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

EXAM 1 ANSWER KEY

Version A

I. Multiple choice

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

II. Problems

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

  1. decrease.
  2. 2 percent.
  3. increase.
  4. 8 percent

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

  1. 4.1 percent.
  2. 60.2 percent.
  3. 62.7 percent.

(3) [Budget constraint: 6 pts]

(4) [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.

(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 a 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) = ($25,40 hours), ($10,50 hours). Aaron'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* = 90.
  2. Using production function, q* = 360 units of output.
  3. profit = Total Revenue - Total Cost = $100.

(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 B.
  2. Industry D.
  3. Industry E.

III. Critical thinking

(1) By definition, the elasticity of demand for minimum-wage workers = % chg E / % chg W. We are given % chg W = 10% but we are not given % chg E. However, we are given % chg income = 8%. Now since income = W × E, then for small changes, % chg income = % chg W + % chg E. Substituting, 8% = 10% + % chg E, so % chg E = -2%. So the elasticity of demand = -2%/10% = -0.2 .

(2)
Group19992000DifferenceDID
TANF-TANF27.7%35.7%8%9.5%
TANF-NIT28.0%45.5%17.5%
Using the difference-in-differences approach, the change in the percentage of people who worked caused by the new program is 9.5%.

Version B

I. Multiple choice

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

II. Problems

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

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

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

  1. 3.9 percent.
  2. 60.6 percent.
  3. 63.1 percent.

(3) [Budget constraint: 6 pts]

(4) [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) = $100. 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.

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

  1. 50 hours.
  2. $100.
  3. $10 per hour.
  4. $30 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. -15 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. +5 hours.
  9. total effect: work less.
  10. -10 hours.
  11. (w,h) = ($10,40 hours), ($30,30 hours). Aaron'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* = 100.
  2. Using production function, q* = 800 units of output.
  3. profit = Total Revenue - Total Cost = $1200.

(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 B.
  2. Industry C.
  3. Industry E.

III. Critical thinking

Same as Version A.

[end of answer key]