Suppose there are just two towns in California, Fresno and San Jose. Residents can easily move there residence to the other city, but not elsewhere in the U.S. Utility in town j is given by U = Aj + wj - rj, where w is the income that can be earned there, and r is equal to the price of housing.

Firms produce output using the production function F(N)=XNa. The total California

population is normalized to 1, so that N is a town's population share - everyone works. Recall that with just two towns, this means that NF = 1- NSJ. Let X=10, a=.5 in San Jose, while in Fresno those values are X=4 and a=0.

Housing supply is perfectly elastic in each city, and rents are given by rsj=6 and rF = 2. Amenity levels are ASJ = 2 and AF=0.

a. Use the production function to find what the wage rate will be in San Jose as a function of the number of residents. What about Fresno?