An economy has the following Money demand function: (M/P)d= .4Y/i^.5 . Where i i

Question

An economy has the following Money demand function: (M/P)d= .4Y/i^.5 . Where i is the nominal interest rate.

a. Derive an expression for the velocity of money. What does it depend on? Explain why this dependency may occur.

b. Calculate velocity if the nominal interest rate is 4 percent

c. If Y is 1000 units and money supply is 1200, what is the price level P?

d. Suppose expectations of inflation increases by 5 percentage points. According to the Fisher effect, what is the new nominal interest rate?

e. Calculate the new velocity of money.

f. If after the effect of part d, both the economy’s output and current money supply are unchanged, what happens to the price level? Explain why this occurs

g. If the central bank wants to keep the price level the same after part d what should they set the money supply to be?

Explanation / Answer

The Money Demand Function= (M/P)d = .4Y/(i^.5)------------------------------A)

The relation between Velocity of Money, Price level (P) , Real Output (Y) and Money Supply (M) is

MV=PY --------------------------B)

Now V= (P/M)*(Y)
V = [(i^.5)/(.4Y)]-------------------- (from A)

Here that P/M is the inverse of the real money supply, which is equal to real money demand. So the Velocity of Money is

V=( i^5/.4Y)*Y (As explained above)

V= i^.5/(.4) ---------------------- ANswer

B) If i=4 then V= 5 (Put the i=4 in above equation and solve)

C)

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