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/(i^(1/2)). a. Derivean expression for the velocity o… … for the velocity of money. What does velocity depend on? Explainwhy 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 =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 we know that 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 demandqs = money supply and given y=1000 money supply=1200 and 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 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

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