(1) Money in Utility: Consider a 2-period economy composed of many consumers with the following identical optimization problem: max Inc+In c.M.S [Inc + In + 3ne} s.t. M y = +S+ P M = (1+r)S+ P The consumer solves the constrained maximization problem by choosing savings (S) and nominal money holdings (M) today and consumption tomorrow (c). The endowment (y), consumption today (e), the real interest rate (r), the time discount (3), and the price level (P) are given. (i) Combine the budget constraints into one equation by eliminating S from the problem. Do not introduce any new notation. (ii) Use your answer from (i) to sub in for c in the objective function. (iii) Find the optimal choice of money demand as a function of y, c, r, 3, and P. (iv) Let 3 =1, and y=3, and = 1. If the government sets the money supply equal to one, what condition determines the equilibrium nominal price level (PE)? Find PE as a function of r. (v) If the money supply is increased in both periods (say from one to two), does this effect c' (yes or no)? Justify your answer with the equations.