Equation of exchange
In economics, the equation of exchange is the relation:
where, for a given period,
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:
where
The foundation of the equation of exchange is the more complex relation
where
The equation
is based upon the presumption of the classical dichotomy — that there is a relatively clean distinction between overall increases or decreases in prices and underlying, “real” economic variables — and that this distinction may be captured in terms of price indices, so that inflationary or deflationary components of p may be extracted as the multiplier P, which is the aggregate price level:
where is a row vector of relative prices; and likewise for
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