Cambridge equation
Encyclopedia
The Cambridge equation formally represents the Cambridge cash-balance theory, an alternative approach to the classical quantity theory of money
. Both quantity theories, Cambridge and classical, attempt to express a relationship among the amount of goods produced
, the price level
, amounts of money, and how money moves. The Cambridge equation focuses on money demand instead of money supply
. The theories also differ in explaining the movement of money: In the classical version, associated with Irving Fisher
, money moves at a fixed rate and serves only as a medium of exchange
while in the Cambridge approach money acts as a store of value
and its movement depends on the desirability of holding cash.
Economists associated with Cambridge University, including Alfred Marshall
, A.C. Pigou, and John Maynard Keynes
(before he developed his own, eponymous school of thought) contributed to a quantity theory of money that paid more attention to money demand than the supply-oriented classical version. The Cambridge economists argued that a certain portion of the money supply will not be used for transactions; instead, it will be held for the convenience and security of having cash on hand. This portion of cash is commonly represented as k, a portion of nominal income (the product of real income and the price level,
). The Cambridge economists also thought wealth would play a role, but wealth is often omitted from the equation for simplicity. The Cambridge equation is thus:
Assuming that the economy is at equilibrium (
), 
is exogenous, and 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 Cambridge version of the quantity theory led to both Keynes's attack on the quantity theory and the Monetarist revival of the theory. Marshall recognized that k would be determined in part by an individual's desire to hold liquid cash. In his General Theory of Employment, Interest and Money, Keynes expanded on this concept to develop the idea of liquidity preference
, a central Keynesian concept.
Quantity theory of money
In monetary economics, the quantity theory of money is the theory that money supply has a direct, proportional relationship with the price level....
. Both quantity theories, Cambridge and classical, attempt to express a relationship among the amount of goods produced
Output (economics)
Output in economics is the "quantity of goods or services produced in a given time period, by a firm, industry, or country," whether consumed or used for further production.The concept of national output is absolutely essential in the field of macroeconomics...
, the price level
Price level
A price level is a hypothetical measure of overall prices for some set of goods and services, in a given region during a given interval, normalized relative to some base set...
, amounts of money, and how money moves. The Cambridge equation focuses on money demand instead of money supply
Money supply
In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...
. The theories also differ in explaining the movement of money: In the classical version, associated with Irving Fisher
Irving Fisher
Irving Fisher was an American economist, inventor, and health campaigner, and one of the earliest American neoclassical economists, though his later work on debt deflation often regarded as belonging instead to the Post-Keynesian school.Fisher made important contributions to utility theory and...
, money moves at a fixed rate and serves only as a medium of exchange
Medium of exchange
A medium of exchange is an intermediary used in trade to avoid the inconveniences of a pure barter system.By contrast, as William Stanley Jevons argued, in a barter system there must be a coincidence of wants before two people can trade – one must want exactly what the other has to offer, when and...
while in the Cambridge approach money acts as a store of value
Store of value
A recognized form of exchange can be a form of money or currency, a commodity like gold, or financial capital. To act as a store of value, these forms must be able to be saved and retrieved at a later time, and be predictably useful when retrieved....
and its movement depends on the desirability of holding cash.
Economists associated with Cambridge University, including Alfred Marshall
Alfred Marshall
Alfred Marshall was an Englishman and one of the most influential economists of his time. His book, Principles of Economics , was the dominant economic textbook in England for many years...
, A.C. Pigou, and John Maynard Keynes
John Maynard Keynes
John Maynard Keynes, Baron Keynes of Tilton, CB FBA , was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments...
(before he developed his own, eponymous school of thought) contributed to a quantity theory of money that paid more attention to money demand than the supply-oriented classical version. The Cambridge economists argued that a certain portion of the money supply will not be used for transactions; instead, it will be held for the convenience and security of having cash on hand. This portion of cash is commonly represented as k, a portion of nominal income (the product of real income and the price level,
). The Cambridge economists also thought wealth would play a role, but wealth is often omitted from the equation for simplicity. The Cambridge equation is thus:Assuming that the economy is at equilibrium (
), is exogenous, and k is fixed in the short run, the Cambridge equation is equivalent to the equation of exchangeEquation of exchange
In economics, the equation of exchange is the relation:M\cdot V = P\cdot Qwhere, for a given period,M\, is the total nominal amount of money in circulation on average in an economy.V\, is the velocity of money, that is the average frequency with which a unit of money is spent.P\, is the price...
with velocity equal to the inverse of k:
History and significance
The Cambridge equation first appeared in print in 1917 in Pigou's "Value of Money". Keynes contributed to the theory with his 1923 Tract on Monetary Reform.The Cambridge version of the quantity theory led to both Keynes's attack on the quantity theory and the Monetarist revival of the theory. Marshall recognized that k would be determined in part by an individual's desire to hold liquid cash. In his General Theory of Employment, Interest and Money, Keynes expanded on this concept to develop the idea of liquidity preference
Liquidity preference
In macroeconomic theory, Liquidity preference refers to the demand for money, considered as liquidity. The concept was first developed by John Maynard Keynes in his book The General Theory of Employment, Interest and Money to explain determination of the interest rate by the supply and demand...
, a central Keynesian concept.