Answer to Question #201004 in Macroeconomics for Aasia Tariq

Question

Consider an economy with a constant nominal money supply, a constant level of real output Y = 100, and a constant real interest rate r= 0.10. Suppose that the income elasticity of money demand is 0.5 and the interest elasticity of money demand is -Q.1. a. By what percentage does the equilibrium price level differ from its initial value if output increases to Y = 106 (and r remains at 0.10)? (Hint: Use Eq. 7.11.) b. By what percentage does the equilibrium price level differ from its initial value if the real interest increases to r= 0.11 (and Y remains at 100)? c. Suppose that the real interest rate increases to r= 0.11. What would real output have to be for the equilibrium price level to remain at its initial value? 

Answer 1

Solution:

a.). The rate of inflation can be computed from a general equation that associates the growth rate of money supply and the adjustment from the growth rate of real money demand arising from the growth in real output.

The equation is given by:

π^e = $\frac{\triangle M}{M} - ny\frac{\triangle Y}{Y}$

 

Where: π is inflation

          M is the money supply

          Y is the real income

         y is the income elasticity of money demand.

% Change in Md = Income elasticity of money demand $\times$ % change in real income + Interest elasticity of money demand $\times$ change in interest rate

% Change in real income = $\frac{106 - 100}{100} = 6\%$

% Change in Md = $(0.5\times 6\% ) - (0.1\times0) = 3\%$

π^e = $3\% - (0.5\times 6\%) = 0\%$

Percentage change in the equilibrium price level = 3% - 0% = 3%

 

 

b.). % Change in Md = $(0.5\times 0\% ) - (0.1\times10\%) = 1\%$

% Change in real interest rate = $\frac{0.11 - 0.10}{0.10} = 10\%$

π^e = $1\% - (0.5\times 10\%) = -4\%$

Percentage change in the equilibrium price level = 1% - (-4%) = 5%

 

c.). Real output = (5%*100) + 100 = 105