《劳动经济学》(作者Borjas)第九章习题答案

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 in each of the three periods. If the worker moves to Illinois, he will earn $22,000 in each of the three periods. What is the highest cost of migration that a worker is willing to incur and still make the move?
The worker must compare the present value of staying in Pennsylvania to the present value of moving to Illinois. A worker will move if the present value of earnings in Illinois minus the costs of moving there exceed the present value of earnings in Pennsylvania:
74.710,54$)1.1(000,201.1000,20000,202=++=PA PV and
82.181,60$)1.1(000,221.1000,22000,222=++
=IL PV
The worker will move, therefore, if
PV IL – C > PV PA ,
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. Nick’s present value of
lifetime earnings in his current employment is $300,000, and Jane’s present value is $200,000. They are contemplating moving to Texas, where each of them would earn a lifetime income of $260,000. The couple’s 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 additional $2,000 to him. Jane, on the other hand, prefers Minnesota’s frigid winters, so she figures she would be $2,000 worse off because of Texas’s 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 account. On the monetary side, the sum of Nick’s and Jane’s 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.
9-3. Mickey and Minnie live in Orlando. Mickey’s net present value of lifetime earnings in Orlando is $125,000. Minnie’s net present value of lifetime earnings in Orlando is $500,000. The cost of moving to Atlanta is $25,000 per person. In Atlanta, Mickey’s net present value of lifetime earnings would be $155,000, and Minnie’s 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 couple, 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, because 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, staying 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 worker’s skill is captured by his efficiency units of 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 (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 of 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 least 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, moves to the United States).
(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 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 population, 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 it 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
66080
9-5. Suppose the United States enacts legislation granting all workers, including newly arrived immigrants, a minimum income floor of 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.
(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 program?
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 who find it profitable to move: those who have very high skill levels (above s P ) as well as those workers who have very low skill levels (below s L ). 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 welfare 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 countries where unskilled workers have incentives to migrate even in the absence of wage floors.
α αL P Dollars αN y −α
9-6. The immigration surplus, though 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 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 w 0 B F w 1 in Figure 9-11. The area of this rectangle is given by:
Loss to Native Workers = (w 1 - w 0) × N .
We can calculate 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:
M
N N Q M N w w w w Q +×+×−=)( Workers Native to Loss 0001.
Thus, the native loss (as a fraction of GDP) equals the percentage change in the native wage caused by immigration times labor’s 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 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 States 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 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 Neolandia’s skill distribution. What type of Neolandian would now migrate to the United States?
No one would migrate from Neolandia. The policy does 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 composition of the immigrant flow only if changes target immigrants who wished to migrate to the United States in the first place.
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 million 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 wage 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, the 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 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:
w N = $20 – .5E N and w S = $20 – .5E S,
where E N and E S are millions 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 result 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 will 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 authority to resettle the immigrants wherever you want. How should you distribute immigrants across the regions to maximize the country’s immigration surplus? Besides maximizing the immigration surplus in the short-run, in what other ways does your distribution of immigrants help the economy?
Let I N and I S be the number of immigrants (in millions) placed in the North and in the South respectively, so that I N + I S = 2. After immigration, the new wages are:
w N = $17 – .5I N and w S = $11 – .5I S
and the immigrant surpluses are:
S N = 0.25(I N)2 and S S = .25(I S)2.
Using that I N + I S = 2, therefore, the total immigrant surplus is
S = 0.25(I N)2 + 0.25(2–I N)2 = 1 – I N + .5(I N)2.
One can use calculus to solve for the optimal value for I N, 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:
I N S I N S I N S I N S
0.00
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 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 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 potentially 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 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 Phil’s value to the firm is uncertain, he is offered a wage of $48,000. After 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 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 found to be a bad match, he should return to the old job. After all, the old job pays a higher wage than what Phil’s current employer is willing to pay and what another new firm would offer him. Finally, if he tries a new job and is found to be a good match, he should certainly accept their offer. In the end, Phil only has two potentially viable strategies.
Strategy one: Keep the old job in both periods. The earnings path associated with this choice is flat and deterministic – Phil earns $50,000 in each period. The present discounted value of the outcome of this strategy is PV1 = 50,000 + 50,000/1.1 = $95,455.
Strategy two: Try a new job. If it is a good match, keep it. If it is a bad match, return to the old job. If Phil adopts this strategy, he will earn $48,000 in period 1. In period 2, he will earn either $56,000 or $50,000, each with probability ½. The expected present discounted value of the outcome of that strategy is PV2 = 48,000 + ((½× 56,000) + (½ × 50,000))/1.1 = $96,182.
As the second strategy generates a higher present value, this is the strategy Phil adopts.
9-11. Under the recently enacted 2001 tax legislation in the United States, all income tax filers can now deduct from their total income half of their expenses incurred when moving more than 50 miles to accept a new job. Prior to the change, only tax filers who itemized their deductions were allowed to deduct their moving expenses. (Typically, homeowners itemize their deductions and renters do not itemize.) How would this change in the tax bill likely affect the mobility of homeowners and renters?
The policy change has no affect on homeowners, whereas the policy change reduces the cost of moving for renters. Therefore, the policy is predicted to increase the mobility of renters.。