Answer to Question #201005 in Macroeconomics for Aasia Tariq

Question

Suppose that the real money demand function is L(y e) == 0.01 Y ,r + '1T e ' r + '1T where Y is real output, r is the real interest rate, and '1Te is the expected rate of inflation. Real output is constant over time at Y = 150. The real interest rate is fixed in the goods market at r = 0.05 per year. a. Suppose that the nominal money supply is growing at the rate of 10°/o 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°/o 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.

Answer 1

a)

Expected rate of inflation$=\frac{ change\space in \space money \space supply}{ money\space supply }= 10\%$

$i = r + expected \space rate\space of\space inflation \\= 5\% + 10\% = 15\%$

Value of Real Money supply will be:

$=\frac{ M}{P}= L = \frac{0.01 Y}{i ​} = \frac{0.01 \times 150}{0.15 }= 10$

Current Price level$=\frac{ M}{L} =\frac{ 300}{10} = 30$

b. 

$Expected inflation= ​5$ ; $i = r + expected\space inflation​=​0.05 + 0.05 = 0.10 ;$

then

Real money supply :

$=\frac{ M}{P}= L =\frac{ 0.01 \times 150}{0.10} = 15$

Current Price level

$=\frac{ M}{L} = \frac{300}{15 }= 20$

A  slowdown in money growth decreases expected inflation, increases real money demand, and then lowers the price level