# Quantity Theory of Money

The quantity theory of money states that the price level that prevails in an economy is the direct consequence of the money supply. If the velocity of money is constant, any increase in money supply causes a proportionate increase in price level.

The quantity theory of money is the classical interpretation of what causes inflation. It states that if the number of times a dollar is used for a transaction, i.e. the money’s velocity is constant, any increase in quantity of money changes only prices and not the real output.

## Equation of Exchange

Let P be the price index, i.e. an assessment of the overall price level and Y the real GDP, the equation for nominal value of an economy’s output can be written as follows:

$$\text{Output}=\text{P}\times \text{Y}$$

Let M be the amount of money in the economy and V the velocity i.e. the average number of times each dollar changes hands, the dollar sum of all transactions that occur in the economy is given by the following equation:

$$\text{Transactions}\ =\ \text{M}\ \times \text{V}$$

The total dollar value of transactions that occur in an economy must equal the nominal value of total output. We can write this as follows:

$$\text{Sum of Transactions}=\text{Nominal Output}$$

$$\text{M}\ \times \text{V}=\text{P}\times \text{Y}$$

The equation above is called the quantity equation or equation of exchange. It means that when the velocity of money doesn’t change, any increase in money causes increase in price level.

## Velocity of Money

The quantity theory of money assumes that the circulation of money in an economy is constant. The circulation of money in measured by its velocity. Velocity of money is the average turnover of a dollar i.e. it is the number of times a dollar is used in a transaction over a period of time.

The quantity theory of money can be defined using the definition of velocity i.e. velocity must equal the value of economy’s output measured in today’s dollars divided by number of dollars in the economy:

$$\text{V}=\frac{\text{PY}}{\text{M}}$$

If V is constant, P and M must balance each other.

Empirical studies show that velocity of money has indeed remained stable over the long-run. However, in the short-run, it can exhibit certain variability. If the change in velocity of money is significant the conclusion of quantity theory of money do not hold.

## Example

Nominal GDP of Winterfell was 3.2 million golden dragons (the currency of Westeros) in 270 AC. Corresponding real GDP based on 260 AC prices was 3 million golden dragons. If the velocity of money is 10, what is the quantity of money that circulated in Winterfell? If the money supply increases by 10% next year but the real GDP remains the same, what would be the nominal GDP and what’s the percentage increase in price?

Using the equation of exchange, we can find the value of M using the following equation:

$$\text{M}=\frac{\text{3,200,000}}{\text{10}}=\text{320,000}$$

A 10% increase in quantity of money means that the new money supply is 352,000 golden dragons. If the real GDP is constant, the nominal GDP next year would be 3,520,000 golden dragons:

$$\text{PY}=\text{10}\times\text{352,000}=\text{3,520,000}$$

Since the real GDP is constant, the increase in nominal GDP of 10% is solely due to change in prices:

$$\text{Increase in Price}=\frac{\text{3,520,000}-\text{3,200,000}}{\text{3,200,000}}=\text{10%}$$