The equation of exchange enjoyed its greatest popularity in the United States, due largely to the work of Fisher in the early twentieth century. In contemporary Europe, however, a slightly different approach known as the cash-balances approach was propounded, particularly by the Cambridge economists, Marshall, Pigou, Robertson and Keynes.
According to the cash-balances theory, the value of money depends upon the supply of and the demand for money. The value of money is at any time fixed at that level at which its supply is equated to demand and the variations in its value through time arise out of the changes in either its supply or its demand, or both.
The basic postulate of the cash-balances theory is that the community’s demand for money or cash- balances, induced by the transactions and precautionary motives, constitutes a certain proportion of its annual real national income which the community desires to hold in the form of money.
Thus, at a given time, the community’s aggregate demand for real money balances can be represented as a certain fraction of the annual real national income. It is against the community’s aggregate demand for money cash balances that the supply of money is set to determine the level of prices or the value of money.
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It follows that the people in a community fix the amount of purchasing power that they wish to hold in the form of money. They thereby determine the aggregate purchasing power of the money supply.
Since the demand for money determines the aggregate purchasing power of the money supply, it follows that, with a given demand, the purchasing power of each unit of money varies inversely, and the price level directly, with the quantity of money.
On the other hand, the supply remaining constant, the value of money depends upon the changes in the demand for holding money or cash-balances.
An increase in the demand for money means lesser demand for goods and services, as the people can have larger cash holdings only by reducing their expenditure on goods and services. As a result, the price level will fall and the value of money will rise. Converse will be the case with the fall in the demand for money.
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The relation between the supply of, and the demand for, money, so conceived is exposed by the advocates of the cash-balances approach, by formulating cash- balance equations, also know as the ‘Cambridge equations.’ Like the equation of exchange, the cash-balance equations also are identities or definitional equations.
Marshall, Pigou, Robertson and Keynes are the four noted authors of Cambridge version. Each of them has framed his own type of cash-balance equation to interpret the QTM.