ECON 115 - Labor Economics Drake University, Spring 2018 William M. Boal

EXAM 1 ANSWER KEY

### Version A

I. Multiple choice

(1)c. (2)b. (3)d. (4)b. (5)c. (6)a. (7)a. (8)b. (9)b. (10)d. (11)b.

II. Problems

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

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

(2) [Measuring the labor force: 6 pts]

1. 4.2 percent.
2. 60.4 percent.
3. 63.0 percent.

(3) [Budget constraint: 6 pts]

• Endowment point is at L=60 hours and C=\$100.
• Kink point is at L=20 hours and C=\$500.
• Intercept on consumption axis is at C=\$800.

(4) [Optimal choice: 8 pts]

1. The reservation wage equals the MRS at the endowment bundle. MRS = MUL/MUC = (C-10)/(L-20). Inserting nonlabor income for C and total available time for L gives reservation wage = \$2.
2. Budget constraint is spending = income, or C = 90 + (60-L) 20 = 1290 - 20 L.
3. Tangency condition is MRS = wage, or (C-10)/(L-20) = \$20. Solve this equation jointly with the budget constraint found in part (b), to get L*= 42 hours, C*= \$450.
4. h*= total available time - L* = 18 hours.

(5) [Individual labor supply - income and substitution effects: 22 pts]

1. 50 hours.
2. \$200.
3. \$10 per hour.
4. \$20 per hour.
5. income effect: work less. An increase in the wage is like an increase in nonlabor income in that the budget line is now farther from the origin. So the income effect is to "purchase" more leisure and more consumption.
6. -5 hours.
7. substitution effect: work more. An increase in the wage is an increase in the price of leisure compared to the price of consumption. So the substitution effect is to "purchase" less leisure and more consumption.
8. +10 hours.
9. total effect: work more.
10. +5 hours.
11. (w,h) = (\$10,30 hours), (\$20,35 hours). Alison's labor supply slopes upward.

(6) [SR labor demand: 9 pts]

1. VMPE = price of output × MPE. Set VMPE = wage, insert given values, and solve to get E* = 160.
2. Using production function, q* = 240 units of output.
3. profit = Revenue - Total Cost = \$400.

(7) [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.

(8) [Hicks-Marshall rules: 6 pts]

1. Industry #1.
2. Industry #4.
3. Industry #5.

III. Critical thinking

1. Yes, the unemployment rate can fall while the employment rate remains constant. This could happen, for example, if some unemployed people stop looking for work and drop out of the labor force. Recall that the unemployment rate is the number of unemployed workers divided by the sum of unemployed and employed workers. The employment rate is the number of employed workers divided by the entire working-age population, which includes persons out of the labor force.
As a numerical example, suppose there are 76 million employed people, 4 million unemployed, and 20 million out of the labor force. The unemployment rate is 4/(76+4) = 5 percent, and the employment rate is 76/(76+4+20) = 76 percent. Now suppose half of the unemployed people stop looking for work. The new unemployment rate is 2/(76+2) = 2.56 percent, but the employment rate is unchanged.
2. A supply curve shows how many people want to work at any given wage. The supply of labor to a particular employer like Walmart is more elastic--that is, more responsive to the wage--than the supply of labor to the entire economy, for the following reason.
The supply response to the entire economy from a wage increase occurs on two margins: more people working who did not work before, and more hours worked by those people already working. The supply response to a particular employer like Walmart occurs on these margins, plus additional margins: people switching occupations and people switching employers to take advantage of Walmart's now higher wage.
In fact, the supply to a particular employer like Walmart may be nearly perfectly elastic, meaning the employer can hire all the workers it wants if it matches the wage paid by other employers.

### Version B

I. Multiple choice

(1)d. (2)a. (3)b. (4)c. (5)d. (6)d. (7)b. (8)d. (9)a. (10)a. (11)a.

II. Problems

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

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

(2) [Measuring the labor force: 6 pts]

1. 4.1 percent.
2. 60.1 percent.
3. 62.7 percent.

(3) [Budget constraint: 6 pts]

• Endowment point is at L=60 hours and C=\$0.
• Kink point is at L=14 hours and C=\$0.
• Intercept on consumption axis is at C=\$140.

(4) [Optimal choice: 8 pts]

1. The reservation wage equals the MRS at the endowment bundle. MRS = MUL/MUC = (C-50)/(L-30). Inserting nonlabor income for C and total available time for L gives reservation wage = \$3.
2. Budget constraint is spending = income, or C = 200 + (80-L) 15 = 1400 - 15 L.
3. Tangency condition is MRS = wage, or (C-50)/(L-30) = \$15. Solve this equation jointly with the budget constraint found in part (b), to get L*= 60 hours, C*= \$500.
4. h*= total available time - L* = 20 hours.

(5) [Individual labor supply - income and substitution effects: 22 pts]

1. 60 hours.
2. \$100.
3. \$25 per hour.
4. \$10 per hour.
5. income effect: work more. A decrease in the wage is like an decrease in nonlabor income in that the budget line is now closer to the origin. So the income effect is to "purchase" less leisure and less consumption.
6. +15 hours.
7. substitution effect: work less. A decrease in the wage is a decrease in the price of leisure compared to the price of consumption. So the substitution effect is to "purchase" more leisure and less consumption.
8. -5 hours.
9. total effect: work more.
10. +10 hours.
11. (w,h) = (\$10,50 hours), (\$25,40 hours). Beth's labor supply bends backward.

(6) [SR labor demand: 9 pts]

1. VMPE = price of output × MPE. Set VMPE = wage, insert given values, and solve to get E* = 16.
2. Using production function, q* = 64 units of output.
3. profit = Revenue - Total Cost = \$240.

(7) [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.

(8) [Hicks-Marshall rules: 6 pts]

1. Industry #2.
2. Industry #4.
3. Industry #5.

III. Critical thinking

Same as Version A.

[end of answer key]