Problem 2. (20 points) Consider the standard model of production. Recall that the production function is Y = AK/3 12/3 and the marginal products of labor and capital are given, respectively, by MPL = A(K/L)1/3 and MPK = A(L/K) 2/3. The initial supply of labor and capital are fixed at L = 8 and K = 1, and the productivity parameter = 1. 1. (10 points) Consider the market for capital. Derive the capital demand function for L = 8 and = 1. Find the equilibriure values of the rental price of capital and output. MPK = A (011) 213 1/2 = (1/8) 113 APR r = re 3 (8) TIM 312 K = () 2/3 2/3 :) 3 ( 2. (10 points) Now focus on the labor market. Suppose that the supply of labor goes down by 10%. Illustrate the consequences of this change on the labor market diagram. By how much does the equilibrium wage change?