4. [A Monetary Surprise] Consider an economy in which the demand for money is of the form MI = P.Y for t = 0, 1, 2, . .., where output is 150, the money velocity is 1.5. The money supply is 100 for t = 0, 1. In period 2, the central bank surprises people and announce that money supply will grow at 2 percent forever, that is, Mo = 100, M1 = 100, M2 = (1.02) M1, M3 = (1.02) M2, and so on. (a) What is the inflation rate in period 1, m1? What is real money balance in period 1, 41? What is the expected inflation in period 2, given the information available in period 1, E12? (b) What is the inflation rate in period 2, 72? What is real money balance in period 2, 2?What is expected inflation in period 3, given the informa- tion available in period 2, E273? (c) What is the inflation rate in period 3, 73? What is real money balance in period 2, P3 (d) Compare E172 and 72