Question

1. Consider an economy with a constant nominal money supply, a constant level of real output ?=100Y=100, and a constant real interest rate ?=0.10r=0.10. Suppose that the income elasticity of money demand is 0.5 and the interest elasticity of money demand is -0.1.

a) By what percentage does the equilibrium price level differ from its initial value if output increases to ?=106Y=106(and ?r remains at 0.10)?

b) By what percentage does the equilibrium price level differ from its initial value if the real interest increases to ?=0.11r=0.11 (and ?Y remains at 100)?

c) Suppose that the real interest rate increases to ?=0.11r=0.11. What would real output have to be for the equilibrium price level to remain at its initial value?

Answer 1

A. Given
output increases to Y=106 (where r remains at 0.10)

So the increase is 6/100 =0.06 = 6% So the change in price level will be equal to -0.5 x 6% = -3

Hence, the price level will decrease by 3%

B. The real interest rate increases to r=0.11 (and Y remains at 100)

i.e, there is 1% increase, and the price level will increase by :

(0.1 x 0.1) = 0.01, by 1%

C. Now, the real interest rate increases to r=0.11

In order to remain equal, the difference between (0.5 x (Y – 100)/100) and (0.1)(0.1) needs to be zero.

{(0.5 x (Y – 100)/100) - (0.1)(0.1)} = 0

or, { (Y – 100)200) - .01} = 0

or, y = 102

Hence, when the interest rate increases by 1%, output would have to increase by 2%