1 Chapter 11 - Optimality of the CE (40) Consider the two-period intertemporal model with investment from Chapter 11. The representative consumer has utility function: 1 1-0 U(C1, 12, C2, 12) = log q + 1 -o - + Blog c2 + 1 - where B E (0, 1) is a discount factor. In each period the consumer is endowed with 1 unit of time they can split between labor and leisure and must pay lump-sum tax T. The government expenditure is given by G1, G2 in period 1 and 2 respectively. The firm is endowed with K1 in the first period and makes investments in second period capital. Their production function is given by F(K;, NJ) = =Ke(Na)]-. Capital depreciates at rate d. a) Derive the consumer's lifetime budget constraint. b) Define a CE in this environment. c) Summarize the CE with a series of equations. d) What is the SPP? e) Is this CE allocation Pareto Optimal? Prove why or why not