# An economy has the following money demand function: (M/P)^d = 0.2Y/(i^(1/2)). a. Derive an expression for the velocity o… … for the velocity of money. What does velocity depend on? Explain why this dependency may occur

An *economy has* the *following money demand function*: (M/P)^d = 0.2Y*Derive*an *expression* for the *velocity* o… … for the *velocity* of *money*. What *does velocity depend* on? *Explain*why this *dependency may occur.*

answer:

a. as we all know from cambridge cash balance approach that 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 = and k=M^{D}/PY

on solving we get k= and from both versions of quantity theory of money we know that k=1/v hence velocity of money = . 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= =1

c. at equilibrium money demandqs = money supply and given y=1000 money supply=1200 and nominal interest at 4% we get M^{D}= 0.2PY/i^{1/2}

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

d. fisher equation on ingerest 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. from the given information 1200=0.2*P*1000/(0.09)^{1/2 }hence price level = 1.8

g.base on the given information price level=1.2 hence M=0.2*1.2*1000/0.3

M=800. HENCE BY REDUCING THE MONEY SUPPLY FROM 1200 TO 800 THE PRICE LEVEL WOULD REMAIN AT 1.2