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

FINAL EXAM ANSWER KEY

### Version A

I. Multiple choice

(1)a. (2)b. (3)c. (4)a. (5)a. (6)c. (7)e. (8)b. (9)c. (10)d. (11)a. (12)b. (13)b. (14)c. (15)c. (16)b. (17)a. (18)a. (19)a. (20)c. (21)d.

II. Problems

(1) [Individual labor supply--optimal choice: 12 pts]

1. MRS = MUL/MUC = (C-20)/(L).
2. The reservation wage equals the MRS at the endowment bundle. Inserting nonlabor income for C and total available time for L gives reservation wage = \$16.
3. Budget constraint is spending = income, or C = 500 + (30-L) 80 = 2900 - 80 L.
4. Tangency condition is MRS = wage, or (C-20)/(L) = \$80. Solve this equation jointly with the budget constraint found in part (b), to get L*= 18 days, C*= \$1460.
5. h*= total available time - L* = 12 days.

(2) [LR labor demand - scale and substitution effects: 16 pts]

1. Slope of any isocost line = -w/r, where r = price of capital. The slope of isocost line #1 is -1. We are given that r = \$10, so w = \$10 on isocost line #1.
2. Similarly, the slope of isocost line #2 is -3, so w = \$30 on isocost line #2.
3. substitution effect: use less labor.
4. -20 units of labor.
5. scale effect: use less labor.
6. -30 units of labor.
7. total effect: use less labor.
8. 50 units of labor.

(3) [Mandated benefits: 16 pts]

1. demand.
2. New demand curve is \$3 below old demand curve. Employers are \$3 less willing to pay for workers because of the cost of the mandated benefit.
3. 50 million.
4. \$13.
5. supply.
6. New supply curve is \$1.50 below old supply curve. Workers are willing to work for \$1.50 less because they value the mandated benefit.
7. 55 million.
8. \$12.50.

(4) [Elasticity of labor demand: 8 pts]

1. increase.
2. 2 percent.
3. decrease.
4. 3 percent.

(5) [VSL, safety regulation: 12 pts]

1. VSL = Δ earnings / Δ risk = 625 / (1/10,000) = \$6.25 million.
2. Cost per statistical life saved = cost / reduction in death rate = \$3 million / (1.3-1.2) = \$30.0 million.
3. No, the system should not be required becasuse VSL < cost per statistical life saved.

(6) [Simple model of schooling decision: 10 pts]

1. NPV "no college" = 100,000 + (100,000/1.05) = \$195,238.
2. NPV "college" = -50,000 + (260,500/1.05) = \$198,095.
3. Chooses "college" because NPV is larger.
4. Set 100,000 + 100,000/(1+r) = -50 + 260,500/(1+r) and solve to get r*=7 percent.
5. Chooses "no college" because the benefits from "college" lie entirely in the future. As r increases, then NPV of "college" falls more than NPV of "no college."

(7) [Shifts in relative supply and demand: 8 pts]

1. decrease.
2. 1.176, because 1.7 = 2.00 / (percent change (WC/WH).
3. Relative demand for skilled workers must have shifted to the right even faster than relative supply did.

(8) [Immigration surplus: 8 pts]

1. \$40 thousand.
2. \$30 thousand.
3. \$800 billion.
4. \$100 billion.

(9) [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 2.6 - 1.7 = 0.90.
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 (14-10) = 0.4.
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 (1.2-0.9) + (0.10-0.08)10 = 0.5. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

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

1. MLCG = 3 + (EG /50). MLCB = 1 + (EG /25).
2. For each group, set VMP equal to MLC and solve for E. This gives EG = 1100 and EB = 600.
3. Substitute into supply equations to get wG = \$14 and wB = \$13.
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 = \$15 < efficient wage = \$25. So substitute the minimum wage into the supply equation for each group and solve to get EG = 1200 and EB = 700.

(11) [Monopoly unionism: 10 pts]

1. E = 450.
2. Labor demand curve has intercepts at W=\$60 and E=600.
3. W=\$30 and E=300.
4. Plot outcome on demand curve at W=\$30 and E=300.
5. Efficiency loss = \$1125.

(12) [Piece rates and time rates: 10 pts]

1. 120 toys.
2. \$30.
3. \$14.40.
4. \$12.
5. Prefers Firm #1.

(13) [Markov model: 10 pts]

1. 0.03.
2. 0.27.
3. 3 percent.
4. 27 percent.
5. 10 percent.

(14) [Job search: 10 pts]

1. W = \$15.
2. Would not accept because \$12 is less than the reservation wage.
3. MC would shift right (or down) because the marginal cost of further search would fall if the worker enjoys unemployment insurance (UI) benefits.
4. The reservation wage would therefore increase because the worker could hold out for a higher wage offer.
5. Time to find a new job would increase because the reservation wage would be higher.

III. Critical thinking

(1) General training at a hospital training might include standard health care principles, methods, and techniques. This training is general because it would be make the worker more productive at any hospital or clinic. Specific training at a hospital might include procedures used only at this hospital. This training is specific because, while it would make the worker more productive at this hospital, it would not make the worker more productive at other potential employers.

(2) Adam Smith anticipated the modern theory of compensating differentials. It is neessary to pay workers higher wages if their job is "disagreaable" because workers choose the best combination of wages and "agreeableness"--that is, the combination that maximizes their utility. So in equilibrium, a more disagreeable job must pay a higher wage to attract workers.

### Version B

I. Multiple choice

(1)b. (2)c. (3)b. (4)c. (5)b. (6)d. (7)b. (8)c. (9)d. (10)d. (11)b. (12)d. (13)b. (14)a. (15)d. (16)d. (17)c. (18)e. (19)c. (20)b. (21)e.

II. Problems

(1) [Individual labor supply--optimal choice: 12 pts]

1. MRS = MUL/MUC = C/(L-10).
2. The reservation wage equals the MRS at the endowment bundle. Inserting nonlabor income for C and total available time for L gives reservation wage = \$10.
3. Budget constraint is spending = income, or C = 200 + (30-L)100 = 3200 - 100 L.
4. Tangency condition is MRS = wage, or C/(L-10) = \$80. Solve this equation jointly with the budget constraint found in part (b), to get L*= 21 days, C*= \$1100.
5. h*= total available time - L* = 9 days.

(2) [LR labor demand - scale and substitution effects: 16 pts]

1. Slope of any isocost line = -w/r, where r = price of capital. The slope of isocost line #1 is -4. We are given that r = \$10, so w = \$40 on isocost line #1.
2. Similarly, the slope of isocost line #2 is -2, so w = \$20 on isocost line #2.
3. substitution effect: use more labor.
4. 10 units of labor.
5. scale effect: use more labor.
6. 20 units of labor.
7. total effect: use more labor.
8. 30 units of labor.

(3) [Mandated benefits: 16 pts]

1. demand.
2. New demand curve is \$3 below old demand curve. Employers are \$3 less willing to pay for workers because of the cost of the mandated benefit.
3. 60 million.
4. \$14.
5. supply.
6. New supply curve is \$1.50 below old supply curve. Workers are willing to work for \$1.50 less because they value the mandated benefit.
7. 65 million.
8. \$13.50.

(4) [Elasticity of labor demand: 8 pts]

1. decrease.
2. 2 percent.
3. increase.
4. 3 percent.

(5) [VSL, safety regulation: 12 pts]

1. VSL = Δ earnings / Δ risk = 943 / (1/10,000) = \$9.43 million.
2. Cost per statistical life saved = cost / reduction in death rate = \$1 million / (1.3-1.1) = \$5.0 million.
3. Yes, the system should be required becasuse VSL > cost per statistical life saved.

(6) [Simple model of schooling decision: 10 pts]

1. NPV "no college" = 100,000 + (100,000/1.10) = \$190,909.
2. NPV "college" = -50,000 + (262,000/1.05) = \$188,182.
3. Chooses "no college" because NPV is larger.
4. Set 100,000 + 100,000/(1+r) = -50 + 262,000/(1+r) and solve to get r*=8 percent.
5. Chooses "college" because the benefits from "college" lie entirely in the future. As r decreases, then NPV of "college" rises more than NPV of "no college."

(7) [Shifts in relative supply and demand: 8 pts]

1. decrease.
2. 1.425, because 1.6 = 2.28 / (percent change (WC/WH).
3. Relative demand for skilled workers must have shifted to the right even faster than relative supply did.

(8) [Immigration surplus: 8 pts]

1. \$50 thousand.
2. \$30 thousand.
3. \$1200 billion.
4. \$400 billion.

(9) [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 2.9 - 2.3 = 0.60.
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 = 0.12 (15-14) = 0.12.
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 (1.1-0.9) + (0.12-0.10)14 = 0.48. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

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

1. MLCG = 4 + (EG /25). MLCB = 2 + (EG /15).
2. For each group, set VMP equal to MLC and solve for E. This gives EG = 350 and EB = 240.
3. Substitute into supply equations to get wG = \$11 and wB = \$10.
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 = \$18. So substitute the minimum wage into the supply equation for each group and solve to get EG = 400 and EB = 300.

(11) [Monopoly unionism: 10 pts]

1. E = 250.
2. Labor demand curve has intercepts at W=\$40 and E=400.
3. W=\$20 and E=200.
4. Plot outcome on demand curve at W=\$20 and E=200.
5. Efficiency loss = \$125.

(12) [Piece rates and time rates: 10 pts]

1. 50 toys.
2. \$15.
3. \$2.50.
4. \$5.10.
5. Prefers Firm #2.

(13) [Markov model: 10 pts]

1. 0.98.
2. 0.62.
3. 2 percent.
4. 38 percent.
5. 5 percent.

(14) [Job search: 10 pts]

1. W = \$11.
2. Would accept because \$12 is greater than the reservation wage.
3. MC would shift left (or up) because the marginal cost of further search would rise if the worker unemployment insurance (UI) benefits were reduced.
4. The reservation wage would therefore decrease because the worker would need a job sooner.
5. Time to find a new job would decrease because the reservation wage would be lower.

III. Critical thinking

Same as Version A.

[end of answer key]