Version A

I. Multiple choice

(1)b. (2)d. (3)a. (4)a. (5)b. (6)e. (7)b. (8)b. (9)d. (10)b. (11)c. (12)a. (13)b. (14)c. (15)b. (16)b. (17)a. (18)b. (19)a. (20)c. (21)a. (22)b.

II. Problems

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

1. The reservation wage equals the MRS at the endowment bundle. MRS = MU_L/MU_C = (C-200)/(L-10). Inserting nonlabor income for C and total available time for L gives reservation wage = $4.
2. Budget constraint is spending = income, or C = 400 + (60-L) 10 = 1000 - 10 L.
3. 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.
4. h*= total available time - L* = 15 hours.

(2) [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 -4, so w = $40 on isocost line #2.
3. substitution effect: use less labor.
4. 10 units of labor.
5. scale effect: use less labor.
6. 20 units of labor.
7. total effect: use less labor.
8. 30 units of labor.

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

1. 80 million.
2. $16.
3. 12.
4. $85 million.
5. $255 million.
6. $320 million.
7. $20 million.

(4) [VSL, safety regulation: 12 pts]

1. VSL = Δ earnings / Δ risk = 82 / (1/100,000) = $8.2 million.
2. Cost per statistical life saved = cost / reduction in death rate = $500,000 / 0.2 = $2.5 million.
3. Yes, the system should be required becasuse VSL > cost per statistical life saved.

(5) [Immigration surplus: 8 pts]

1. $15.
2. $13.
3. Immigration surplus = area of triangle = $20 million.
4. Transfer from domestic workers to employers = $200 million.

(6) [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 3.4 - 2.2 = 1.2.
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 = 0.15 (16-13) = 0.45.
3. The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes times blue workers' average schooling, or (1.0-0.9) + (0.15-0.10)13 = 0.75. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

(7) [Monopsony wage discrimination: 12 pts] This is similar to problem (2) on Exam 2, but with two groups of workers.

1. MLC_G = 8 + (2 E_G / 20). MLC_B = 4 + (2 E_G / 10).
2. For each group, set VMP equal to MLC and solve for E. This gives E_G = 120 and E_B = 80.
3. Substitute into supply equations to get w_G = $14 and w_B = $12.
4. Substitute the minimum wage into the supply equation for each group to get E_G = 140 and E_B = 110.

(8) [Monopoly unionism: 10 pts]

1. E = 250.
2. Labor demand is a straight line with intercepts at W=$40 and E=400.
3. W = $20, E = 200.
4. "Wage-bill max." should be plotted on the labor demand curve at W=$20, E=200.
5. Efficiency loss = area of triangle = $125.

(9) [Efficient bargaining: 8 pts]

1. W = $25, E = 60.
2. W = $20, E = 120.
3. W = $15, E = 110.
4. W = $30, E = 130. Contract curve should be plotted so as to connect answers to (b), (c), and (d).

(10) [Union wage effects: 6 pts]

1. 25 percent.
2. 50 percent.
3. A threat of 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.

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

1. 120 = N. (Found by setting MC = piece rate wage.)
2. $30. (Found by multiplying piece rate wage × answer to part (a).)
3. $14.40 . (Found by subtracting TC(120) from part (b).)
4. $12.00 . (Found by subtracting TC(50) from time rate.)
5. Prefers Firm 1 because net benefit is higher.

(12) [Mandatory retirement: 12 pts]

1. 15 years.
2. 30 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
      30,000 × t,
   while the area under the rising wage up to time t is a trapezoid whose area is given by
      (15,000 + 15,000 + 1000 t)/2 × t.
   Set these equal to each other and solve for t.
3. Loss = $100,000. 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.

(13) [Markov model: 10 pts]

1. 0.97 .
2. 0.53 .
3. 3 percent.
4. 47 percent.
5. 6 percent. (Found by setting E × 0.03 = U × 0.47 and using algebra to solve for U/(E+U), which is the definition of the unemployment rate.)

(14) [Job search: 10 pts]

1. Reservation wage = $14.
2. Yes, the worker would accept this job because the wage exceeds 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 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) If a worker enjoys an increase in hourly wage, this will have two effects on her choice of hours of work.

1. The substitution effect of the wage increase makes leisure more expensive, and would influence her to choose less leisure and consequently more hours of work.
2. The income effect makes the worker feel richer, and would influence her to "purchase" more leisure, by working fewer hours of work.

(2) A "tournament" pay scheme has both advantages and disadvantages.

1. One advantage relative to straight hourly pay is that sales workers have an incentive to work harder. Unlike a simple piece rate, however, a "tournament" shelters workers from firm-wide shifts in output due to factors that are beyond their control such as changes in the firm's advertising or pricing, competition from rival firms, and recessions.
2. One disadvantage over straight hourly pay is that sales workers now face a disincentive to help each other. Since pay is determined by a worker's output relative to other workers, no one will want to help increase anyone else's output by, for example, sharing sales leads and contact information. Workers might even have an incentive to sabotage each other's work. Alternatively, workers might collude. Workers might all agree to reduce effort and share the bonuses. In either case, output and profit are reduced.

Version B

I. Multiple choice

(1)c. (2)c. (3)b. (4)b. (5)d. (6)b. (7)a. (8)c. (9)a. (10)a. (11)c. (12)d. (13)d. (14)a. (15)d. (16)b. (17)c. (18)c. (19)a. (20)d. (21)c. (22)c.

II. Problems

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

1. The reservation wage equals the MRS at the endowment bundle. MRS = MU_L/MU_C = (C-100)/(L-10). Inserting nonlabor income for C and total available time for L gives reservation wage = $4.
2. Budget constraint is spending = income, or C = 300 + (60-L) 20 = 1500 - 20 L.
3. Tangency condition is MRS = wage, or (C-100)/(L-10) = $20. Solve this equation jointly with the budget constraint found in part (b), to get L*= 40 hours, C*= $700.
4. h*= total available time - L* = 20 hours.

(2) [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 -1, so w = $10 on isocost line #2.
3. substitution effect: use more labor.
4. 20 units of labor.
5. scale effect: use more labor.
6. 10 units of labor.
7. total effect: use more labor.
8. 30 units of labor.

1. 100 million.
2. $14.
3. 18.
4. $95 million.
5. $285 million.
6. $400 million.
7. $20 million.

1. VSL = Δ earnings / Δ risk = 48 / (1/100,000) = $4.8 million.
2. Cost per statistical life saved = cost / reduction in death rate = $800,000 / 0.1 = $8.0 million.
3. No, the system should not be required becasuse VSL < cost per statistical life saved.

1. $13.
2. $9.
3. Immigration surplus = area of triangle = $80 million.
4. Transfer from domestic workers to employers = $480 million.

1. Raw log wage differential is found by substituting each group's average schooling into its own wage equation, to give 2.8 - 2.3 = 0.5.
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 = 0.12 (15-14) = 0.12.
3. The log wage differential due to discrimination is given by the difference in intercepts, plus the difference in slopes times blue workers' average schooling, or (1.0-0.9) + (0.12-0.10)14 = 0.38. Alternatively, the differential due to discrimination may be computed as the raw log wage differential minus the differential due to schooling.

1. MLC_G = 6 + (2 E_G / 10). MLC_B = 2 + (2 E_G / 5).
2. For each group, set VMP equal to MLC and solve for E. This gives E_G = 70 and E_B = 45.
3. Substitute into supply equations to get w_G = $13 and w_B = $11.
4. Substitute the minimum wage into the supply equation for each group to get E_G = 90 and E_B = 65.

(8) [Monopoly unionism: 10 pts]

1. E = 450.
2. Labor demand is a straight line with intercepts at W=$60 and E=600.
3. W = $30, E = 300.
4. "Wage-bill max." should be plotted on the labor demand curve at W=$30, E=300.
5. Efficiency loss = area of triangle = $1125.

(9) [Efficient bargaining: 8 pts]

1. W = $35, E = 50.
2. W = $30, E = 100.
3. W = $25, E = 90.
4. W = $35, E = 110. Contract curve should be plotted so as to connect answers to (b), (c), and (d).

(10) [Union wage effects: 6 pts]

1. 50 percent.
2. 25 percent.
3. A threat of 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.

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

1. 50 = N. (Found by setting MC = piece rate wage.)
2. $15. (Found by multiplying piece rate wage × answer to part (a).)
3. $2.50 . (Found by subtracting TC(5) from part (b).)
4. $5.10 . (Found by subtracting TC(30) from time rate.)
5. Prefers Firm 2 because net benefit is higher.

(12) [Mandatory retirement: 12 pts]

1. 22 years.
2. 44 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
      25,000 × t,
   while the area under the rising wage up to time t is a trapezoid whose area is given by
      (14,000 + 14,000 + 500 t)/2 × t.
   Set these equal to each other and solve for t.
3. Loss = $120,000. 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.

(13) [Markov model: 10 pts]

1. 0.98 .
2. 0.52 .
3. 2 percent.
4. 48 percent.
5. 4 percent. (Found by setting E × 0.02 = U × 0.48 and using algebra to solve for U/(E+U), which is the definition of the unemployment rate.)

(14) [Job search: 10 pts]

1. Reservation wage = $16.
2. No, the worker would wait for an offer greater than or equal to the worker's reservation wage.
3. If unemployment benefits were decreased, the MC curve would shift up (or to the left) because the cost of search would be increased.
4. The reservation wage would decrease because with lower unemployment benefits, the worker would want to find a job quicker.
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]