Equation of exchange

In monetary economics, a 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 assumptions about the money supply, the price level, in addition to the effect of interest rates on velocity to throw a concepts about the causes of inflation as well as 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

Applications

The quantity theory of money is nearly often expressed and explained in mainstream economics by character to the equation of exchange. For example, a rudimentary theory could begin with the rearrangement

If and were fixed or growing at the same fixed rate as regarded and specified separately. other, then:

and thus

where

That is to say that, whether and were constant or growing at earn up fixed rates, then the inflation rate would exactly constitute the growth rate of the money supply.

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 or of to .

Economists nominal income . The Cambridge economists also thought wealth would play a role, but wealth is often omitted for simplicity. The Cambridge equation for demand for cash balances is thus:

which, precondition the classical dichotomy and that real income must symbolize expenditures , is equivalent to

Assuming that the economy is at equilibrium , that real income is exogenous, and that k is fixed in the short run, the Cambridge equation is equivalent to the equation of exchange with velocity equal to the inverse of k:

The money demand function is often conceptualized in terms of a liquidity function, ,

where is real income and is the real rate of interest. whether is taken to be a function of , then in equilibrium