. Substituting and solving for S gives S > 70.
- Positively selected, since workers from the high end of the distribution of S will move.
(5) [Oaxaca decomposition: 12 pts]
- Raw log wage differential is found by substituting each group's average schooling into its own wage equation, to give 2.5 - 1.8 = 0.7.
- 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) = 0.3.
- The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes times blue workers' average schooling, or (1.2-1.0) + (0.10-0.08)10 = 0.4. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.
(6) [Employer 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 also 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.
(7) [Monopsony wage discrimination: 12 pts] This is similar to problem (3) on Exam 2, with two groups of workers.
- For each group, set VMP equal to MLC and solve for E. This gives E_{G} = 700 and E_{B} = 550.
- Substitute into supply equations to get w_{G} = $8.50 and w_{B} = $6.50.
- Substitute the minimum wage into the supply equation for each group to get E_{G} = 1000 and E_{B} = 900.
III. Critical thinking
Same as Version A.
[end of answer key]