2. Sophocles' labor market. The farming town of Sophocles, Southern Michigan, is about 200 miles away from any major metropolitan area. There are about 100 independent farms around Sophocles, all producing the same crop, that share the production function y = All/2. Here A = 10 is total factor productivity and l is labor input. The price of the crop is p = 1. Because of technical considerations, the minimum employment at each farm is l = 0.1. There are no other employers. Each of the 2,500 inhabitants has individual supply function S (w) = :10, for w 6 [1,10]. (a) Suppose that the Sophocles' labor market is perfectly competitive. Compute the equilibrium wage and equilibrium employment. (10 points) (b) Assume that 100 more people move into Sophocles. How does the equilibrium wage and employment change? (10 points) (0) The new governor of Southern Michigan was elected mostly because of her promise to institute a minimum wage of 2.50. What is the effect of such measure on wages and employment? What is the effect of the minimum wage on workers' and producers' surplus? (10 points)