Question

3. Heterogeneous Agents Con sider an economy occupied by many households with two types denoted by i, (i-A, B) who are facing the two-period consumption problem. Each household i-A, B is facing the following utility maximization problem max where yl and yå are household i's exogenous income in period t-1,2 cl and c are hou sehold is con sumption in period t-1,2. b, bi is household i's bond holdings of which bo is exogenously given, r is the real interest rate, and 0 < β < 1 is the household discount factor (a) Set up and solve the household's problem. What are the equilibrium conditions of the model? (b) Solve for the household's optimal consumption plan (c1,c2) and bond holdings for each household (b1, b2) NOW: Assume each household's endowments are given by the following Furthermore assume that there are precisely N individuals of type A and M individuals of type B (c) What are the market clearing conditions of the economy? (d) Now solve for each type's consumption in each period as a function of g, N and M (e) How does the interest rate change with respe ct to changes in g?

Answer 1