(3) [24 points] Consider a simple version of the Cagan model of inflation. Suppose that the demand for money depends linearly on expected inflation, mt - Pt = -Y(Pi+1 - Pt), where me is the log of the money supply at time t, p is the log of the price level at time t, Pi+1 denotes the expectation of pr+1 formed in time t, and y 2 0. (a) [6 points] Assuming perfect foresight, Pi+1 = P:+1, find the log of price level at time t, pt, as a function of the log of money supplies. (b) [6 points] Explain how the price level in part (a) depends on y, a parameter that governs the sensitivity of money demand to the rate of (expected) inflation. Now the future is not known certainty. Suppose that the money supply is expected to grow at some constant rate u so that for any k 2 0, milk = me + ku, where my , is the forecast of my k set in time t. Then the log of price level at time t can be shown to imply that Pt = my + 7/. (c) [6 points] Using this result, briefly explain the relationship between real money balances and money growth rate. (d) [6 points] If a central bank is about to reduce the rate of money growth but wants to hold the price level pr constant, what should it do with me