## Quantitative Problems

 1. What are the likely consequences of the recent housing slump on U.S. mobility rates? (Distinguish between the cases of renters and homeowners.) 2. In the context of Model 20.1, suppose the facts are as follows: (a) t0 = 10, t1 = 20, (b) w0 = \$10K < wS = \$20K < w1 = \$40K, (c) 1/1(l + r) = 0.3. Despite these compelling numbers, suppose that the individual chooses not to move. What might account for this? 3. Consider a risk-averse would-be migrant, whose utility . In the context of Model 20.2, suppose that migration is irreversible; the mobility cost, C, is zero; . If there is a 50-50 chance that the state is either good or bad, and if the individual is interested in maximizing his expected utility, should he stay or should he go? (As in the text, this question ignores the effects of a costly assimilation period in the interests of simplicity.) Suppose that return migration is possible, but costs \$6K. Would this change his decision? 4. Betsy's got a new job offer! It will require that she and Dougal move from New York to Chicago but will increase her earnings by a handsome \$30K for the remaining 20 years of her career. The snag is that they both expect Dougal's earnings will suffer. In fact they expect they will decline by \$35K for the first years he is in Chicago, and they will merely catch up with his New York earnings during the years that remain in his career. The cost of moving (psychic and economic) is \$50K and 1/(1 + r) = 0.3. Will they move to Chicago or stay put in New York? 5. Consider an economy with two separate regions: A and B. There are 100 million workers in total who supply their labor inelastically. The demand for labor (in millions) in region A is , and in region B it is .(a) Assume that initially θ = 1 and that the regional labor market has settled down to its long-run equilibrium. What are the equilibrium wages and employment levels in the two regions?(b) Now suppose that a positive demand shock strikes region A and that θ increases from θ = 1 to θ = 1.5.Immediately after the shock, and before any migration takes place, what happens to the wages in the two regions?What is the new long-run equilibrium? How many workers migrate from region B to A?Suppose that, like the Chinese government (see page 711), the authorities attempt to restrict internal migration by issuing mobility permits. What is the outcome if the government provides only 10 million permits to region B's residents?