Equation of Exchange

The equation of exchange is an economic equation that showcases the relationship between money supply, the velocity of money, the price level and an index of expenditures. The equation was derived by John Stuart Mill and based on the early ideas of David Hume. The equation of exchange is as follows:

Where:
M = money supply
V = velocity of money
P = average price level of goods
T = index of expenditures (such as the total number of economic transactions)

The equation of exchange has two primary uses. It represents a founding principle used by the quantity theory of money, which relates increases in the money supply to increases in the overall level of prices. Additionally, solving the equation for M can serve as an indicator of the demand for money.

Using the equation of exchange can offer a conceptual understanding of how the elements of the equation can be used in concert to forecast the direction of the economy. Through the equation, the effect the money supply can have on elevating or lowering process can be postulated. The money supply is affected by decisions made by a country’s central banking, which may decide to increase these elements in response to the flow of commerce. This speaks to monetarist economic theories, which hold that the monetary supply in its relation to the price of goods as a direct, prime determinant in the health of the economy. This differs from the Keynsian perspective that the money supply’s influence over interest rates and, subsequently, payroll levels indirectly influences the direction of the economy.

Based on the equation, if the velocity of money and the index of expenditures are known to be constant, then changes in the money supply should have a direct effect on average price levels. Theoretically, if the money supply were to double, average prices should double as well. Likewise, declines in the money supply should have a directly proportional effect on prices.

The figure T in the equation (sometimes shown as Y, Q, or other characters) can represent a variety of different factors that relate to the output of the economy. This includes industrial production. Further, the average price level of goods might be expressed as the nominal GDP divided by real GDP. The nominal GDP can also be found by multiplying money supply by the velocity of money.

There can be instances wherein the figures represented in the equation go into decline, despite what the framework might predict. This can stem from weaknesses within the economy.