Question

3. An economy has the following money demand function: (M/P 2Y a. Derive an expression for the velocity of money. What does velocity depend on? Explain why this dependency may occur. b. Calculate velocity if the nominal interest rate i is 4 e. If output Y is 1,000 units and the money supply M d. Suppose the announcement of a new head of the percent. is $1,200, what is the price level P? central bank, with a reputation of being soft on inflation, increases expected inflation by 5 percentage points. According to the Fisher effect, what is the new nominal interest rate? e. Calculate the new velocity of money. r. If, in the aftermath of the announcement, both the economy's output and the current money supply are unchanged, what happens to the price level? Explain why this occurs. g. If the new central banker wants to keep the price level the same after the announcement, at what level should she set the money supply?

Answer 1

a. cambridge cash balance approach, money demand = kPY and from fishers equation of exchange that MV=PT comparing both the equationgs k=1/v.

now given the money demand function nomindal money demand =$0.2py/i^{1/2}$ and k=MD/PY

on solving we get k=$0.2/i^{1/2}$ and from both versions of quantity theory of money k=1/v hence velocity of money = $5i^{1/2}$. hence velocity of money depends on the nominal interest rates level since nominal interest rate represents the opprtunity cost associated with holding money

b. if i=4% then v=$5.(0.04^{1/2})$ =1

c. at equilibrium money demand (qs) = money supply

given y=1000, money supply=1200 , nominal interest at 4% we get MD= 0.2PY/i1/2

1200 = 0.2*P*1000/0.2 HENCE PRICE LEVEL = 1.2

d. fisher equation on interest rates is r=i-inflation level hence from this nominal interest would be

i=r+inflation thus a 5% increase in inflation leads to a 5% rise in nominal interest rate hence the new nominal interest rate = 9%

e. new velocity of money =5*(0.09)1/2 = 1.5

f. 1200=0.2*P*1000/(0.09)1/2   hence price level = 1.8

g. price level=1.2

M=0.2*1.2*1000/0.3

M=800. By reducing the money supply from 1200 to 800 the price levelremains at 1.2.