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Emercise 1 (The Cagan Model and Output Growth). Suppose that the demand for money is given by M3 Y, P, _ 1+2;1 where M3 is the nominal demand for money, B is the price level, Y; is real output, and it is the nominal interest rate, in period t. Suppose that people have rational expectations. Suppose further that Y: grows at 3 percent, that Y0 = 1, that the nominal money supply, denoted Mt, grows at 5 percent, that M0 = 100, and that the real interest rate, denoted 5'", is constant and equal to 4 percent. 1. Guess the equilibrium growth rate of the real money supply, M, /Pt, and explain why you think your guess makes sense. Let 7r, E 19:le 1 be the ination rate in period 1:. Given your guess, what is the ination rate in periods 1, 2, . . . . 2. Given your guess, use the Fisher equation to calculate the nominal interest rate, it, in periods t = 0, 1,2, Check whether your guess is correct, that is, check whether, given your guess, the real demand for money, 13:? grows at the same rate as the real money supply, Mt/PE. 3. Given your guess, what is the price level in period 0, Po