Optimality of the CE. The problem is contained in the screen shot. Thank you for your help!

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 c1 + 1 - 0 - + B[log 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(Ki, NJ) = zK.(Na)1-a. 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