When the total quantity of money is M the general price level is Pi- When the quantity of money increases from M1 to M2, the corresponding price level rises from P1 to P2. Similarly when the total quantity of money in circulation decreases from M3 to M1, the price level falls from P3 to P1.

The quantity theory of money was put in the form of an equation of exchange by Fisher. The exact inverse relationship between the supply of money and its value is a peculiarity of money. To prove that changes in the value of money depend upon changes in the quantity of money, the quantity theory proceeds in this way.

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The value of money like the value of any other commodity is determined by the demand for and supply of money. Money is the medium of exchange and is demanded whenever there is some exchange to be made.

Demand for money comes from the volume of goods offered for sale. The volume of goods in turn depends on the aggregate volume of production.

The aggregate volume of production is determined by such factors as the supply and efficiency of the factors of production, organisation of production etc. and not on the value of money.

Thus during a given period, when the quantity of money changes, the aggregate volume of production will remain the same and the volume of goods offered for sale will also remain constant. In other words, demand for money remains constant during a given period when the quantity of money changes but no other change takes place in the meantime.

As the demand for money remains constant, the value of money will be determined by the supply i.e. the quantity of money. A doubling of the quantity of money would double the price level.

What determines the supply of money during a given period? It is equal to the quantity of money which is used to purchase the goods offered for sale. It is different from the total amount of currency and bank deposits.

Each piece of money may be used several times in course of a given period to purchase goods and services. Each time a money changes hand for buying goods, it adds to the supply of money. If one rupee is used three times in course of a day for buying goods, the total supply of money is equal to three times one rupee i.e. three rupees.

The average number of times a unit of money changes hands for buying goods during a given period is known as the Velocity Circulation of Money.

The supply of money is therefore equal to the total amount of money multiplied by the average velocity of circulation. Changes in the supply of money will cause proportionate changes in the price level.

According to the quantity theory, the Demand for Money is equal to the total value of goods and services exchanged for money. Let

P = Price level

T = Total amount of goods + services exchanged for money

Then PT = Total cash value of all goods and services exchanged for money = Demand for Money

The Supply of Money depends on two factors—the quantity of money and its velocity of circulation. Let

M = Total quantity of legal tender money M1 = Total quantity of credit tender money V = Velocity of circulation of M V1 = Velocity of circulation of M1.

The quantity of money must be multiplied by its velocity in order to obtain total money supply. If one unit of legal tender money can be used V number of times, then the total value of all transactions which can be done with M unit of money is MV.

Similarly the total value of all transactions which can be done with credit money is M1V1. Hence the supply of Money = MV+M^1

But the total demand for money must be equal to its supply. Hence PT=MV+M1V1

The equation PT=MV+M1V1 is known as the Fisher’s Equation for the value of money. It can be rewritten in this form also.

From this equation it is quite clear that the price level varies directly with money supply and inversely with the volume of goods and services. Fisher’s equation is based on what is called the Cash Transaction Approach. 