where, for a given period,
is the total nominal
amount of money supply
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).
is the level of nominal expenditures. This equation is a rearrangement of the definition of velocity: V
. As such, without the introduction of any assumptions, it is a tautology
. The quantity theory of money
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.
is the transactions velocity of money
, that is the average frequency across all transactions with which a unit of money is spent (including not just expenditures on newly produced goods and services, but also purchases of used goods, financial transactions involving money, etc.).
is an index of the real value
of aggregate transactions.
The foundation of the equation of exchange is the more complex relation:
are the respective price and quantity of the i
is a row vector of the
is a column vector of the
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
components of p
may be extracted as the multiplier P
, which is the aggregate price level:
In 2008 economist Andrew Naganoff
: Эндрю Наганов) proposed an integral form of the equation of exchange, where on the left side of the equation is
under the integral sign, and on the right side is a sum
from i=1 to
could be infinite. There are two variants of this formula:
The simplest cases for the dissipative scaling factors and
can be determined by the methods of the fuzzy sets
were constant or growing at the same fixed rate as each other, then:
That is to say that, if
were constant or growing at equal fixed rates, then the inflation rate would exactly equal 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
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 , a portion of nominal
). (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, given the classical dichotomy and that real
income must equal 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
is real income and is the real rate of interest
is taken to be a function of , then in equilibrium
- ^ Froyen, Richard T. Macroeconomics: Theories and Policies. 3rd Edition. Macmillan Publishing Company: New York, 1990. p. 70-71.
- ^ Mill, John Stuart; Principles of Political Economy (1848).
- ^ Hume, David; “Of Interest” in Essays Moral and Political.
Last edited on 11 February 2021, at 03:00
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