Measuring the economy from different angles.
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The equation of exchange is an identity that expresses the same economic activity in two ways:
It is written as MV = PQ, and because it is an identity, the two sides must always be equal.
American economist Irving Fisher gave the equation its classic formulation in his 1911 book The Purchasing Power of Money. The equation became a foundation of the quantity theory of money, which links changes in the money supply to changes in prices across the economy.
Two sides of the equation
The equation is expressed as MV = PQ, where:
- M is the money supply, which includes currency in circulation and money held in bank accounts and other liquid forms.
- V is the velocity of money, or the average number of times a single dollar changes hands to purchase something in a given time frame.
- P represents the overall price level of goods.
- Q is the quantity of goods and services produced during a given period (often a year).
Modern textbooks often substitute Q with Y, which stands for real (inflation-adjusted) economic output, typically measured by real gross domestic product (GDP). PY represents nominal GDP, or the economyâs total output valued at current prices.
The equation itself doesnât establish cause and effect; it only shows how the variables are related. The quantity theory of money goes a step further, using assumptions about velocity and real output to explain how changes in the money supply affect prices.
Imagine an economy made up of three items: bus fares, sandwiches, and T-shirts. Suppose the total money supply is $200 million and each dollar is spent, on average, four times in a given year. That gives us $200 million (M) Ă 4 (V) = $800 million in nominal economic activity.
The value of the economyâs output can also be calculated from the prices and quantities of the three items. For simplicity, assume the following prices and quantities sold:Â
- Bus fares: $2 x 200 million rides sold (Q) = $400 million
- Sandwiches: $5 x 60 million sold (Q) = $300 million
- T-shirts: $10 x 10 million sold (Q) = $100 million
The total is $800 millionâthe nominal value of the economyâs output, represented by PQâmatching the MV side of the equation.
A real economy is vastly more complicated, with millions of goods and services sold at different prices. In the United States, for example, nominal GDPâthe current-dollar value of all goods and services producedâruns into the tens of trillions of dollars. But the same basic relationship holds: MV and PQ are two ways of expressing the value of economic activity.
From the equation to the real world
By definition, the two sides of the equation balance. But because MV="PQ" is an identity, it shouldnât be understood as proof of causation. If M rises, for instance, V could fall, P or Q could rise, or several variables could change at once. The equation itself canât tell you which variable will moveâor why.
Economist Milton Friedman, echoing Fisherâs basic principle, famously said: âInflation is always and everywhere a monetary phenomenon.â But the relationship between money and prices depends in part on what happens to the other variables in the equation.
- Changes in velocity. V isnât always stable. During the Great Depression, velocity collapsed, weakening the relationship between the money supply and nominal spending. By contrast, velocity was relatively stable during much of the postwar period when Friedmanâs monetarist ideas gained influence. It became less predictable beginning in the 1980s and plunged again during the COVID-19 pandemic.
- Changes in output. Q isnât a fixed component. When labor or industrial capacity is underutilized, an increase in the money supply can be accompanied by higher output rather than higher prices, at least in the short term. As an economy approaches its productive capacity, however, further increases in nominal spending are more likely to be reflected in higher prices.
The equation of exchange remains a useful framework for understanding the relationship among the money supply, velocity, prices, and economic output. But the equation itself doesnât explain what causes those variables to change. The quantity theory of money goes further by making assumptions about those relationshipsâand those assumptions have been the subject of economic debate for centuries.
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