Money Growth, Money Velocity, and Inflation

Because low, stable inflation is necessary for optimal economic growth, it is one of the main economic objectives of central banks, which they try to control by using their tools of monetary policy. However, to control inflation, its causes and their interrelationship must be understood.

The classical theory of inflation, as espoused by the philosopher David Hume and other early thinkers, only considered money growth, which is the increase in the money stock supplied by the government, to be the main cause of inflation, but money growth is a necessary, but not sufficient, condition for inflation. The velocity of money must also be considered, since there can be no inflation unless the money is spent. For instance, if the money supply has expanded, but the people take it home and stuff it in their mattresses, then it will have no effect on inflation.

Velocity of Money

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Inflation results when the providers of goods and services raise their prices because of an increased aggregate demand, which is the demand of all goods and services in an economy. As is well-established in economics, when aggregate demand increases relative to aggregate supply, which is the supply of all goods and services in an economy, prices increase. The greater the increase in demand relative to supply, the greater the inflation rate.

When people receive money, they eventually spend it by giving it to someone else in exchange for a product or service. In turn, the person who received the money will also eventually spend it, and so on.

Imagine a simple scenario. You provide a service for the government. The government decides to create $100 and pay you with it. You use that $100 to buy groceries. The grocery story uses that $100 it received from you to pay its suppliers. The suppliers uses that $100 to pay their own employees.

In this simple scenario, the government created $100, but that $100 was used for $400 worth of transactions, and that $100 will continue on in many other financial transactions. When people receive more money, they tend to spend more, so this increases aggregate demand, which will eventually cause businesses to raise prices. However, since this process does take time, increases either in the money supply or in the velocity of money will not immediately raise prices. So the following discussion will focus only on the long-term effects.

How fast money changes hands per unit of time is called the velocity of money:

Velocity of Money =Average Number of Times an Average Dollar is Spent to Buy Final Goods and Services
Unit of Time

To determine the effect on inflation, changes in money growth or in the velocity of money must be compared to the growth of goods and services provided by an economy, which, in the United States, is measured by the Gross Domestic Product (GDP).

Real GDP is the aggregate quantity of the goods and services provided by the United States economy. Nominal GDP is the sum of the prices of those goods and services, which is essentially calculated by multiplying the price of each good or service times it's quantity. Since money is used in virtually every transaction and because nominal GDP is the price of all final goods and services provided by the economy, the following relation must be true:

Nominal GDP = Quantity of Money × Velocity of Money

Although it is virtually impossible to measure the velocity of money directly, it can be determined from government statistics on the quantity of money (M) and the nominal GDP, from which the velocity of money (V) can be determined by dividing the nominal GDP by the quantity of money:

V =Nominal GDP

Since nominal GDP equals the real quantity of goods and services, or real GDP, commonly depicted as Y, times the prices (P) of those goods and services, then the following equation of exchange must also be true:


The equation of exchange can be transformed to yield prices in terms of the quantity and velocity of money divided by real GDP:


Hence, it can easily be seen that when either the quantity of money or the velocity of money or their combination increases faster than real GDP, then prices will increase in proportion to how much MV exceeds Y.

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It can also be derived from the equation of exchange, for small changes in the factors, that the change in money growth (∆M) plus the change in the velocity of money (∆V) equals the change in prices (∆P) plus the change in real GDP (∆Y):

∆M + ∆V = ∆P + ∆Y

Thus, as is evident from the above equation, if ∆Y is zero, then any increases in prices will result from either increases ∆M or ∆V.

However, the cause of inflation can be limited even further. The economist Irving Fisher realized, in the early 20th century, that when interest rates are fixed and there is no financial innovation that would alter the people's desire to hold money, then the velocity of money is relatively constant.

Graph of the velocity of money from 1994 - March 2011. The 2 gray areas are periods of recession. MZM stands for Money Zero Maturity, which is equal to M2 minus time deposits. In other words, think of money as being a bond or certificate of deposit with zero maturity.

If money velocity is constant, then:

Money Growth = Real GDP Growth + Inflation

or, rearranged:

Inflation = Money Growth – Real GDP Growth

With the above equation, it is easy to see that if money growth is equal to increases in real GDP, then there will be no inflation. Hence, a fast-growing economy will allow the government to create more money to help pay for its services without causing inflation. Inflation results when money growth is faster than real GDP growth.

Furthermore, since it takes time to develop economic resources and technology, real GDP is also relatively constant over the short run, so:

Inflation = Money Growth

Consequently, the inflation rate is directly proportional to money growth, which is referred to as the quantity theory of money. The equation for the quantity theory of money is derived from the equation of exchange by setting the velocity of money and real GDP constant. As the famed economist Milton Friedman has said, "Inflation is always and everywhere a monetary phenomenon."

Because real GDP is relatively constant over the short run, an increase in money supply causes an increase in aggregate demand, which causes an increase in prices.

Over the longer term, an increase in the money supply will increase real GDP by increasing aggregate demand. Likewise, a decrease in the money supply will decrease real GDP by decreasing aggregate demand.

In countries with hyperinflation, which is usually defined as an inflation rate higher than 50% per month, the money supply increases much faster than real GDP, causing rapid increases in prices, which causes people to spend the money that they receive as quickly as possible, before it diminishes in value. Hence, a very high inflation rate will also maximize the velocity of money, which will increase the inflation rate even further.

Although the velocity of money is relatively constant over the long term, it can fluctuate considerably over months or quarters, which will change the inflation rate over the short term. To predict short-term inflation rates, the causes of changes in the velocity of money, or the changes in the demand for money, must be understood and quantified.