where, for a given period,
is the total nominal amount of money in circulation on average in an economy. is the velocity of money, that is the average frequency with which a unit of money is spent. is the price level. is an index of real expenditures (on newly produced goods and services).
Thus PQ is the level of nominal expenditures. This equation is a rearrangement of the definition of velocity: V = PQ / M. As such, without the introduction of any assumptions, it is a tautology. The quantity theory of money adds assumptions about the money supply, the price level, and the effect of interest rates on velocity to create a theory about the causes of inflation and the effects of monetary policy.
In earlier analysis before the wide availability of the national income and product accounts, the equation of exchange was more frequently expressed in transactions form: