### Introduction to Quantity Theory

The relationship between the supply of money and inflation, as well as deflation, is an important concept in economics. The quantity theory of money is a concept that can explain this connection, stating that there is a direct relationship between the supply of money in an economy and the price level of products sold.

Read on for a further explanation of the quantity theory of money, its levels and growth rates equation forms and thoughts on its effect on real output.

### What Is the Quantity Theory of Money?

The quantity theory of money is the idea that the supply of money in an economy determines the level of prices, and changes in the money supply result in proportional changes in prices.

In other words, the quantity theory of money states that a given percentage change in the money supply results in an equivalent level of inflation or deflation.

This concept is usually introduced via an equation relating money and prices to other economic variables, which will now be explained.

### The Quantity Equation and Levels Form

Let's go over what each variable in the above equation represents.

- M represents the amount of money available in an economy; the money supply
- V is the velocity of money, which is how many times within a given period, on average, a unit of currency gets exchanged for goods and services
- P is the overall price level in an economy (measured, for example, by the GDP deflator)
- Y is the level of real output in an economy (usually referred to as real GDP)

The right side of the equation represents the total dollar (or other currency) value of output in an economy (known as nominal GDP). Since this output is purchased using money, it stands to reason that the dollar value of output has to equal the amount of currency available times how often that currency changes hands. This is exactly what this quantity equation states.

This form of the quantity equation is referred to as the "levels form" since it relates the level of money supply to the level of prices and other variables.

### A Quantity Equation Example

Let's consider a very simple economy where 600 units of output are produced and each unit of output sells for $30. This economy generates 600 x $30 = $18,000 of output, as shown in the right-hand side of the equation.

Now suppose that this economy has a money supply of $9,000. If it is using $9,000 of currency to purchase $18,000 of output, then each dollar has to change hands twice on average. This is what the left-hand side of the equation represents.

In general, it's possible to solve for any one of the variables in the equation as long as the other 3 quantities are given, it just takes a bit of algebra.

### Growth Rates Form

The quantity equation can also be written in "growth rates form," as shown above. Not surprisingly, the growth rates form of the quantity equation relates changes in the amount of money available in an economy and changes in the velocity of money to changes in the price level and changes in output.

This equation follows directly from the levels form of the quantity equation using some basic math. If 2 quantities are always equal, as in the levels form of the equation, then the growth rates of the quantities must be equal. In addition, the percentage growth rate of the product of 2 quantities is equal to the sum of the percentage growth rates of the individual quantities.

### Velocity of Money

The quantity theory of money holds if the growth rate of the money supply is the same as the growth rate in prices, which will be true if there is no change in the velocity of money or in real output when the money supply changes.

Historical evidence shows that the velocity of money is pretty constant over time, so it's reasonable to believe that changes in the velocity of money are in fact equal to zero.

### Long-Run and Short Run Effects on Real Output

The effect of money on real output, however, is a bit less clear. Most economists agree that, in the long run, the level of goods and services produced in an economy depends primarily on the factors of production (labor, capital, etc.) available and the level of technology present rather than the amount of currency circulating, which implies that the money supply cannot affect the real level of output in the long run.

When considering the short-run effects of a change in the money supply, economists are a bit more divided on the issue. Some think that changes in the money supply are reflected solely in price changes rather quickly, and others believe that an economy will temporarily change real output in response to a change in the money supply. This is because economists either believe that the velocity of money is not constant in the short run or that prices are "sticky" and don't immediately adjust to changes in the money supply.

Based on this discussion, it seems reasonable to take the quantity theory of money, where a change in the money supply simply leads to a corresponding change in prices with no effect on other quantities, as a view of how the economy works in the long run, but it doesn't rule out the possibility that monetary policy can have real effects on an economy in the short run.