**have two types. First is fisher's quantity theory of money and second is Cambridge version of**

*Quantity theory of money equation**. Here we discuss about both Quantity theory of money equation. But before understanding What is the quantity theory of money we should know about the value of money.*

**quantity theory of money****is the purchasing power of money over goods and services in a country. The value of money is related to the price level because goods and services are purchased with a money unit at given prices. But value of money(V) and the price level(P) have an inverse relation.**

*Value of money*
V=1/P

###
What is Fisher's quantity theory of money?

This theory of money equation states that the quantity of
money is the main factor which determine value of money and the price level. In
the words of Fisher's, "Other things remaining unchanged, as the quantity
of money in circulation increases , the price level also increases in direct
proportion and the value of money decreases and vice versa". If quantity
of money is doubled, the price level will also double and the value of money
will be one half.

#### Fisher's Quantity theory of money equation: -

He explained this theory in terms of equation of exchange
(Quantity theory of money equation)

PT=
MV+M'V'

P=MV+M'V'/T

Where, M=the total quantity of legal tender money

V=the velocity
of circulation of M

M'=the total
quantity of credit money

V'=the velocity
of circulation of M'

T=total amount
of goods and services exchanged for money

P=Price level

Fisher in his quantity theory of money equation indicated
that price level (P) varies directly as the quantity of money (M+M') provided
the volume of trade (T) and velocity of circulation (V, V') remain unchanged. If
M and M 'are doubled, while V, V 'and T remains constant, P is also double, but
the value of money is reduced to half.

Fisher's quantity theory of money equation is explained by
the diagram also. In the given diagram we see relation between value of money
and the price level. As quantity of money is increasing from M to M and M

_{2}to M_{4}we noticed that price level is increasing from P to P_{2}and P_{4}and the value of money start decreasing from 1/P to 1/P_{2}and 1/P_{4}.####
Assumptions of quantity theory of money: -

1.Full employment in the economy.

2.This theory is applicable in long run.

3.Price level is affected by another factor but other factor
is not affected by price level.

4. V, V', T is constant.

5.It is assumed that the demand for money is proportional to
the value of transaction.

### Cambridge version of quantity theory of money: -

Marshall, Pigou, Robertson and Keynes explain quantity
theory of money in Cambridge version of quantity theory of money equation. This
is also named as cash balance approach. They regarded the determination of
value of money in terms of supply and demand. Demand of money is controlled by
the Public and they demand money for their day to day consumption. Supply of
money is controlled by the Banking system.

This theory of quantity of money considered the demand for
money not as the medium of exchange but money as a store of value. Cambridge
version of quantity theory of money equation show that given the supply of money at a
point of time, the value of money is determined by the demand for cash
balances. whenever demand for money rises, people will reduce their
expenditures and as expenditure reduces value of goods and services start
decreasing and reduce the price level and rise in the value of money.

Cambridge quantity theory of money equation of Marshall, Pigou,
Robertson and Keynes are as follow

#### Marshall Equation: -

Marshall did not put his theory in equation form but Friedman
was the first who put Marshall concept in the equation form. His equation is:

Where, M=supply of money

K=fraction of real money

P=Price level

Y=Aggregate real income

#### Pigou equation: -

Pigou was the first who gave equation on his own concept. His
equation is: -

Where, P=purchasing power of money

K=income

R=total real income

M=Number of actual units of legal tender
money

According to Pigou, the demand for money consist not only of
legal money or cash but also bank notes and bank balance, then Pigou modifies
his equation as

P=KR/M{c+h(1-c)}

Where, c=proportion of total real income

1-c=banks notes or bank balance

h=actual legal tender money

Pigou also explain his concept by the help of diagram. In
this diagram we can easily noticed that as money demanded and supplied
increases value of money starts decreasing. The demand curve for money DD

_{1}is a rectangular hyperbola because it shows changes in the value of money exactly in reverse proportion to the supply of money.####
Robertson equation: -

The only difference between the Pigou and the Robertson
equation is that Pigou use total real resources R but Robertson use volume of
total transaction T.

P=M/KT

Where, P=price level

K=total amount of goods and services

T=total volume of goods and services

####
Keynes equation: -

Keynes equation

n=PK

If K is constant, a proportionate increase in n (Quantity of
money) will lead to a proportionate increase in P (price level).

This equation can be expanded by taking into account bank
deposits. Let K' the number of consumption units in the forms of bank deposits,
and r the cash reserve ratio of banks, then the expanded equation is

n=P(K+rK')

again, if K, K' and r are constant, P will change in exact
proportion to the change in n.

The other

*fails to point how the price level (P) can be regulated. Since the cash balance (K) held by the people are outside the control of the monetary authority, P can be regulated by controlling n and r. It is also possible to regulate bank deposits K' by appropriate in the bank rate. So, P can be controlled by making appropriate changes in n, r and K so as to offset changes in K.***quantity theory of money equation**
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