**Let us make an in-depth study of the Fisher’s version of the quantity theory. **

Let M represent the amount of money, including demand deposits in banks, used in transactions (buying and selling); V, the velocity, the rate at which the money changes hands; P, the price level, the average p rice of the things bought and sold; T, the volume of transactions, i.e., the number of things bought and sold.

Let us assume that M= Rs. 10,000; V = 1, P = Rs. 2, and T = 5,000.

Then Rs. 10,000 x 1 = Rs. 2 x 5,000

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Or, Rs. 2 = Rs. 10, 000 x 1/5, 000.

**Using the symbols we can state the relationship as follows:**

MV = PT, or, P = MV/T.

The total amount of money spent in the purchase of goods, services and securities (M x V) is equal to the quantity of things purchased, given the unit price (P x T); and P is equal to M x F divided by T. Thus, the price level varies directly with M and F and inversely with T.

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Now, in the above illustration, if M is doubled so that it is Rs. 20,000 and V and T remain unchanged, the price level will be doubled. And if M is reduced to Rs. 5,000, the price level will fall to Re. 1. These results follow if all the goods, services and securities are bought and sold.

However, if all the three variables—M, V and T—keep on changing at the same time, P may rise or fall. This is why Irving Fisher assumed V and T to remain constant in the short run. F is constant because it depends on people’s behaviour, i.e., their spending habit. It is unlikely to change in the short run. Likewise, T is constant because a society’s total output or gross national product remains fixed in the short run. Thus, these two assumptions make enormous good sense. As soon as these two assumptions are made the equation of exchange is converted into the quantity theory of money.

If V and T remain constant, changes in money supply would lead to proportionate changes in the price level. All other things remaining the same, a 3% rise in M would lead to exactly 3% rise in P. According to the Quantity Theory, prices vary directly, and the value of money inversely with the quantity of money and credit available for purchases. In other words, the Quantity Theory predicts that inflation is caused mainly by a rise in money supply or, in other words, inflation is a purely monetary phenomenon.

Irving Fisher further maintained that the Quantity Equation is true in the dynamic sense. When a change occurs in any one or more of the items included in the equation, the equation does not break down; the different components of the equation continue to be related to one another in the way shown in the equation.

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Fisher’s equation is based on what is called the **“Cash Transaction”** approach.

In the above equation, 1/V(= MJPT ) measures the amount of money required per unit of transaction, and its inverse F measures the rate of turnover of each unit of money per period.

In this formulation of the quantity equation the price level must refer to all the transactions which take place, which vary directly with income. So the price level can now be defined to refer to the price of real output.

**The quantity equation becomes: **

MV = PY

Where Y is real income and V is now the income velocity of circulation. Here V shows the number of times a unit of money circulates as income.

According to Paul Samuelson, the equation of exchange is an identity (which is always true) but the quantity theory of money is a hypothesis (a provisional statement the truth of which is not yet fully established).