Problem 2 [From GL5) Suppose we have two types of households: A and E. The utility maximization problem for a consumer of typei is max InCr r10 1 Chou "' + '31 \"+1 IE J subject to G + Cu\" = . + m\" (2) u 1+n J 1+n Note that A and B households have the same discount factor and utility function. The only thing that may differ is their endowments. (a) Write dmvn the Euler equation for households A and B. {b} Solve for the time t and t + 1 consumption functions for A and B. (c) Suppose [TA ,1! YA 3+1] = [1,2] and (YB 3,13; 3+1) = [2,1]. Solve for the equilibrium interest rate. {Remember that the equilibrium interest rate is such that the sum of savings across households is equal to zero.)