The quantitative theory of money is an economic theory of determining the level of prices that establishes the existence of a direct relationship between the quantity of money and the general level of prices.

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## Formulation of the theory

The quantitative theory of money, part of an identity, the equation of change, according to which the value of the transactions that are made in an economy must be equal to the amount of money existing in that economy for the number of times that the Money changes hands:

P * Q = M * V

Where:

P = price level

Q = production level

M = amount of money

V = number of times money changes hands, is the speed of circulation of money

Originally:

PT = MV

## Origin

The formulation of the quantitative theory of money is usually attributed to Jean Bodin (1568); nevertheless, one can find a first formulation of it in the works of Martín de Azpilcueta (1556), of the School of Salamanca. David Hume formulated it clearly in his criticism of mercantilism, underlining that the accumulation of precious metals, according to the mercantilist proposals, would generate an increase in the price level

## Enunciation of the theory by Fisher

It was Irving Fisher (1911) who endowed this identity with economic content. Fisher, adopted a macroeconomic perspective, considered that the amount of money in an economy can be approximated by the supply of money made by the central bank and that can be considered as given (constant). The speed of circulation would be constant, dependent only on institutional factors. Similarly, the number of transactions when the economy is in full employment, would be given. In this way, the price level would be determined based on the other three variables.

The equality between supply and demand of money would make it possible to consider the quantitative equation as a function of demand for money:

M/p=1/v*Y

## The approach of Marshall and Pigou

In contrast to Fisher's approach, Marshall (1871) and Pigou (1917) develop the so – called Cambridge approach. These economists adopt a microeconomic approach to analysis and try to establish the factors that explain the individual's decision to keep money. They consider that the speed of circulation of money will depend on individual preferences and that, in addition, money plays a role as a reserve of value, so that demand will depend on the level of wealth and interest rates. Pigou assumes interest rates as constants and approximates wealth by nominal income, and, so, the demand for individual money would be proportional to nominal income:

M=k*p*Y

which, as can be seen, is similar to Fisher's expression, although, nevertheless, it should be noted that both theories are based on different approaches.

## Milton Friedman and the New Quantitative Theory

In the 1950s, and as part of his criticism of the Keynesian system, Milton Friedman establishes what is known as the new quantitative theory. Friedman justifies the demand for money by the utility derived from maintaining real balances, since they allow transactions to be made. In this way, derives the demand for money from the usual axioms of consumer theory, and establishes that the demand for money will depend on the opportunity cost of maintaining money. It uses a portfolio allocation approach and establishes that demand for money will depend on a set of interest rates on other assets and on the wealth of the individual, which is approximated by permanent income:

M / P = g (r, π) * Yp

Friedman considers that g (r, π) is a long-term stable function, that if we approximate it to the velocity of circulation we would obtain, again, the quantitative equation.

## The critics

John Maynard Keynes criticized the quantitative theory of money in general theory of occupation, interest and money. Keynes had originally been an advocate of the theory, but opposed it in his General Theory. Keynes argued that the price level was not strictly determined by the supply of money. Changes in the money supply can have effects on real variables such as output.

Ludwig von Mises shares that there is a kernel of truth in quantitative theory; but its focus on the supply of money continues without adequately explaining the demand for money. According to Mises, the theory "does not explain the mechanism of variations in the value of money". Nevertheless, the quantitative theory of money continued to be a fundamental part of the investigations of Milton Friedman and the Chicago school.

Walter Beveraggi Allende, Argentine nationalist economist, wrote his book The Qualitative Theory of the Currency, where he criticizes and exposes, as opposed to quantitative theory, qualitative theory.