ECON 115 - Labor Economics
Drake University, Spring 2020
William M. Boal

EXAM 1 ANSWER KEY

Version A

I. Multiple choice

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

II. Problems

(1) [Budget constraint: 6 pts]

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

  1. MRS = MUL/MUC = (C-200)/(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 = $4.
  3. Budget constraint is spending = income, or C = 400 + (60-L) 10 = 1000 - 10 L.
  4. Tangency condition is MRS = wage, or (C-200)/(L-10) = $10. Solve this equation jointly with the budget constraint found in part (b), to get L*= 45 hours, C*= $550.
  5. h*= total available time - L* = 15 hours.

(3) [Individual labor supply--income and substitution effects: 22 pts] Note that the "hypothetical budget line" is drawn tangent to the new indifference curve, but parallel to budget line #1.

  1. 50 weeks.
  2. $5000.
  3. $400 per week.
  4. $2000 per week.
  5. Income effect: work less. Reason: An increase in the wage is like an increase in nonlabor income in that the budget line is now further from the origin. So the income effect is to "purchase" more leisure and more consumption. More precisely, income effect is movement between indifference curves and parallel budget lines, here from budget line #1 to hypothetical iscost line.
  6. -10 weeks.
  7. Substitution effect: work more. Reason: 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. More precisely, substitution effect is movement along indifference curve from hypothetical budget line to budget line #2.
  8. +20 weeks.
  9. Total effect: work more. Reason: total effect = substitution effect + income effect.
  10. +10 weeks.
  11. (w,h) = ($400,25 weeks), ($2000,35 weeks). Aaron's labor supply slopes upward.

(4) [Household specialization: 10 pts]

  1. Household's joint production-possibility curve has intercepts at $300 of market goods and 250 units of household services, and a kink point (which should be circled) at $200 of market goods and 200 units of household services. When the production possibility curve is plotted on the graph with the indifference curve, it is obvious that this household reaches its highest attainable indifference curve at the kink point, where ...
  2. Party A works zero hours in the labor market, and
  3. Party B works 10 hours in the labor market (i.e, full time).

(5) [SR labor demand: 9 pts]

  1. The firm maximizes profit by choosing E so that wage = VMPE, where VMPE is defined as price of output × MPE. So set wage = VMPE, insert values given, and solve to get E* = 32.
  2. Using production function, q* = 160 units of output.
  3. profit = Total Revenue - Total Cost = $1600 - $1200 = $400.

(6) [LR labor demand--scale and substitution effects: 16 pts] Note that the "hypothetical isocost line" is drawn tangent to the old isoquant curve, but parallel to isocost line #2.

  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 wage must = $10 on isocost line #1.
  2. Similarly, the slope of isocost line #2 is -3, so wage must = $30 on isocost line #2.
  3. Substitution effect: use less labor. Reason: Substitution effect is movement along isoquant from isocost line #1 to hypothetical isocost line with the new slope.
  4. -10 units of labor.
  5. Scale effect: use less labor. Reason: Scale effect is movement between isoquants and parallel iscost lines, from hypothetical iscost line to budget line #2.
  6. -30 units of labor.
  7. Use less labor. Reason: total effect = substitution effect + scale effect.
  8. -40 units of labor.

III. Critical thinking

(1) An inferior good is one that consumers buy less of as their income rises and nothing else changes. But even while income rose over the last 100 years, the "price" of children also rose. The "price" of children includes monetary costs like food, clothing, medical care, and schooling, but also opportunity costs. 100 years ago, when more people lived on farms, children could help with chores, but that is less possible today. Also, 100 years ago, women had fewer opportunities in the labor market. As both monetary and opportunity costs of children have risen, so the quantity demanded of children has fallen.

(Indifference-curve diagram should show family's budget line with children on one axis and other goods on other axis. To show effect of rising "price" of children, a second budget line should be drawn with same intercept on "other goods" axis but smaller intercept on "children" axis. Indifference curves should be drawn tangent to each budget line. Tangencies show family's choice. Second tangency should show fewer children than first tangency.)

(2)
Group19992000DifferenceDID
TANF to TANF12.8 hrs13.2 hrs+0.4 hrs-1.0 hrs
TANF to NIT12.5 hrs11.9 hrs-0.6 hrs

Using the difference-in-differences approach, the change in hours of work by those people who worked caused by the new program was a decrease of one hour.

Version B

I. Multiple choice

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

II. Problems

(1) [Budget constraint: 6 pts]

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

  1. MRS = MUL/MUC = (C-100)/(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 = $4.
  3. Budget constraint is spending = income, or C = 300 + (60-L) 20 = 1500 - 20 L.
  4. Tangency condition is MRS = wage, or (C-100)/(L-10) = $10. Solve this equation jointly with the budget constraint found in part (b), to get L*= 40 hours, C*= $700.
  5. h*= total available time - L* = 20 hours.

(3) [Individual labor supply--income and substitution effects: 22 pts] Note that the "hypothetical budget line" is drawn tangent to the new indifference curve, but parallel to budget line #1.

  1. 60 hours.
  2. $200.
  3. $5 per hour.
  4. $20 per hour.
  5. Income effect: work less. Reason: An increase in the wage is like an increase in nonlabor income in that the budget line is now further from the origin. So the income effect is to "purchase" more leisure and more consumption. More precisely, income effect is movement between indifference curves and parallel budget lines, here from budget line #1 to hypothetical iscost line.
  6. -20 hours/
  7. Substitution effect: work more. Reason: 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. More precisely, substitution effect is movement along indifference curve from hypothetical budget line to budget line #2.
  8. +10 hours.
  9. Total effect: work less. Reason: total effect = substitution effect + income effect.
  10. -10 hours.
  11. (w,h) = ($5,40 hours), ($20,30 hours). Brianna's labor supply bends backwards.

(4) [Household specialization: 10 pts]

  1. Household's joint production-possibility curve has intercepts at $300 of market goods and 250 units of household services, and a kink point (which should be circled) at $100 of market goods and 200 units of household services. When the production possibility curve is plotted on the graph with the indifference curve, it is obvious that this household reaches its highest attainable indifference curve at $200 of market goods and 100 units of household services, where ...
  2. Party A works 5 hours in the labor market (i.e., part time), and
  3. Party B works 10 hours in the labor market (i.e., full time).

(5) [SR labor demand: 9 pts]

  1. The firm maximizes profit by choosing E so that wage = VMPE, where VMPE is defined as price of output × MPE. So set wage = VMPE, insert values given, and solve to get E* = 25.
  2. Using production function, q* = 100 units of output.
  3. profit = Total Revenue - Total Cost = $500 - $350 = $150.

(6) [LR labor demand--scale and substitution effects: 16 pts] Note that the "hypothetical isocost line" is drawn tangent to the old isoquant curve, but parallel to isocost line #2.

  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 wage must = $4 on isocost line #1.
  2. Similarly, the slope of isocost line #2 is -1, so wage must = $10 on isocost line #2.
  3. Substitution effect: use more labor. Reason: Substitution effect is movement along isoquant from isocost line #1 to hypothetical isocost line with the new slope.
  4. +20 units of labor.
  5. Scale effect: use more labor. Reason: Scale effect is movement between isoquants and parallel iscost lines, from hypothetical iscost line to budget line #2.
  6. +30 units of labor.
  7. Use more labor. Reason: total effect = substitution effect + scale effect.
  8. +50 units of labor.

III. Critical thinking

Same as Version A.

[end of answer key]