# The Quantity Equation in Income Form | Money and Prices

In equations MVT=PTT (12.1) and MVT + M'VT= PTT. (12.4) of the transactions approach to the Quantity Theory of Money( QTM) the magnitudes designated as T and PT are conceptually ambiguous and difficult to measure with available data. Therefore, with the development of social accounting and Keynes' theory of income in the 1930s and consequent emphasis on national income, an important change occurred in the specification of the quantity equation, too.

MVT=PTT (12.1)

MVT + M'VT= PTT. (12.4)

A tendency developed to express this equation in terms of real income (y) rather than transactions (T). With this PT got replaced by P the average level of prices of final goods and services that make up the national income of a country.

National income accounting gives reasonably satisfactory measures of both y and the associated implicit deflator, P. Appropriately enough, the transactions velocity VT has given place to 'income velocity of money' V, which defines the average number of times per period a unit of money is used in making income transactions (that is, payments for final goods and services) rather than all transactions.

When all these changes are incorporated in equation (12.1), we get the quantity theory equation in income form:

MV=Py. (12.5)

The above equation is both conceptually and empirically more satisfactory than equation MVT=PTT (12.1). Its categories do not suffer from the twin problems of conceptual ambiguity and difficulty of statistical measurement surrounding the categories of equation MVT=PTT (12.1). The new equation is also closer in conception to the Cambridge Cash-Balance equation and to the modem version of the QTM. This makes movement from one to the other easier and helps view the QTM as one unified approach to monetary theory.

The main thrust of the approach remains unaltered. However, the change in the variables should be kept in mind. The posture of the modem QTM with respect to them.

Like equation MVT=PTT (12.1), equation MV=Py. (12.5) can be and has been interpreted both as an identity and as a genuine equation. Ex post it, too, is an identity, or something which is definitionally true. This can be shown very simply. By definition,

V= Y/M (12.6)

In fact, this is how actual V is measured. Multiplying both sides of V= Y/M (12.6) by M and recalling that Y=P Y, we have equation MV=Py. (12.5) as an identity.

However, this is not the QTM proper, whatever its other faults. As a theory, its equation MV=Py. (12.5) is a P determining equation, given V, y, and M. More important, on the assumption that V is a constant and y is determined by the real-sector forces operating elsewhere in the system," autonomous changes in M lead to equiproportionate changes in P.