In economics, the equation of exchange is the relation:
Contents
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
Foundation
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
Quantity theory of money
The quantity theory of money is most often expressed and explained in mainstream economics by reference to the equation of exchange. For example, a rudimentary theory could begin with the rearrangement
If
and thus
where
That is to say that, if
An opponent of the quantity theory would not be bound to reject the equation of exchange, but could instead postulate offsetting responses (direct or indirect) of
Money demand
Economists Alfred Marshall, A.C. Pigou, and John Maynard Keynes, associated with Cambridge University, focusing on money demand instead of money supply, argued that a certain portion of the money supply will not be used for transactions, but instead it will be held for the convenience and security of having cash on hand. This proportion of cash is commonly represented as
which, given the classical dichotomy and that real income must equal expenditures
Assuming that the economy is at equilibrium (
The money demand function is often conceptualized in terms of a liquidity function,
where
History
The equation of exchange was stated by John Stuart Mill who expanded on the ideas of David Hume. The algebraic formulation comes from Irving Fisher, 1911.