Assignment 2, Econ 751-
1. Consider the Hicks-Marshall analysis of the elasticity of labor demand for the case where the supply of capital to the industry is infinitely elastic, and the demand for the industry's product is also infinitely elastic. Does your result make economic sense?
2. [Robert Lucas] Consider land prices in a rectangular country. The northern edge of the country is a desirable seacoast, which is 100 indivisible lots wide. From north to south the country is 1000 lots deep. There are 10,050 families, each of which can occupy just one lot. Each family's utility function is U(c, x) = (c/x)a, where c is consumption of a single composite good, a is positive, and x is distance from the coast, in lots (x = 1, 2,..., 1000). Each family is endowed with y units of the consumption good, and owns one share in each lot.
a. Find the competitive allocation of families over lots, and the price of each lot.
b. Explain what this has to do with labor economics.
3. a. The prices of labor, capital and other factors of production in Los Angeles and Miami are different: some things are cheaper in Miami, while others are cheaper in Los Angeles. Suppose the price of every factor in Houston is exactly halfway between the Miami price of that factor and the Los Angeles price. A market research firm surveys 1000 firms, in various industries. The firms are asked to rank these three cities in terms of the profits they could make in each place. The result of the survey is that 450 firms rank Los Angeles first, 350 rank Houston first and 200 rank Miami first. Is this consistent with the standard theory of profit maximization? Prove any claims that you make.
b. Surprised by the results of its survey of firms, the market research firm conducts a survey of workers, who have different preferences, and different incomes. Suppose the price of every consumer good in Houston is exactly halfway between the Miami price of that good and the Los Angeles price (and this remains true for the wage rate). The workers are asked to rank these three cities in terms of the consumption and leisure bundles that they could afford in each place. The result of the survey is that 450 workers rank Miami first, 350 rank Houston first and 200 rank Los Angeles first. Is this consistent with the standard theory of household behavior? Prove any claims that you make.