Quantity Theory of Money- Fisher and Cambridge Equations of Quantity Theory + Neutrality of Money+ Real and Nominal Interest rate + Fisher Effect

1. Quantity theory of money, inflation, real money balance and
interest rates: Fischer effect

2. Quantity theory of money
• Main concern is the effect of money on economy
• Effect on price and income
• Neutrality of money
• Fisher Equation- MV=PT
M= Volume of Money,
 V=Velocity of money (how many times the money is transferred
from one hand to another in a time period)
T= Number of transactions
P=Price of each transaction

3. Velocity of money
• MV= PT
• Or𝑉 =
𝑃𝑇
𝑀
• Lets consider the total volume of money is $ 200
• Transaction volume – 1000 Kg
• Price- $ .6/kg
• Hence 𝑀 =
1000 𝑋 .6
200
=
600
200
= 3
• In every year $1 changes three hands through transactions .

4. Quantity theory of money: Cambridge version
• In Fisher’s equation it’s difficult to measure the number of transactions
• T is replaced by Y= O/t produced in a time period (more output=> more transactions
• New equation 𝑀𝑉 = 𝑃𝑌 , 𝑉 =
𝑃𝑌
𝑀
=> income velocity of money ( how many times income is transferred in a time
period)
• We can also write
𝑀
𝑃
=
𝑌
𝑉
• LHS is known as real money balance (purchasing power of the stock of money)
• RHS can be written as 𝑘𝑌 when 𝑘 =
1
𝑉
(how much money people wish to hold for every unit of income)
• Money demand function or demand for real balance is inversely related to the velocity of money, higher the velocity of
money, higher would be the speed of transactions and lower would be the need to hold cash in hand.

5. Money demand-Money supply and equilibrium
• (
𝑀
𝑃
) 𝐷= 𝑘𝑌– demand for real money balance (directly related to
output cause higher output means higher demand for real balance)
• If real money supply is
𝑀
𝑃
; the money market equilibrium condition is
given as
𝑀
𝑃
= 𝑘𝑌 or
• 𝑀 = 𝑘𝑃𝑌 ; 𝑘 =
1
𝑉
this 𝑀 = 𝑘𝑃𝑌 is known as the Cambridge Version
of Quantity Theory of Money. (𝑘= constant)

6. Money and inflation
• 𝑌= determined by the factors of production and technology
• Velocity of money is constant, hence 𝑘 = 1/𝑉 also constant
• If we differentiate the Cambridge equation
•
Δ𝑀
𝑀
=
Δ𝑘
𝑘
+
Δ𝑃
𝑃
+
Δ𝑌
𝑌
• (Rate of change in money supply= sum of rate of change in 𝑘, rate of change in Y
and rate of change in Price level)
• Y and 𝑘 are constants=>
Δ𝑘
𝑘
=
Δ𝑌
𝑌
=0
• Hence
Δ𝑀
𝑀
=
Δ𝑃
𝑃
(rate of increase in money supply= rate of increase in price = rate of
inflation)
• This also proves the neutrality of money i.e. any change in money supply would
cause a change in price level at the same rate keeping the real sector unchanged.
• Inflation is a monetary phenomenon

7. Seigniorage
• Revenue earned by Central Bank by printing new money.
• Central bank enjoys exclusive right over printing new money
• Increase in money supply => inflation=> decline in purchasing
power of money in hand of people (burden on people)
• More money printed => decline in value of old money
• By the power of printing money central bank increases its revenue at
the cost of the real balance in people’s hand
• In case of hyperinflation Seigniorage becomes the chief source of
revenue of the government

8. Interest Rate
• The interest rate equation is given as
• 𝑖 = 𝑟 + π (𝑖= nominal interest rate, 𝑟 = real interest rate and π= rate
of inflation)
• Rate of inflation indicates the fall in purchasing power of money
• Hence 𝑟= 𝑖 − π
• This real interest rate indicates interest gain on money in terms of
purchasing power

9. Fisher’s effect
• The interest identity is
• 𝑖 = 𝑟 + π (Fisher equation)
• Higher the rate of inflation higher would be the difference between
real and nominal interest rate.
• Higher rate of growth in money supply => higher inflation rate =>
higher difference between nominal and real interest rates
• There is an one to one correspondence between rate of growth of
money supply and rate of growth of nominal interest rate
• This is called Fisher effect