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(c,1) + 0.9 ln(C2,1+1) Each agent in the economy produces 10 apples when young, and nothing when old. Let Ut denote the value of money in terms of apples in Period t, and let my denote the money demand at time 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 (C,1, C2,1+1) of a generation given Ut, U+1. ** Part d. (4 marks) Find the market clearing condition for money. (Assume stationarity so that the path (C, C) of all generations are the same. Note that it does not mean that C = C2.) ** Part e. (4 marks) Find (C1, C) in the stationary monetary equilibrium. 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(c,1) + 0.9 ln(C2,1+1) Each agent in the economy produces 10 apples when young, and nothing when old. Let Ut denote the value of money in terms of apples in Period t, and let my denote the money demand at time 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 (C,1, C2,1+1) of a generation given Ut, U+1. ** Part d. (4 marks) Find the market clearing condition for money. (Assume stationarity so that the path (C, C) of all generations are the same. Note that it does not mean that C = C2.) ** Part e. (4 marks) Find (C1, C) in the stationary monetary equilibrium