Consider an economy consisting of a constant population of infinitely-lived individuals. The representative individual maximizes the expected value of Ct-x(C+2C+St+3) (1+p)t where p > 0 and x > 0 are preference parameters. Assume that the values of Care such that marginal utility is always positive, and that 's are mean zero i.i.d. taste shocks (white noise process). Production function is proportional to capital: Yt=pKt. There is no depreciation, thus K++1 = Kt + Yt - Ct, and the real interest rate is fixed over time and equal to p. t=0 1. Find the Euler equation relating C and Et (Ct+1) and explain its meaning. (25 points) 2. Guess that consumption takes the form Ct = a + BKt +0t. Given this guess, what is Kt+1 as a function of K and t? What range of values for ensures stationarity of capital stock? Assuming stationarity, what is the average capital stock? (20 points) 3. What values must the parameters a, 8 and 9 be for the first-order condition in part 1 to be satisfied for all values of K and t? Is the capital stock stationary? (30 points) 4. Suppose = 0 until a one-time realization of t = (1+p) in period t. From period t + 1 onwards, = 0 again. What are the effects of this one-time negative shock to & on the paths of Y, K and C for periods t, t + 1,t+2,...? Interpret your results. (25 points)