TRANSACTIONS-VELOCITY APPROACH: The Equation of Exchange

As noted, the classical theory of money held that the more money people have, the more they will spend, and the more they spend, the greater the nominal national income will be. This view of the role of money in the economy was given its most definitive statement in the writings of the great American economist Irving Fisher about seventy-five years ago. Because Fisher, like the classical writers before him, focused attention on the reasons why people spend money, his theory is usually referred to as the transections-velocity approach to monetary theory.

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The Equation of Exchange:

The centerpiece of the transactions-velocity approach to monetary theory is the equation of exchange. The equation of exchange is, in fact, an identity; that is, it is necessarily true by definition at all times and under all circumstances. To see that this is so and to help the reader in understanding the nature of the equation of exchange, it is best to begin by putting the matter in its most tautological form. To do so, consider the simplest possible market transaction- buying a loaf of bread in a grocery store, say. If the loaf of bread cost s 50 cents, then when you buy it you will spend 50 cents and the grocer will receive 50 cents. that is the amount of money you spend is necessarily equal to the amount of money the grocer receives. But this same statement holds equally well for all market transactions. thus we can write in the aggregate-

[Total money expenditures for goods and services = total money receipts from the sale of goods and services]......(1)

Equation (1) is merely an identity; in itself, it tells us nothing that we didn't already know. But don't dismiss it on that account. Remember, for example, .that a balance sheet is also an identity, but it is certainly a useful business device. What is needed to make eq? (1) a useful tool for economic analysis is a classification of each side of the equation in meaningful terms, that is, a classification in terms of those variables that we are interested in.

First, consider the right-hand side of eq. (1), total money receipts from the sale of goods and services. This is the exchange transaction when viewed from the sale of goods and services. This is the exchange transaction when viewed from the seller's side, and therefore it immediately suggests that prices are somehow involved. We can lend concreteness to this idea in the following fashion. Let us suppose that we can count every market transaction on the economy during a given period, say. one year. Keep in mind that what we are counting are transections, not the goods themselves. Thus, when an automobile is sold, that is one transaction, and when a pencil is sold, that also is one transaction. at the end of the year, we would, therefore, have an accurate count of the total number of transactions that took place during the past twelve months. Now suppose that in addition to keeping count of the number of transactions, we also keep an accurate record of the price at which each transaction is made. At the end of the year, we could add up all these prices and then take their mean, or average, which would give us the average price at which all transactions occurred. Finally, by multiplying these two magnitudes together, we obtain the total money receipts from the sale of goods and services during the year. That is,

[Total money receipts from the sale of goods and services = average price of transaction x total number of transactions]............(2)

Next, consider the left-hand side of eq. (1), total money expenditures for goods and services. Since we are trying to construct a theory of money, it seems sensible to have one component of our breakdown of total expenditures by the quantity of money in the economy. The question then becomes, what can we multiply the quantity of money by so that the product of the two equals the total expenditures? But to ask the question is virtually to answer it. Consider a dollar bill, for example. During one year, this dollar bill may be spent, say, ten times. If we then multiply this dollar bill by the number of times it was spent, we obtain the total expenditures carried out by that piece of money- in this case, $10. To obtain the total expenditures for the entire economy, we could do this for each piece of money. But it is easier and logically amounts to the same thing to multiply the total quantity of money by its average rate of turnover, or velocity. Thus we can write, again as an identity,

[Total money expenditure on goods and services = mone supply x velocity of money]........(3)

Substituting Eqs. (2) and (3) into Eq. (1) then gives 

[Money supply x velocity of money = average price of transaction x total number of transaction]................(4)

Here M = money, V = velocity, P = average price level, and T = transactions 

The equation (4) can be written as,

MV = PT...........(5)

This equation (5) is the equation of exchange. as indicated, it is an identity; that is there is no possibility of its not being true. It is, in fact, simply a restatement of equation (1). The equation of exchange is therefore not a theory, any more than a balance sheet is a theory. But the equation of exchange is nevertheless a good deal more useful than equation (1) because it permits us to develop a theory of the role of money in the economy. We can do this by developing behavioral explanations for each of the four variables in equation (5)

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