Equation of the definition of exchange
What is the exchange equation?
The exchange equation is an economic identity that shows the relationship between the money supply, the speed of money, the price level and an expenditure index. Classical English economist John Stuart Mill derived the exchange equation, based on earlier ideas by David Hume. He says the total amount of money changing hands in the economy will always equal the total dollar value of goods and services changing hands in the economy.
Key points to remember
- The exchange equation is a mathematical expression of the quantitative theory of money.
- In its basic form, the equation says that the total amount of money changing hands in an economy is equal to the total monetary value of goods changing hands, or that nominal expenditure is equal to nominal income.
- The exchange equation has been used to argue that inflation will be proportional to changes in the money supply and that the total demand for money can be decomposed into demand for use in transactions and demand for holding money for its liquidity. .
Understanding the exchange equation
The original form of the equation is:
M × V = P × Tor:M= the money supply, or the average monetary units inV= the speed of money, or the average number ofP=the average level of commodity prices during the year
M x V can then be interpreted as the average number of currency units in circulation in a year, multiplied by the average number of times each currency unit changes hands in that year, which is equal to the total amount of money spent in an economy during the year. .
On another side, P x T can be interpreted as the average price level of goods during the year multiplied by the real value of purchases in an economy during the year, which is equal to the total money spent on purchases in an economy during the year ‘year.
So, the exchange equation says that the total amount of money changing hands in the economy will always equal the total dollar value of goods and services changing hands in the economy.
Later economists reformulate the equation more often as follows:
M × V = P × Qor:Q = an index of actual expenditure
So now the trading equation says that total nominal expenses are always equal to total nominal income.
The exchange equation has two main uses. It represents the main expression of the quantitative theory of money, which relates changes in the money supply to changes in the overall price level. In addition, solving the equation for M can serve as an indicator of the demand for money in a macroeconomic model.
The quantitative theory of money
In the quantitative theory of money, if the speed of money and real output are assumed to be constant, in order to isolate the relationship between the money supply and the price level, then any change in the money supply will be reflected by a change proportional to the price level.
To show this, first solve for P:
P = M × (QV)
And differentiate in relation to time:
DtDP = DtDM
This means that inflation will be proportional to any increase in the money supply. This then becomes the fundamental idea behind monetarism and the impetus for Milton Friedman’s saying that “Inflation is always and everywhere a monetary phenomenon”.
Alternatively, the exchange equation can be used to derive the total demand for money in an economy by solving for M:
M = (VP × Q)
Assuming that the money supply equals the demand for money (i.e. financial markets are in equilibrium):
MD = (VP × Q)
MD = (P × Q) × (V1)
This means that the demand for money is proportional to nominal income and the inverse of the speed of money. Economists generally interpret the inverse of the speed of money as the demand to hold cash balances, so this version of the trading equation shows that the demand for money in an economy is made up of the demand for money. ‘use in transactions, (P x Q), and demand for liquidity, (1 / V).