ECON 115 - Labor Economics Drake University, Spring 2022 William M. Boal

### Version A

I. Multiple choice

(1)b. (2)c. (3)a. (4)d. (5)c. (6)b. (7)a. (8)a. (9)b. (10)b. (11)b. (12)d. (13)c.

II. Problems

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

1. decrease.
2. 4 percent. Set -0.4 = percent change in jobs / 10 percent, and solve.
3. increase.
4. 6 percent. Percent change in workers' income = percent change in jobs + percent change in wage.

(2) [Budget constraint: 6 pts]

• Endowment point is at L=16 hours and C=\$0.
• Intercept on leisure axis is at L=14 because she must work two hours to pay commuting costs.
• Intercept on consumption axis is at C=\$140.

(3) [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.

(4) [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. \$100. The graph shows that if Beth works zero hours, she can still enjoy \$100 in consumption.
3. \$25 per hour. The wage is the negative of the slope of the budget line.
4. \$10 per hour. The wage is the negative of the slope of the budget line.
5. Income effect: work more. Reason: 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. More precisely, the income effect is a movement between indifference curves and parallel budget lines, here from tangency with budget line #1 to tangency with the hypothetical budget line.
6. +15 hours.
7. Substitution effect: work less. Reason: 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. More precisely, the substitution effect is a movement along a single indifference curve from tangency with hypothetical budget line to tangency with budget line #2.
8. -5 hours.
9. Total effect: work more. Reason: total effect = substitution effect + income effect.
10. +10 hours.
11. (w,h) = (\$25,40 hours), (\$10,50 hours). Labor supply bends backward.

(5) [Household specialization: 10 pts]

1. Household's joint production-possibility curve has intercepts at \$400 of market goods and 150 units of household services, because these are the points where both parties are working in the market or both are working in the household.
To find the rest of the curve, begin where both parties are working in the household, producing zero market goods and 150 units of household services. If market goods are desired, who should work in the market? Party A has a comparative advantage. Sending Party A into the market creates a line segment with slope = -6, because giving up 5 units of household services gains \$30 in market goods for the household. This continues until Party A is working full-time in the market, producing \$300 in market goods but no household services. At that point, the household enjoys \$300 in market goods (produced by Party A) and 100 units of household services (produced by Part B). This kink point should be circled. The remainder of the PP curve is a line segment joining the kink point to the vertical intercept.
When the production possibility curve is plotted on the graph with the indifference curves, it is obvious that this household reaches its highest attainable indifference curve at the kink point, where ...
2. Party A works 10 hours in the labor market (i.e, full time), and
3. Party B works zero hours in the labor market.

(6) [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 and insert values given: \$10 = \$25 (32/E)1/2, and solve to get E* = 200.
2. Using production function, q* = 2 (32×200)1/2 = 160 units of output.
3. Profit = total revenue - total cost
= total revenue - cost of labor - cost of capital
= \$4000 - \$2000 - \$1600
= \$400.

(7) [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 graph shows slope of isocost line #1 is -4. We are given that r = \$10, so wage must = \$40 on isocost line #1.
2. Similarly, the slope of isocost line #2 is -2, so wage must = \$20 on isocost line #2.
3. Substitution effect: use more labor. Reason: Substitution effect is movement along isoquant from tangency with isocost line #1 to tangency with hypothetical isocost line with the new slope.
4. +10 units of labor (from 20 units of labor to 30 units).
5. Scale effect: use more labor. Reason: Scale effect is movement between isoquants and parallel iscost lines, from hypothetical iscost line to isocost line #2.
6. +20 units of labor (from 30 units of labor to 50 units).
7. Use more labor. Reason: total effect = substitution effect + scale effect.
8. +30 units of labor.

III. Critical thinking

(1) A "universal basic income" would create a pure income effect. There would be no substitution effect because the wage would not change. Therefore, assuming leisure is a normal good, workers would choose more leisure and would decrease their hours of work. (The diagram should show the budget line under the "universal basic income" to be higher to the original budget line, but parallel. The new intercept on the consumption axis should be \$1000 higher than the old intercept, and similarly for the new endowment point. The worker chooses a point on each budget line that is tangent to the highest indifference curve they can reach. The tangency on the new budget line should be to the right of the tangency on the old budget line, assuming leisure is a normal good.)

(2) A wage subsidy would create both an income effect and a substitution effect for workers who were already working. The income effect would prompt workers to work less while the substitution effect would prompt them to work more. It cannot be determined from economic theory whether workers would on balance work more or less. However, for those who were not working before the subsidy, there would only be a substitution effect. They might start working if the new wage (twice the old one) exceeded their reservation wage. (The diagram should show the original budget line and a new budget line with the same endowment point but twice the slope. On each budget line the worker, chooses a point on each budget line that is tangent to the highest indifference curve they can reach. Economic theory cannot predict whether the tangency on the new budget line would be the left or to the right of the tangency on the old budget line--the answer depends on the individual worker's preferences.)

### Version B

I. Multiple choice

(1)a. (2)b. (3)b. (4)b. (5)a. (6)d. (7)d. (8)b. (9)c. (10)a. (11)c. (12)b. (13)d.

II. Problems

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

1. decrease.
2. 6 percent. Set -0.6 = percent change in jobs / 10 percent, and solve.
3. increase.
4. 4 percent. Percent change in workers' income = percent change in jobs + percent change in wage.

(2) [Budget constraint: 6 pts]

• Endowment point is at L=60 hours and C=\$100.
• Kink point at L=20 and C=\$500 because earns \$10 per hour for the first 40 hours of work but \$15 per hour for the last 20 hours of work.
• Intercept on consumption axis is at C=\$800.

(3) [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.

(4) [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 hours.
2. \$200. The graph shows that if Alison works zero hours, she can still enjoy \$200 in consumption.
3. \$10 per hour. The wage is the negative of the slope of the budget line.
4. \$20 per hour. The wage is the negative of the slope of the budget line.
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, the income effect is a movement between indifference curves and parallel budget lines, here from tangency with budget line #1 to tangency with the hypothetical budget line.
6. -5 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, the substitution effect is a movement along a single indifference curve from tangency with hypothetical budget line to tangency with budget line #2.
8. +10 hours.
9. Total effect: work more. Reason: total effect = substitution effect + income effect.
10. +5 hours.
11. (w,h) = (\$20,35 hours), (\$10,30 hours). Labor supply slopes up.

(5) [Household specialization: 10 pts]

1. Household's joint production-possibility curve has intercepts at \$400 of market goods and 250 units of household services, because these are the points where both parties are working in the market or both are working in the household.
To find the rest of the curve, begin where both parties are working in the household, producing zero market goods and 250 units of household services. If market goods are desired, who should work in the market? Party A has a comparative advantage. Sending Party A into the market creates a line segment with slope = -4, because giving up 5 units of household services gains \$20 in market goods for the household. This continues until Party A is working full-time in the market, producing \$200 in market goods but no household services. At that point, the household enjoys \$200 in market goods (produced by Party A) and 200 units of household services (produced by Party B). This kink point should be circled. The remainder of the PP curve is a line segment joining the king point to the vertical intercept.
When the production possibility curve is plotted on the graph with the indifference curves, it is obvious that this household reaches its highest attainable indifference curve at a tangency, where ...
2. Party A works 10 hours in the labor market (i.e, full time), and
3. Party B works 2.5 hours in the labor market.

(6) [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 and insert values given: \$20 = \$10 (5)(16/E)1/2. Solve to get E* = 100.
2. Using production function, q* = 10 (16×100)1/2 = 400 units of output.
3. Profit = total revenue - total cost
= total revenue - cost of labor - cost of capital
= \$4000 - \$2000 - \$800
= \$1200.

(7) [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 = \$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 tangency with isocost line #1 to tangency with hypothetical isocost line with the new slope.
4. -20 units of labor (from 70 units of labor to 50 units).
5. Scale effect: use less labor. Reason: Scale effect is movement between isoquants and parallel iscost lines, from hypothetical iscost line to isocost line #2.
6. -30 units of labor (from 50 units of labor to 20 units).
7. Use less labor. Reason: total effect = substitution effect + scale effect.
8. -50 units of labor.

III. Critical thinking

Same as Version A.