《劳动经济学》(作者Borjas)第九章习题答案

1、 60 CHAPTER 9 9-1. Suppose a worker with an annual discount rate of 10 percent currently resides in Pennsylvania and is deciding whether to remain there or to move to Illinois. There are three work periods left in the life cycle. If the worker remains in Pennsylvania, he will earn $20,000 per year i

2、n each of the three periods. If the worker moves to Illinois, he will earn $22,000 in each of the three periods. What is the highest cost of migration that a worker is willing to incur and still make the move? The worker must compare the present value of staying in Pennsylvania to the present value

3、of moving to Illinois. A worker will move if the present value of earnings in Illinois minus the costs of moving there exceed the present value of earnings in Pennsylvania: 74.710,54$ ) 1 . 1 ( 000,20 1 . 1 000,20 000,20 2 =+= PA PV and 82.181,60$ ) 1 . 1 ( 000,22 1 . 1 000,22 000,22 2 =+= IL PV The

4、 worker will move, therefore, if PVIL C PVPA, where C denotes migration costs. Thus, the worker moves if C 60,181.82 - 54,710.74 = $5,471.08 9-2. Nick and Jane are married. They currently reside in Minnesota. Nicks present value of lifetime earnings in his current employment is $300,000, and Janes p

5、resent value is $200,000. They are contemplating moving to Texas, where each of them would earn a lifetime income of $260,000. The couples cost of moving is $10,000. In addition, Nick very much prefers the climate in Texas to that in Minnesota, and he figures that the change in climate is worth an a

6、dditional $2,000 to him. Jane, on the other hand, prefers Minnesotas frigid winters, so she figures she would be $2,000 worse off because of Texass blistering summers. Should they move to Texas? Yes. The “climatic” aspects of the move exactly balance each other, so we should not take them into accou

7、nt. On the monetary side, the sum of Nicks and Janes lifetime present value of earnings in Minnesota is $500,000. The corresponding amount in Texas will be $520,000. The difference between the two ($20,000) exceeds the cost of moving ($10,000), so the move will make the couple jointly better off. 61

8、 9-3. Mickey and Minnie live in Orlando. Mickeys net present value of lifetime earnings in Orlando is $125,000. Minnies net present value of lifetime earnings in Orlando is $500,000. The cost of moving to Atlanta is $25,000 per person. In Atlanta, Mickeys net present value of lifetime earnings would

9、 be $155,000, and Minnies net present value of lifetime earnings would be $510,000. If Mickey and Minnie choose where to live based on their joint well-being, will they move to Atlanta? Is Mickey a tied-mover or a tied-stayer or neither? Is Minnie a tied-mover or a tied-stayer or neither? As a coupl

10、e, the net present value of lifetime earnings of staying in Orlando is $500,000 + $125,000 = $625,000 and of moving to Atlanta is $510,000 + $155,000 $50,000 = $615,000. Thus, as a couple, they would choose to stay in Orlando. Thus, there can only be a tied-stayer. (There cannot be a tied- mover, be

11、cause the couple is not moving.) For Mickey, staying in Orlando is associated with a net present value of $125,000, while moving to Atlanta would yield a net present value of $155,000 $25,000 = $130,000. So Mickey would choose to move to Atlanta. Therefore, Mickey is a tied-stayer. For Minnie, stayi

12、ng in Orlando is associated with a net present value of $500,000, while moving to Atlanta would yield a net present value of $510,000 $25,000 = $485,000. So Minnie would choose to remain in Orlando. Thus, Minnie is not a tied-stayer. 9-4. Suppose a workers skill is captured by his efficiency units o

13、f labor. The distribution of efficiency units in the population is such that worker 1 has 1 efficiency unit, worker 2 has 2 efficiency units, and so on. There are 100 workers in the population. In deciding whether to migrate to the United States, these workers compare their weekly earnings at home (

14、w0) with their potential earnings in the United States (w1). The wage-skills relationship in each of the two countries is given by: w0 = 700 + 0.5s, and w1 = 670 + s, where s is the number of efficiency units the worker possesses. (a) Assume there are no migration costs. What is the average number o

15、f efficiency units among immigrants? Is the immigrant flow positively or negatively selected? The earnings-skills relationship in each country is illustrated in the figure below. The US line is steeper because the payoff to a unit of skills is higher in the United States. All workers who have at lea

16、st 60 efficiency units will migrate to the United States. Therefore, there is positive selection and the average number of efficiency units in the immigrant flow is approximately 80 (the exact answer depends on whether the person with 60 efficiency units, who is indifferent between moving or not, mo

17、ves to the United States). 62 (b) Suppose it costs $10 to migrate to the United States. What is the average number of efficiency units among immigrants? Is the immigrant flow positively or negatively selected? If everyone incurs a cost of $10 to migrate to the United States, the U.S. wage-skill line

18、 drops by $10, and only those persons with more than 80 efficiency units will find it worthwhile to migrate. The immigrant flow is still positively selected and has, on average, 90 efficiency units. (c) What would happen to the selection that takes place if migration costs are not constant in the po

19、pulation, but are much higher for more skilled workers? If migration costs are much higher for skilled workers, it is possible that no skilled workers will find it worthwhile to migrate. We already know that even in the absence of migration costs no worker with fewer than 60 efficiency units finds i

20、t worthwhile to migrate. If highly skilled workers find it very costly to migrate it might be the case that there is no migration to the United States. Income 700 670 60Efficiency Units Source Country US Income Efficiency Units 700 660 80 Source Country US 63 9-5. Suppose the United States enacts le

21、gislation granting all workers, including newly arrived immigrants, a minimum income floor of y y dollars. (a) Generalize the Roy model to show how this type of welfare program influences incentive to migrate to the United States. Ignore any issues regarding how the welfare program is to be funded.

22、(b) Does this welfare program change the selection of the immigrant flow? In particular, are immigrants more likely to be negatively selected than in the absence of a welfare program? (c) Which types of workers, the highly skilled or the less skilled, are most likely to be attracted by the welfare p

23、rogram? U.S. Labor Market U.S. Labor Market The introduction of a wage floor in the United States (at y ) shifts the U.S. earnings-skill relationship to the bold line drawn in the figures. If the returns to skills are higher in the United States (left panel above), there are then two sets of workers

24、 who find it profitable to move: those who have very high skill levels (above sP) as well as those workers who have very low skill levels (below sL). In contrast, if the returns to skills are lower in the United States than in the country of origin (the right panel above), the introduction of the we

25、lfare program does not change the incentives to migrate for any worker (although the incentives of some workers would change if the wage floor was high enough). The welfare program, therefore, acts as a welfare magnet for workers originating in countries that generate “brain drains”, but not in coun

26、tries where unskilled workers have incentives to migrate even in the absence of wage floors. Source Country U.S. Dollars Skills Skills Positive Selection Do Not Move Do Not Move Move Move Move 0 U sL sP Source Country U.S Dollars Negative Selection 0 sN y y U 64 9-6. The immigration surplus, though

27、seemingly small in the United States, redistributes wealth from workers to firms. Present a back-of-the-envelope calculation of the losses accruing to native workers and of the gains accruing to firms. Do these calculations help explain why some segments of society are emotional in their support of

28、changes in immigration policy that would either increase or decrease the immigrant flow? The total loss in earnings experienced by workers in the United States is given by the rectangle w0 B F w1 in Figure 9-11. The area of this rectangle is given by: Loss to Native Workers = (w1 - w0) N. We can cal

29、culate the loss to native workers as a fraction of GDP by dividing both sides by Q (national income). If we do this and rearrange terms we obtain: MN N Q MNw w ww Q+ + = )( WorkersNative toLoss 0 0 01 . Thus, the native loss (as a fraction of GDP) equals the percentage change in the native wage caus

30、ed by immigration times labors share of national income times the fraction of the labor force that is native born. If we continue the numerical example in the text, this calculation yields: (-.03) (.7) (.9) = -1.89 percent of GDP. As national income is on the order of $11 trillion, the loss suffered

31、 by native workers is on the order of $208 billion. Capitalists receive this income plus the immigration surplus of $11 billion (see the text), for a total gain of about $219 billion (about 2 percent of GDP). Even though the net benefits from immigration are small, particular groups in the United St

32、ates either gain or lose substantially from immigration. This explains why the debate over immigration policy is often polarized. 9-7. In the absence of any legal barriers on immigration from Neolandia to the United States, the economic conditions in the two countries generate an immigrant flow that

33、 is negatively selected. In response, the United States enacts an immigration policy that restricts entry to Neolandians who are in the top 10 percent of Neolandias skill distribution. What type of Neolandian would now migrate to the United States? No one would migrate from Neolandia. The policy doe

34、s not change the cost-benefit analysis for the most skilled Neolandians. They did not want to migrate when they could enter the country freely, and they still will not want to migrate when they are the only ones who can obtain visas. The lesson is that changes in immigration policy affect the skill

35、composition of the immigrant flow only if changes target immigrants who wished to migrate to the United States in the first place. 65 9-8. Labor demand for low-skilled workers in the United States is w = 24 0.1E where E is the number of workers (in millions) and w is the hourly wage. There are 120 m

36、illion domestic U.S. low- skilled workers who supply labor inelastically. If the U.S. opened its borders to immigration, 20 million low-skill immigrants would enter the U.S. and supply labor inelastically. What is the market-clearing wage if immigration is not allowed? What is the market-clearing wa

37、ge with open borders? How much is the immigration surplus when the U.S. opens its borders? How much surplus is transferred from domestic workers to domestic firms? Without immigration, the market-clearing wage is $12, at which all 120 million low-skill U.S. workers are employed. With immigration, th

38、e market-clearing wage is $10, at which all 120 million low-skill U.S. workers and all 20 million immigrants are employed. The additional surplus received by the U.S. because of the immigration equals ($12 $10) (140m 120m) / 2 = $20 million. The total transfer from U.S. workers to U.S. firms because

39、 of the immigration equals ($12 $10) (120m) = $240 million. 9-9. A country has two regions, the North and the South, which are identical in all respects except the hourly wage and the number of workers. The demand for labor in each region is: wN = $20 .5EN and wS = $20 .5ES, where EN and ES are mill

40、ions of workers. Currently there are 6 million workers in the North and 18 million workers in the South. (a) What is the wage in each region? The wage in the North is $20 .5 (6) = $17. The wage in the South is $20 .5 (18) = $11. (b) If there were no shocks to the economy, migration over time will re

41、sult in an equalization of wages and employment. What would be the long-run wage and employment level in each region? As labor demand is the same in both regions and workers are identical in their preferences, half of the workers will locate in each region in the long-run. Thus, 12 million workers w

42、ill work in each region, and the hourly wage will be $14. (c) Return to the original set-up where there are 6 million workers in the North and 18 million workers in the South. As a policy maker, you decide not only to allow 2 million immigrants of working age to enter your country, but you have the

43、authority to resettle the immigrants wherever you want. How should you distribute immigrants across the regions to maximize the countrys immigration surplus? Besides maximizing the immigration surplus in the short-run, in what other ways does your distribution of immigrants help the economy? Let IN

44、and IS be the number of immigrants (in millions) placed in the North and in the South respectively, so that IN + IS = 2. After immigration, the new wages are: wN = $17 .5IN and wS = $11 .5IS and the immigrant surpluses are: SN = 0.25(IN)2 and SS = .25(IS)2. 66 Using that IN + IS = 2, therefore, the

45、total immigrant surplus is S = 0.25(IN)2 + 0.25(2IN)2 = 1 I N + .5(I N)2. One can use calculus to solve for the optimal value for IN, but be aware that S is U-shaped, so setting the first order conditions to 0 solves for a minimum. Rather, use Excel to plot S. The data are: IN S IN S IN S IN S 0.00

46、1.00 0.05 0.95 0.55 0.60 1.05 0.50 1.55 0.65 0.10 0.91 0.60 0.58 1.10 0.51 1.60 0.68 0.15 0.86 0.65 0.56 1.15 0.51 1.65 0.71 0.20 0.82 0.70 0.55 1.20 0.52 1.70 0.75 0.25 0.78 0.75 0.53 1.25 0.53 1.75 0.78 0.30 0.75 0.80 0.52 1.30 0.55 1.80 0.82 0.35 0.71 0.85 0.51 1.35 0.56 1.85 0.86 0.40 0.68 0.90

47、0.51 1.40 0.58 1.90 0.91 0.45 0.65 0.95 0.50 1.45 0.60 1.95 0.95 0.50 0.63 1.00 0.50 1.50 0.63 2.00 1.00 Thus, the immigrant surplus is maximized by placing all 2 million immigrants in either of the regions. It would be best, however, to place them all in the high wage region, as this will lead to a

48、 faster equalization of wages and saves natives the trouble and costs of moving. 9-10. Phil has two periods of work remaining prior to retirement. He is currently employed in a firm that pays him the value of his marginal product, $50,000 per period. There are many other firms that Phil could potent

49、ially work for. There is a 50 percent chance of Phil being a good match for any particular firm, and a 50 percent chance of him being a bad match. If he is in a good match, the value of his marginal product is $56,000 per period. If he is in a bad match, the value of his marginal product is $40,000

50、per period. If Phil quits his job, he can immediately find employment with any of the alternative firms. It takes one period to discover whether Phil is a good or a bad match with a particular firm. In that first period, while Phils value to the firm is uncertain, he is offered a wage of $48,000. Af

51、ter the value of the match is determined, Phil is offered a wage equal to the value of his marginal product in that firm. When offered that wage, Phil is free to (a) accept; (b) reject and try some other firm; or (c) return to his original firm and his original wage. Phil maximizes the present value

52、 of his expected lifetime earnings, and his discount rate is 10 percent. What should Phil do? Phil makes decisions at the beginning of each period, and there are a variety of choices at each of these times. To reduce the number of strategies that require the numerical calculation of the expected outcome, first discard unreasonable choices. In particular, if Phil does not quit his job in period 1, he should not do so in period 2. After all, his second-period wage in a new job will be lower than in the old job, and there is no third period. Similarly, if he tries a new job in period 1 and is fo