# Quantity theory of money equation in economics - Economicstool

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

Value 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.
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 M2 to M4 we noticed that price level is increasing from P to P2 and P4 and the value of money start decreasing from 1/P to 1/P2 and 1/P4.

#### 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:
M=KPY

Where, M=supply of money
K=fraction of real money
P=Price level
Y=Aggregate real income
P=M/KY
1/P=KY/M

#### Pigou equation: -

Pigou was the first who gave equation on his own concept. His equation is: -
P=KR/M

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 DD1 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 quantity theory of money equation 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.­­­