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

FINAL EXAM ANSWER KEY

Version A

I. Multiple choice

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

II. Problems

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

  2. 4.2 percent.
  3. 60.4 percent.
  4. 63.0 percent.

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

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

(3) [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.

(4) [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.

(5) [Payroll tax or subsidy: 14 pts]

  1. 110 million.
  2. $13.
  3. $17.
  4. $105 million.
  5. $315 million.
  6. $440 million.
  7. $20 million.

(6) [Monopsony: 18 pts]

  1. Set supply equation w=VMP and solve to get E=600.
  2. MLC = -20 + 2 E/10.
  3. Set VMP=MLC and solve to get E=360.
  4. Substitute E=360 into labor supply equation to get w=$16.
  5. The minimum wage ($15) is less than the monopsonist employer's profit-maximizing wage. So the minimum wage is not binding. The monopsonist employer will choose E=360, as before.

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

  1. NPV "no college" = 150 + 318/1.10 = $439 thousand.
  2. NPV "college" = -50 + 530/1.10 = $432 thousand.
  3. Chooses "no college" because NPV is larger.
  4. Set 150 + 318/(1/r) = -50 + 530/(1+r) and solve to get r*=6 percent.
  5. Chooses "college" because the benefits from "college" lie entirely in the future. As r decreases, then NPV of "college" increases more than NPV of "no college."

(8) [Roy model: 6 pts]

  1. Workers move if the net gain from migration is positive--that is, if wY > wX + moving cost. Substituting and solving for S gives 10 > S.
  2. Negatively selected, since workers from the low end of the distribution of S in country X will move.

(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 2.5 - 1.8 = 0.70.
  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 (13-10) = 0.30.
  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 (1.2-1.0) + (0.10-0.08)10 = 0.40. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

(10) [Monopoly union model: 10 pts]

  1. Set WC = 50 - 0.1 E and solve to get E=400.
  2. Demand curve is a downward-sloping line with intercept at W=$50 and slope = -0.1. WC is a horizontal line at $10.
  3. Set MRS = 0.1 and solve this equation jointly with the labor demand equation to get E=200 and W=$30.
  4. Plot E=200 and W=$30 on the demand curve.
  5. Efficiency loss is the area of a triangle between the demand curve and the horizontal line from E=200 to E=400. That area is $2000.

(11) [Efficient bargaining model: 8 pts]

  1. W=$35 E=60.
  2. W=$30 E=110.
  3. W=$25 E=100.
  4. W=$20 E=100. Contract curve passes through answers to (b), (c), and (d).

(12) [Union wage effects: 6 pts]

  1. 20 percent.
  2. 50 percent.
  3. A threat effect of unionism would cause the nonunion wage to rise. A spillover effect would cause the nonunion wage to fall. Here, the nonunion wage fell, indicating a spillover effect.

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

  1. 50 = N. (Found by setting MC = piece rate wage.)
  2. $25. (Found by multiplying piece rate wage × answer to part (a).)
  3. $12.50 . (Found by subtracting TC(50) from part (b).)
  4. $10.00 . (Found by subtracting TC(30) from time rate.)
  5. Prefers Firm 1 because net benefit is higher.

(14) [Mandatory retirement: 12 pts]

  1. 18 years.
  2. 36 years. There are several ways to find this answer. One way is to note that total pay is the area under the constant wage up to time t, which is a rectangle whose area is given by
       38,000 × t,
    while the area under the rising wage up to time t is a trapezoid whose area is given by
       (20,000 + 20,000 + 1000 t)/2 × t.
    Set these equal to each other and solve for t.
  3. Loss = $90,000. There are several ways to find this answer. One way is to use the formulas given in the previous part, but instead of setting them equal to each other, insert t=20 into both formulas and subtract.

(15) [Markov model: 10 pts]
  1. 0.98 .
  2. 0.62 .
  3. 2 percent.
  4. 38 percent.
  5. 5 percent. (Found by setting E × 0.02 = U × 0.38 and using algebra to solve for U/(E+U), which is the definition of the unemployment rate.)

(16) [Job search: 10 pts]

  1. Reservation wage = $15.
  2. No, the worker would not accept this job because the wage is less than the worker's reservation wage.
  3. If unemployment benefits were increased, the MC curve would shift down (or to the right) because the cost of further search would be lowered.
  4. The reservation wage would increase because with higher unemployment benefits, the worker can hold out for a better wage offer.
  5. Average time to find a new job would increase because of the higher reservation wage.

III. Critical thinking

(1) Adam Smith anticipated the modern theory of human capital. In equilibrium, workers with higher levels of education and training are paid more because they are more productive. However, additional human capital requires time and money. The time that workers spend obtaining additional human capital could have been spent working for pay. Workers would not pay that opportunity cost and money cost without a pay differential.

(2) This manager is considering a change from a time-rate payment scheme to a piece rate payment scheme. One advantage of piece-rate pay is that workers are incented to work faster, even if they are not constantly supervised, so these workers would probably write more lines of code per day. One disadvantage is that the quality of work may suffer as workers focus on speed, so the code they write might have more "bugs" (errors). Another disadvantage is that workers have less incentive to help each other, because to do so would take time away from their own output and lower their pay, so these workers might work less cooperatively.

Version B

I. Multiple choice

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

II. Problems

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

  2. 4.1 percent.
  3. 60.1 percent.
  4. 62.7 percent.

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

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

(3) [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.

(4) [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.

(5) [Payroll tax or subsidy: 14 pts]

  1. 50 million.
  2. $15.
  3. $11.
  4. $55 million.
  5. $165 million.
  6. $200 million.
  7. $20 million.

(6) [Monopsony: 18 pts]

  1. Set supply equation w=VMP and solve to get E=1200.
  2. MLC = -30 + 2 E/20.
  3. Set VMP=MLC and solve to get E=720.
  4. Substitute E=720 into labor supply equation to get w=$6.
  5. If the minimum wage is lower than the efficient (or competitive) wage, then employment is determined by the supply curve. If the minimum wage is higher than the efficient wage, then employment is determined by the VMP curve. Here the efficient wage can be found by inserting the efficient level of employment (found in part a) into either the supply curve or the VMP curve. Since the minimum wage ($10) is lower than the efficient wage ($30), employment is determined by the supply curve. Substitute $10 into the supply curve and solve to get E=800. Thus the $10 minimum wage raises employment slightly.

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

  1. NPV "no college" = 150 + 324/1.05 = $459 thousand.
  2. NPV "college" = -50 + 540/1.05 = $464 thousand.
  3. Chooses "college" because NPV is larger.
  4. Set 150 + 324/(1/r) = -50 + 540/(1+r) and solve to get r*=8 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."

(8) [Roy model: 6 pts]

  1. Workers move if the net gain from migration is positive--that is, if wY > wX + moving cost. Substituting and solving for S gives S > 80.
  2. Positively selected, since workers from the high end of the distribution of S in country X will move.

(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 2.4 - 1.9 = 0.50.
  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 (12-10) = 0.20.
  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 (1.2-1.1) + (0.10-0.08)10 = 0.30. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

(10) [Monopoly union model: 10 pts]

  1. Set WC = 50 - 0.1 E and solve to get E=400.
  2. Demand curve is a downward-sloping line with intercept at W=$50 and slope = -0.1. WC is a horizontal line at $10.
  3. Set MRS = 0.1 and solve this equation jointly with the labor demand equation to get E=250 and W=$25.
  4. Plot E=250 and W=$25 on the demand curve.
  5. Efficiency loss is the area of a triangle between the demand curve and the horizontal line from E=250 to E=400. That area is $1125.

(11) [Efficient bargaining model: 8 pts]

  1. W=$30 E=40.
  2. W=$25 E=80.
  3. W=$20 E=80.
  4. W=$30 E=90. Contract curve passes through answers to (b), (c), and (d).

(12) [Union wage effects: 6 pts]

  1. 50 percent.
  2. 20 percent.
  3. A threat effect of unionism would cause the nonunion wage to rise. A spillover effect would cause the nonunion wage to fall. Here, the nonunion wage rose, indicating a threat effect.

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

  1. 60 = N. (Found by setting MC = piece rate wage.)
  2. $18. (Found by multiplying piece rate wage × answer to part (a).)
  3. $9 . (Found by subtracting TC(60) from part (b).)
  4. $12.75 . (Found by subtracting TC(30) from time rate.)
  5. Prefers Firm 2 because net benefit is higher.

(14) [Mandatory retirement: 12 pts]

  1. 16 years.
  2. 32 years. There are several ways to find this answer. One way is to note that total pay is the area under the constant wage up to time t, which is a rectangle whose area is given by
       38,000 × t,
    while the area under the rising wage up to time t is a trapezoid whose area is given by
       (30,000 + 30,000 + 500 t)/2 × t.
    Set these equal to each other and solve for t.
  3. Loss = $60,000. There are several ways to find this answer. One way is to use the formulas given in the previous part, but instead of setting them equal to each other, insert t=20 into both formulas and subtract.

(15) [Markov model: 10 pts]
  1. 0.03 .
  2. 0.27 .
  3. 3 percent.
  4. 27 percent.
  5. 10 percent. (Found by setting E × 0.03 = U × 0.27 and using algebra to solve for U/(E+U), which is the definition of the unemployment rate.)

(16) [Job search: 10 pts]

  1. Reservation wage = $11.
  2. Yess, the worker would accept this job because the wage is greater than the worker's reservation wage.
  3. If unemployment benefits were decreased, the MC curve would shift up (or to the right) because the cost of further search would be raised.
  4. The reservation wage would decrease because with higher unemployment benefits, the worker would want a job sooner.
  5. Average time to find a new job would decrease because of the lower reservation wage.

III. Critical thinking

Same as Version A.

[end of answer key]