to Answers Questions for Review
1. In the VMPL curve, the firm is a price taker. In the MRP L curve, the firm is a price maker. 2. Because the monopoly would raise price and cut output, it would hire a smaller quantity of labor. 3. Other firms in the area could bid away workers. 4. Employers who discriminate will be driven out of the market by those who do not discriminate.
Answers to Chapter 14 Problems
1. Wages = $4/hr which equals VMP at L = 30 hours. The VMP column numbers are 16, 12, 8, 4, and 0. Wage ($/hr) 16 VMP
4 MP 0 Labor (person-hrs/day) 30
w=4
40
2. The new budget constraint shares M = $0 at h = 24 hours, but has twice the slope due to the wage being twice as high. The M' column numbers are 288, 216, 144, 72, and 0. Income ($/day) 288 216 144 M 72 M'
0
6
12 Leisure (hrs/day)
18
24
3. The monopsonist hires L = 20 units of labor, where VMP = MFC = $8, and pays the wage w = AFC = $4/hr. Wage ($/hr) 16 VMP MFC 8 AFC 4
0 Labor (person-hrs/day)
20
30
4. The value of the marginal product of labor is price times the marginal product of labor. VMP = P(MPL) = 5(22 L) = 110 5L. A perfectly competitive firm hires labor until the point where w = VMP, which in this case occurs at 10 = 110 5L or 100 = 5L or L = 20 units of labor. Wage ($/hr) 60
VMP
10 0 Labor (person-hrs/day) 5. ABC = budget constraint for current job; E1 = current job; CD = budget constraint for new job E2 = new job 20 22
Income ($/day) A 48 D
I1 I2
36
E E1 8 B
2
C 12 16 24 leisure
Since the new budget constraint also contains E1 (the current job), and since Smith's indifference curve was tangent at E1 with a slope of 2.5, it follows that he will accept the new job; at E 1, he values extra leisure at $2.50/hr and the new job lets him get it for only $1.50/hr.
6. Program 1 is more likely to reduce hours worked, assuming leisure is a normal good, because it provides more income while leaving the price of leisure unchanged. Program 2, by contrast, makes leisure more expensive than before.
Income ($/day) 115.2 106 96
Program 2 budget constraint
Program 1 budget constraint
initial budget constraint 10 leisure 11.5
7. a) Equilibrium occurs where MFC = demand:
24
4L = 12 - 2L, which solves for L* = 2 W = 2L* = 4
($/L) 12 MFC AFC
7 4 L 2 2.5 6
7. b) With a minimum wage of 7 in effect: 7 = 12 -2L, which solves for L** = 5/2; W = 7 7. c) 12 - 2L = AFC = 2L, Lc = 3, Wc = 6 With min wage: L = 5/2; W=7 8. The monopolist's demand curve for labor is his marginal revenue product curve, the product of marginal revenue and the marginal product of labor: MRP = (100-2Q)(4) = (100-8L)(4) = 400-32L. Acme's marginal factor cost curve is given by MFC = 40 + 4L. Equating MRP and MFC, we have 400-32L = 40 + 4L, which solves for L=10. The wage is given by W=40+2L=60. 9. a) MFC = 3 + 2L = Demand = W = 35 - 6L, which solves for L = 4 and W = 7 as shown from the supply curve for L = 4. 9. b) At W = 17, we get L = (35 - 17)/6 = 3.
$/L 35 D MFC 17 11 AFC
7 4 7
3 4
L 32/7 35/6
10. Since MR<P for a monopolist, we know that MR<$5, which means that MRP L = (MR)(MPL) is less than (5)(2) = $10/hr. And since w = 10, this means that he should hire less labor. 11. a) MRPL = (MR)(MPL). So MRPL = 5x8 = 40 and MFC = 10 + MFC 2L.
Since = MRP, L = 15 and W = 10 + L = 25. Output = 15(5) = 75. 11. b) MRPL = (102-3.92Q)(5) = 510 - 19.6Q. Since the production function is Q=5L (because of constant marginal cost), when we substitute we get, MRP L = 510 - 98L. MFC = MRPL implies 510 - 98L = 10 + 2L which solves for L = 5 and W = 10 + L = 15 and Q = 5L = 25 and P = 102 - 1.96Q = 53. 11. c) From part (b) MRPL = 510 - 98L. At L=5, MRPL = 20 At L=6, MRPL = -78. Since MRPL becomes negative, no matter what the wage is an extra worker will decrease profits. So Ajax will not increase its labor force. 12. Comparing VMP with marginal willingness to pay for additional vacation time, we see that the optimal vacation lengths for the two types of worker are V*young = 2 weeks; V*old = 4 weeks. Compared to the current arrangement (in which all workers get 5 weeks vacation), older workers would be willing to cut their vacation to 4 weeks for only 150/yr more in pay. Since the older worker's VMP is 175/wk the firm can meet this requirement with 25/yr left to spare. Younger workers would be willing to switch to 2 weeks vacation for an increase in pay of only 325/yr, and since the VMP of each younger worker is 150/wk, the 3 week/yr cut in vacation time will generate 450/yr additional revenue, or 125/yr more than necessary to meet the required pay hike. So the extra profit will be 25/yr for each older worker and 125/yr for each younger worker.
13. a) E(VMP) given that test = 9 and applicant is blue: (1/3) (9) + (2/3) (6) = 7. 13. b) E(VMP) test = 9 and applicant is green: (1/3) (9) + (2/3) (12) = 11. 13. c) No. Statistical discrimination pulls members within each group toward the respective group averages. It says nothing about why the group averages differ. 14. a) The wage schedule described in the diagram below pays the worker less than VMP in the early years, more than VMP in the later years. A shirking employee will be reluctant to work under such a schedule, because of the risk of getting caught and fired for shirking before having a chance to cash in on premium wages. The non-shirker, by contrast, does not have this reason to worry about being fired. Of course, if the probability of being caught were zero, the threat of losing future premium wages would lose all force.
$/hr Wage Value of marginal product
time
14. b) Workers run not only the risk of being fired for shirking but also the risk of being fired because the firm doesn't want to pay the promised wage premiums. Any firm with a reputation for not making good on such promises would have a very difficult time finding workers to agree to work under a future-oriented pay schedule. 15. a) The equilibrium condition for sector 1 is that its expected wage equal the wage in sector 2: (5/N1)100 = 10, so N1 = 50 and N2 = 80-50 = 30. 15. b) GNP= 5(100) + 30(10) = 800, which is the same as if sector 1 didn't exist! 15. c) If we tax in sector 1 at the rate 0.5, the new equilibrium condition is that the expected value of the after-tax wage in sector 1 be equal to the wage in sector 2: (5/N1) (0.5) 100 = 10, so N1' = 25 and N2' = 80-25 = 55. GNP= 5(100) + 55(10) = 1050. 16. MPL = Q / L = (1/2) ( K / L ) = 1/ L VMPL = P MPL = 10/ L 17. MRPL = MR x MPL = (20-2Q) (1/ L ) = (20-4 L )/ L