Suppose that the real money demand is L(Y, i) = 0.05Y i , where Y is real output

Question

Suppose that the real money demand is L(Y, i) = 0.05Y i , where Y is real output and i is the nominal interest rate. Also suppose that the real output is constant over time at 200 and the real interest rate is constant at 2%. Assume that the Fisher equation holds. a. Suppose that the central bank makes a credible announcement that inflation is going to be 3%. If the nominal money supply is 200, what is the current price level? b. Suppose that the central bank makes a credible announcement that the money supply will be growing at 5% per year for long time. What is the value of the expected inflation rate? If the nominal money supply is currently 200, what is the new price level? What happens with the actual inflation because of this announcement (compare the price level with that in (a))?

Explanation / Answer

According to the Fisher equation,

Nominal interest (i) = real interest rate (r) + inflation

a) .We have r = 2% and inflation = 3%

i = 2 + 3 = 5%

The Quantity Theory of Money assumes that the demand for real money balances depends only on real income Y.

According to the money market equilibrium,

Real Money demand = L(Y,i) = the supply of real money balances =M/P

We have, Real Money demand = L(Y,i) = 0.05Yi, M= 200

Then we can calculate, 0.05Yi=200/P

P = 200/((0.05)*(200)*(5) = 4

b). suppose that the central bank makes a credible announcement that the money supply will be growing at 5% per year for long time. What is the value of the expected inflation rate?

New money supply will be growing 5% per year (200 + 200*5% = 210) and real output is constant overtime then

Inflation = 5 -0 = 5

Expected Inflation will be 5% only

Nominal interest rate = 2 + 5 =7

If the nominal money supply is currently 200,

new price =P1 = 200 / (200/((0.05)*(200)*(7))

P1 = 2.85

Old P =4 and new P (P1) =2.85

Price decline.

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