# Consider an economy in which the demand for money is of the formMt =(1/v) PtY        for t = 0, 1, 2, · · · , where output is 150, the money velocity is 1.5. The money supplyis 100 for t = 0, 1. In period 2, the central bank surprises people and announcethat 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. 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.       9. Why are the inflation rate in period 2 from question 1 and question 2 different?

Question

Consider an economy in which the demand for money is of the form
Mt =(1/v) PtY

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, M0 = 100, M1 = 100,
M2 = (1.02)M1, M3 = (1.02)M2, and so on.

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.

9. Why are the inflation rate in period 2 from question 1 and question 2 different?

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