## Quantitative Problems

 1. Let denote the total size of the labor force, where and I represent native-born workers and immigrants, respectively (measured in thousands). Assume that immigrants supply that labor inelastically, and the supply of native-born workers is governed by . The marginal revenue product of labor is .(a) Suppose that initially there is no immigration at all: I = 0. What is the equilibrium wage and level of employment?(b) Now suppose that there is some immigration and I = 6. What happens to the equilibrium wage, total employment, and the employment of native-born workers? 2. Suppose that the marginal revenue product of U.S. labor is given by and a total of Ln native U.S. workers supply their labor inelastically, where L is measured in (say) thousands.(a) In the absence of immigration, what is the equilibrium wage and level of employment of native workers?(b) Suppose that the government allows 24 immigrants, who are perfect substitutes for native workers, to enter the United States. What is the effect of their influx on the equilibrium?(c) What is the total loss in earnings suffered by native U.S. workers? What is the immigration surplus? 3. Suppose that the demand for illegal (i.e., undocumented) immigrants by U.S. employers, denoted L, is governed by the marginal revenue product condition, MRP = 100 − L, and their labor supply is given by S = 3 ÅE w (where L is measured in thousands).(a) In the absence of any enforcement efforts (border or otherwise), how many immigrants enter the United States? What is the equilibrium wage?(b) Now suppose that the government devotes resources to patrolling the border. Suppose that these efforts lead to the capture and repatriation of two-thirds of the S immigrants who seek to cross into the United States illegally. (In the interests of simplicity assume that the supply of labor is still S = 3 ÅE w.) What happens to the equilibrium wage and the level of employment? 4. Suppose that instead of using border enforcement, the government monitors employers and fines them if they are caught employing illegal immigrants. Assume that the fine is F = \$480 per worker and that the probability of detection is q = 5%. What happens to the equilibrium now?Hint: The expected marginal cost of labor is now . 5. Recently, several states have toyed with the idea of a no-questions-asked policy that would allow undocumented workers to obtain drivers' licenses. What are the likely consequences of such a policy? 6. This question deals with the outsourcing of radiological services by U.S. hospitals from Indian providers. Suppose that the supply of labor is inelastic: the U.S. supply of radiologists is 30, and the Indian supply is 70. (A unit might be, say, 100 labor hours.) The U.S. demand for radiologists is , and the Indian demand is .(a) Suppose that because of technological limitations it is initially too costly to outsource radiological services. What is the labor-market equilibrium in this case?(b) Now suppose that the invention of the Internet permits the costless transfer of huge amounts of data, allowing the outsourcing of radiological services to occur. What is the equilibrium now?(c) Who gains and who loses from the emergence of outsourcing capabilities?