Question

Suppose that an economy has a constant nominal money supply, a constant level of real output Y = 1200, and a constant real interest rate r = 0.04, and it’s expected rate of inflation is 1%, i.e, πe = .01. Suppose that the income elasticity of money demand is ηY = 0.4 and the interest elasticity of demand ηi = –0.1.

a. Suppose that Y decreases to 1140, r remains constant at 0.04 and there is no change in the expected rate of inflation. What is the percentage change in the equilibrium price level?

b. Suppose that r increases to 0.05 and Y remains at 1200. Assuming that expected inflation remains at πe = .01, what is the percentage change in the equilibrium price level?

Answer 1

a) income elasticity of money demand is ηY = 0.4

Income elasticity of money demand says, as Y changes by 1%, then price changes by .04 %

So, percentage change in Y is,

((1200-1140)/1200)×100=5%

Percentage change in equilibrium price level is,

5×.4=2

Thus, equilibrium price changes by 2%

Since the elasticity has positive sign so we conclude that there's a direct relation between Y and price. If Y decreases by 5% then price decreases by 2%.

b) interest elasticity of demand ηi = –0.1

Interest elasticity of demand says, as r changes by 1% then price changes by .1%

So, percentage change in r is,

(( .05-.04)/.04)/100=25%

Percentage change in equilibrium price level is,

25×.1=2.5

Equipment price changes by 2.5 percent

Since there's is negative sign with elasticity So we conclude that there's negative/indirect relation between r and price. Thus as r increases by 25%, equilibrium price decreases by 2.5%.