Suppose that the real money demand function is
Where Y is the real output, r is the real interest rate, and is the expected inflation rate. Real output is constant over time at Y = 150. The real interest rate is fixed in the goods market at r = 5% per year.
a) Suppose that the nominal money supply is growing at the rate of 10% per year and that this growth rate is expected to persist forever. Currently, the nominal money supply is M=300. What are the values of the real money supply and the current price level?
b) Suppose that the nominal money supply is M = 300. The central bank announces that from now on the nominal money supply will grow at the rate of 5% per year. If everyone believes this announcement, and if all markets are in equilibrium, what are the values of the real money supply and the current price level? Explain the effects on the real money supply and the current price level of a slowdown in the rate of money growth.
c) Suppose that the money supply is M=300. The central bank announces that from now on the nominal money supply will grow at the rate of 5% per year. If everyone believes this announcement, and if all markets are in equilibrium, what are the values of the real money supply and the current price level? Compare your result to part (A) explain the effects on the real money supply and the current price level of a slowdown in the rate of money growth.