Q3 (20 points) Consider an overlapping generations model with constant population N = 100. Suppose that the money supply is constant M = 400. The agents have a utility function: In(c1,) + 0.9 In(c2,7+1) Each agent in the economy produces 10 apples when young, and nothing when old. Let U, denote the value of money in terms of apples in Period , and let m, denote the t. ** Part a. (4 marks) What are the period budget constraints in Period 1 and 2 respectively? ** Part b. (4 marks) What is the lifetime budget constraint? ** Part c. (4 marks) Find the optimal consumption path (C1,/, (2,1+1 ) of a generation given Up, Uf+1. ** Part d. (4 marks) Find the market clearing condition for money. (Assume stationarity so that the path (c1, C2) of all generations are the same. Note that i C1 = (2.) ** Part e. (4 marks) Find (c1, c2) in the stationary monetary equilibrium