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Equation of Exchange

A mathematical equation for the quantity theory of money in economies

What is the Equation of Exchange?

The equation of exchange is a mathematical equation for the quantity theory of money in economies, which identifies the relationship among the factors of:

  • Money Supply
  • Velocity of Money
  • Price Level
  • Expenditure Level

 

Equation of Exchange

 

The Equation of Exchange Explained

The equation of exchange was derived by economist John Stuart Mill. The equation states that the total amount of money that changes hands in an economy will always be equal to the total monetary value of goods and services that changes hands in an economy.

In other words, the amount of nominal spending will always be equal to the amount of nominal income.

Equation of exchange is also used to make an argument that inflation rates will be proportionate to the change in the money supply and that the demand for money can be broken down into:

  1. The total demand for money for use in transactions; and
  2. The total demand for money for holding in liquidity

The equation is as follows:

Equation of Exchange - Formula

Where:

  • Ms = Money supply, or the average currency units in circulation within a time period
  • V = Velocity of money, or the average number of times that a currency unit changes hands within a time period
  • P = Average price level of goods and services during a time period
  • T = Index of the real value of all aggregate transactions within a time period

 

“Ms x V” is interpreted as the total amount of money that is spent within an economy within a time period

“P x T” is interpreted as the total amount of money that is spent within an economy within a time period.

Therefore, as mentioned earlier, the equation states that the total amount of money that is spent within an economy over a specific period is always equal to the total amount of money that is spent on goods and services during the same period.

The equation can be restated in the following form:

Restated Equation

Where:

  • Ms = Money supply, or the average currency units in circulation within a time period
  • V = Velocity of money, or the average number of times that a currency unit changes hands within a time period
  • P = Average price level of goods and services during a time period
  • Q = Index of all real expenditures within a time period

 

“P x Q” is interpreted as the nominal GDP over a time period.

 

The restated equation states that the total amount of money spent within an economy over a specific period is always equal to the total amount of money earned within the same period; or, nominal expenditures are always equal to nominal income.

It represents the common expression of the quantity theory of money, which is used to explain changes in the money supply and its relationship to the overall level of prices of goods and services.

 

Quantity Theory of Money

The quantity theory of money explains the relationship between price levels and the money supply. The original “neo-quantity theory” states that there is a fixed proportional relationship between the change in the money supply of an economy and the price levels in an economy. This form of the theory was based on the equation derived by economist Irving Fisher.

The theory infers that increases in the amount of money in circulation will spark inflation and that any increases in inflation will create more money in circulation. It is explained with the following example:

The Federal Reserve decides to double the amount of money in the supply by printing excess money. It would subsequently lead to a dramatic increase in prices since more U.S. dollars are chasing the same amount of goods. Demand for goods and the amount of spending should increase and push upward pressure on prices.

 

Quantity Theory of Money in Practice

In 2020, there was a serious outbreak of a pandemic known as “Covid-19.” To slow down the spread of the virus, global economies shut down, and entire populations remained quarantined at home.

To maintain the economy – as many people’s incomes went to zero – central banks and governments released an unprecedented amount of stimulus into the economy, which increased the overall money supply quite dramatically.

However, it did not translate into a proportionate increase in prices since the quantity theory of money assumes that increases in the money supply will lead directly to more spending.

In such a scenario, the money that was injected in the economy was not immediately used for spending, but rather for saving or paying regular bills in place of income. It was a situation in which the quantity theory of money did not hold.

 

Additional Resources

CFI is the official provider of the global Certified Banking & Credit Analyst (CBCA)™ certification program, designed to help anyone become a world-class financial analyst. To keep advancing your career, the additional CFI resources below will be useful:

  • Supply and Demand
  • Equilibrium Quantity
  • Quantity Theory of Money
  • Velocity of Circulation

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