Question

Suppose the money demand function is

Md/P = 1000 + 0.2Y - 1000 (r + πe).

(a) Calculate velocity if Y = 2000, r = .06, and πe = .04.

(b) If the money supply (Ms) is 2600, what is the price level?

(c) Now suppose the real interest rate rises to 0.11, but Y and Msare unchanged. What happens to velocity and the price level? So, if the nominal interest rate were to rise from 0.10 to 0.15 over the course of a year, with Y remaining at 2000, what would the inflation rate be?

Answer 1

a) V= PY/M = Y/(M/P)

From the money demand function,

M^d/P = 1000 + 0.2Y - 1000(r + e)

= 1000 + 0.2(2000) - 1000( 0.06 + 0.04)

= 1000 + 400 - 100

=1300.

So V= 2000/1300 =1.54.

b) P = M^s/(M^d/P)

=2600/1300 = 2

c) When real interest rate rises to 0.11,

M^d/P = 1000 + 0.2(2000) - 1000(0.11 + 0.04)

= 1000 + 400 - 150

= 1250

Now, V = 2000/1250 = 1.6,

P = M^s/(M^d/P) = 2600/1250 = 2.08

Nominal Interest rate = Real Interest rate + Inflation rate

Inflation Rate = Nominal Interest rate - Real Interest Rate

= 0.15 - 0.11 = 0.04

The inflation rate would be 4 %