Equation of Exchange

What Is the Equation of Exchange?

The equation of exchange is an economic identity that shows the relationship between money supply, the velocity of money, the price level, and an index of expenditures. English classical economist John Stuart Mill derived the equation of exchange, in view of prior thoughts of David Hume. It says that the total amount of money that changes hands in the economy will continuously approach the total money value of the goods and services that change hands in the economy.

Figuring out the Equation of Exchange

The original form of the equation is as per the following:
$\begin&M\ \times\ V\ =\ P\ \times\ T\&\textbf\&\beginM=\ &\text{the money supply, or average currency units in}\&\text\end\&\beginV=\ &\text{the velocity of money, or the average number of}\&\text\end\&P=\text\&T=\text\end$
M x V can then be deciphered as the average currency units in circulation in a year, duplicated by the average number of times every currency unit changes hands in that year, which is equivalent to the total amount of money spent in an economy in the year.

On the opposite side, P x T can be deciphered as the average price level of goods during the year duplicated by the real value of purchases in an economy during the year, which is equivalent to the total money spent on purchases in an economy in the year.

So the equation of exchange says that the total amount of money that changes hands in the economy will continuously approach the total money value of the goods and services that change hands in the economy.

Later economists repeat the equation all the more regularly as:
$\begin&M\ \times\ V\ =\ P\ \times\ Q\&\textbf\&Q\ =\ \text\&P\ \times\ Q\ =\ \text\end$
So presently the equation of exchange says that total nominal expenditures is generally equivalent to total nominal income.

The equation of exchange has two primary purposes. It addresses the primary articulation of the quantity theory of money, which relates changes in the money supply to changes in the overall level of prices. Furthermore, tackling the equation for M can act as an indicator of the demand for money in a macroeconomic model.

The Quantity Theory of Money

In the quantity theory of money, in the event that the velocity of money and real output are assumed to be steady, to seclude the relationship between money supply and price level, then, at that point, any change in the money supply will be reflected by a proportional change in the price level.

To show this, first settle for P:
$P\ =\ M\ \times\ \left(\frac\right)$
Furthermore, separate with respect to time:
$\frac\ =\ \frac$
This means inflation will be proportional to supply any increase in the money. This then turns into the fundamental thought behind monetarism and the catalyst for Milton Friedman's decree that, "Inflation is dependably and wherever a monetary phenomenon."

Money Demand

On the other hand, the equation of exchange can be utilized to determine the total demand for money in an economy by settling for M:
$M\ =\ \left(\frac{P\ \times\ Q}\right)$
Expecting that money supply is equivalent to money demand (i.e., that financial markets are in equilibrium):
$M_D\ =\ \left(\frac{P\ \times\ Q}\right)$
Or on the other hand:
$M_D\ =\ \left(P\ \times\ Q\right)\ \times\ \left(\frac{1}\right)$
This means the demand for money is proportional to nominal income and the inverse of the velocity of money. Economists regularly decipher the inverse of the velocity of money as the demand to hold cash balances, so this rendition of the equation of exchange shows that the demand for money in an economy is comprised of demand for use in transactions, (P x Q), and liquidity demand, (1/V).

Features

• The equation of exchange is a mathematical articulation of the quantity theory of money.
• In its essential form, the equation says that the total amount of money that changes hands in an economy equals the total money value of goods that change hands, or that nominal spending equals nominal income.
• The equation of exchange has been utilized to contend that inflation will be proportional to changes in the money supply and that total demand for money can be broken down into demand for use in transactions and demand to hold money for its liquidity.