Now, consider an economy in which the demand for money is of the formY / (1 + it) for t = 0, 1, 2, · · · , where output is 150 and it denotes the nominal interest rate inperiod t. The real interest rate, denoted r, is constant and equal to 4%. In period0 and 1, the money supply is 100 and people expect that money supply wouldbe 100 forever. People have rational expectations. In period 2, the central banksurprises people and sets the money supply will grow at 2 percent forever, that is,M0 = 100, M1 = 100, M2 = (1.02)M1, M3 = (1.02)M2, and so on. A . Find the inflation rate, nominal interest rate, real money balance in period 1,and expected inflation in period 2, given the information available in period1, π1, i1, M1 / P1 and, E1π2. B . Find the inflation rate, nominal interest rate, real money balance in period 2, and expected inflation in period 3, given the information available in period 2, π2, i2, M2 / P2 and E2π3. C . Compare E1π2 and π2.
Now, consider an economy in which the demand for money is of the form
Y / (1 + it) for t = 0, 1, 2, · · · , where output is 150 and it denotes the nominal interest rate in
period t. The real interest rate, denoted r, is constant and equal to 4%. In period
0 and 1, the money supply is 100 and people expect that money supply would
be 100 forever. People have rational expectations. In period 2, the central bank
surprises people and sets the money supply will grow at 2 percent forever, that is,
M0 = 100, M1 = 100, M2 = (1.02)M1, M3 = (1.02)M2, and so on.
A . Find the inflation rate, nominal interest rate, real money balance in period 1,
and expected inflation in period 2, given the information available in period
1, π1, i1, M1 / P1 and, E1π2.
B . Find the inflation rate, nominal interest rate, real money balance in period 2, and expected inflation in period 3, given the information available in period 2, π2, i2, M2 / P2 and E2π3.
C . Compare E1π2 and π2.
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