Quantity theory of money (1885)

Developed by the Americans SIMON NEWCOMB (1835-1909) and Irving Fisher (1867-1947), the latter of whom’s original equation stated in simple terms that the amount of money in circulation equals money national income; that is,


where M is money stock, V is velocity of circulation, P is average price level and T the number of transactions. The equation assumes that the velocity of circulation of money is stable (at least in the short term) and that transactions are fixed by consumer tastes and the behavior of firms.

Quantity theory of money was superseded by Keynesian analysis. Members of the Cambridge School were concerned with the volume of money held given the number of transactions carried out. They argued that the greater the number of transactions, the greater the amount of money held. English economist Arthur Cecil Pigou (1877-1959), in particular, asserted that the nominal demand for money was a constant percentage of nominal income.

In the Cambridge Equation, PT is replaced by Y (the income velocity of circulation). The equation is:

V = Y / M

where M is money stock in economy, Y income velocity of circulation and V average velocity of circulation.

Monetarists argue that an increase in prices would not lead to inflation unless the government increased the money supply.

Also see: commodity theory of money, monetarism

S Newcomb, Principles of the Political Economy (New York, 1885);
I Fisher, The Purchasing Power of Money (New York, 1911);
M Friedman, ed., Studies in the Quantity of Money (Chicago, 1956)

Origins and development

The quantity theory descends from Nicolaus Copernicus,[1][5] followers of the School of Salamanca like Martín de Azpilicueta,[6] Jean Bodin,[3] Henry Thornton, and various others who noted the increase in prices following the import of gold and silver, used in the coinage of money, from the New World. The “equation of exchange” relating the supply of money to the value of money transactions was stated by John Stuart Mill[7] who expanded on the ideas of David Hume.[8] The quantity theory was developed by Simon Newcomb,[9] Alfred de Foville,[10] Irving Fisher,[11] and Ludwig von Mises[12] in the late 19th and early 20th century.

Henry Thornton introduced the idea of a central bank after the financial panic of 1793, although, the concept of a modern central bank was not given much importance until Keynes published “A Tract on Monetary Reform” in 1923. In 1802, Thornton published An Enquiry into the Nature and Effects of the Paper Credit of Great Britain in which he gave an account of his theory regarding the central bank’s ability to control price level. According to his theory, the central bank could control the currency in circulation through book keeping. This control could allow the central bank to gain a command of the money supply of the country. This ultimately would lead to the central bank’s ability to control the price level. His introduction of the central bank’s ability to influence the price level was a major contribution to the development of the quantity theory of money.[13]

Karl Marx modified it by arguing that the labor theory of value requires that prices, under equilibrium conditions, are determined by socially necessary labor time needed to produce the commodity and that quantity of money was a function of the quantity of commodities, the prices of commodities, and the velocity.[14] Marx did not reject the basic concept of the Quantity Theory of Money, but rejected the notion that each of the four elements were equal, and instead argued that the quantity of commodities and the price of commodities are the determinative elements and that the volume of money follows from them. He argued…

The law, that the quantity of the circulating medium is determined by the sum of the prices of the commodities circulating, and the average velocity of currency may also be stated as follows: given the sum of the values of commodities, and the average rapidity of their metamorphoses, the quantity of precious metal current as money depends on the value of that precious metal. The erroneous opinion that it is, on the contrary, prices that are determined by the quantity of the circulating medium, and that the latter depends on the quantity of the precious metals in a country;this opinion was based by those who first held it, on the absurd hypothesis that commodities are without a price, and money without a value, when they first enter into circulation, and that, once in the circulation, an aliquot part of the medley of commodities is exchanged for an aliquot part of the heap of precious metals.

John Maynard Keynes, like Marx, accepted the theory in general and wrote…

This Theory is fundamental. Its correspondence with fact is not open to question.

Also like Marx he believed that the theory was misrepresented. Where Marx argues that the amount of money in circulation is determined by the quantity of goods times the prices of goods Keynes argued the amount of money was determined by the purchasing power or aggregate demand. He wrote

Thus the number of notes which the public ordinarily have on hand is determined by the purchasing power which it suits them to hold or to carry about, and by nothing else.

In the Tract on Monetary Reform (1923),[15] Keynes developed his own quantity equation: n = p(k + rk’),where n is the number of “currency notes or other forms of cash in circulation with the public”, p is “the index number of the cost of living”, and r is “the proportion of the bank’s potential liabilities (k’) held in the form of cash.” Keynes also assumes “…the public,(k’) including the business world, finds it convenient to keep the equivalent of k consumption in cash and of a further available k’ at their banks against cheques…” So long as k, k’, and r do not change, changes in n cause proportional changes in p.[16] Keynes however notes…

The error often made by careless adherents of the Quantity Theory, which may partly explain why it is not universally accepted is as follows… the Theory has often been expounded on the further assumption that a mere change in the quantity of the currency cannot affect kr, and k‘, – that is to say, in mathematical parlance, that n is an independent variable in relation to these quantities. It would follow from this that an arbitrary doubling of n, since this in itself is assumed not to affect kr, and k’, must have the effect of raising p to double what it would have been otherwise. The Quantity Theory is often stated in this, or a similar, form.

Now “in the long run” this is probably true. If, after the American Civil War, that American dollar had been stabilized and defined by law at 10 per cent below its present value, it would be safe to assume that n and p would now be just 10 per cent greater than they actually are and that the present values of kr, and k’ would be entirely unaffected. But this long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is long past the ocean will be flat again.

In actual experience, a change in n is liable to have a reaction both on k and k’ and on r. It will be enough to give a few typical instances. Before the war (and indeed since) there was a considerable element of what was conventional and arbitrary in the reserve policy of the banks, but especially in the policy of the State Banks towards their gold reserves. These reserves were kept for show rather than for use, and their amount was not the result of close reasoning. There was a decided tendency on the part of these banks between 1900 and 1914 to bottle up gold when it flowed towards them and to part with it reluctantly when the tide was flowing the other way. Consequently, when gold became relatively abundant they tended to hoard what came their way and to raise the proportion of the reserves, with the result that the increased output of South African gold was absorbed with less effect on the price level than would have been the case if an increase of n had been totally without reaction on the value of r.

…Thus in these and other ways the terms of our equation tend in their movements to favor the stability of p, and there is a certain friction which prevents a moderate change in n from exercising its full proportionate effect on p. On the other hand, a large change in n, which rubs away the initial frictions, and especially a change in n due to causes which set up a general expectation of a further change in the same direction, may produce a more than proportionate effect on p.

Keynes thus accepts the Quantity Theory as accurate over the long-term but not over the short term. Keynes remarks that contrary to contemporaneous thinking, velocity and output were not stable but highly variable and as such, the quantity of money was of little importance in driving prices.[17]

The theory was influentially restated by Milton Friedman in response to the work of John Maynard Keynes and Keynesianism.[18] Friedman understood that Keynes was like Friedman, a “quantity theorist” and that Keynes Revolution “was from, as it were, within the governing body”, i.e. consistent with previous Quantity Theory.[17] Friedman notes the similarities between his views and those of Keynes when he wrote…

A counter-revolution, whether in politics or in science, never restores the initial situation. It always produces a situation that has some similarity to the initial one but is also strongly influenced by the intervening revolution. That is certainly true of monetarism which has benefited much from Keynes’s work. Indeed I may say, as have so many others since there is no way of contradicting it, that if Keynes were alive today he would no doubt be at the forefront of the counter-revolution.

Friedman notes that Keynes shifted the focus away from the quantity of money (Fisher’s M and Keynes’ n) and put the focus on price and output. Friedman writes…

What matters, said Keynes, is not the quantity of money. What matters is the part of total spending which is independent of current income, what has come to be called autonomous spending and to be identified in practice largely with investment by business and expenditures by government.

The Monetarist counter-position was that contrary to Keynes, velocity was not a passive function of the quantity of money but it can be an independent variable. Friedman wrote:

Perhaps the simplest way for me to suggest why this was relevant is to recall that an essential element of the Keynesian doctrine was the passivity of velocity. If money rose, velocity would decline. Empirically, however, it turns out that the movements of velocity tend to reinforce those of money instead of to offset them. When the quantity of money declined by a third from 1929 to 1933 in the United States, velocity declined also. When the quantity of money rises rapidly in almost any country, velocity also rises rapidly. Far from velocity offsetting the movements of the quantity of money, it reinforces them.

Thus while Marx, Keynes, and Friedman all accepted the Quantity Theory, they each placed different emphasis as to which variable was the driver in changing prices. Marx emphasized production, Keynes income and demand, and Friedman the quantity of money.

Academic discussion remains over the degree to which different figures developed the theory.[19] For instance, Bieda argues that Copernicus’s observation

Money can lose its value through excessive abundance, if so much silver is coined as to heighten people’s demand for silver bullion. For in this way, the coinage’s estimation vanishes when it cannot buy as much silver as the money itself contains […]. The solution is to mint no more coinage until it recovers its par value.[19]

amounts to a statement of the theory,[20] while other economic historians date the discovery later, to figures such as Jean Bodin, David Hume, and John Stuart Mill.[19][21]

The quantity theory of money preserved its importance even in the decades after Friedmanian monetarism had occurred. In new classical macroeconomics the quantity theory of money was still a doctrine of fundamental importance, but Robert E. Lucas and other leading new classical economists made serious efforts to specify and refine its theoretical meaning. For new classical economists, following David Hume’s famous essay “Of Money”, money was not neutral in the short-run, so the quantity theory was assumed to hold only in the long-run. These theoretical considerations involved serious changes as to the scope of countercyclical economic policy.[22]

Historically, the main rival of the quantity theory was the real bills doctrine, which says that the issue of money does not raise prices, as long as the new money is issued in exchange for assets of sufficient value.[23]

Fisher’s equation of exchange

In its modern form, the quantity theory builds upon the following definitional relationship.

{\displaystyle M\cdot V_{T}=\sum _{i}(p_{i}\cdot q_{i})=\mathbf {p} ^{\mathrm {T} }\mathbf {q} }


{\displaystyle M\,} is the total amount of money in circulation on average in an economy during the period, say a year.
{\displaystyle V_{T}\,} is the transactions velocity of money, that is the average frequency across all transactions with which a unit of money is spent. This reflects availability of financial institutions, economic variables, and choices made as to how fast people turn over their money.
{\displaystyle p_{i}\,} and {\displaystyle q_{i}\,} are the price and quantity of the i-th transaction.
{\displaystyle \mathbf {p} } is a column vector of the {\displaystyle p_{i}\,}, and the superscript T is the transpose operator.
{\displaystyle \mathbf {q} } is a column vector of the {\displaystyle q_{i}\,}.

Mainstream economics accepts a simplification, the equation of exchange:

{\displaystyle M\cdot V_{T}=P_{T}\cdot T}


{\displaystyle P_{T}} is the price level associated with transactions for the economy during the period
{\displaystyle T} is an index of the real value of aggregate transactions.

The previous equation presents the difficulty that the associated data are not available for all transactions. With the development of national income and product accounts, emphasis shifted to national-income or final-product transactions, rather than gross transactions. Economists may therefore work where

{\displaystyle V} is the velocity of money in final expenditures.
{\displaystyle Q} is an index of the real value of final expenditures.

As an example, {\displaystyle M} might represent currency plus deposits in checking and savings accounts held by the public, {\displaystyle Q} real output (which equals real expenditure in macroeconomic equilibrium) with {\displaystyle P} the corresponding price level, and {\displaystyle P\cdot Q} the nominal (money) value of output. In one empirical formulation, velocity was taken to be “the ratio of net national product in current prices to the money stock”.[24]

Thus far, the theory is not particularly controversial, as the equation of exchange is an identity. A theory requires that assumptions be made about the causal relationships among the four variables in this one equation. There are debates about the extent to which each of these variables is dependent upon the others. Without further restrictions, the equation does not require that a change in the money supply would change the value of any or all of {\displaystyle P}{\displaystyle Q}, or {\displaystyle P\cdot Q}. For example, a 10% increase in {\displaystyle M} could be accompanied by a change of 1/(1 + 10%) in {\displaystyle V}, leaving {\displaystyle P\cdot Q} unchanged. The quantity theory postulates that the primary causal effect is an effect of M on P.

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