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 interrelationships must be understood.

Inflation typically 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. The factors affecting aggregate demand and supply are complex, but the role of money is significant. Because of its simplicity and the obvious connection, economists have studied the role of money variables as causes of inflation, especially the supply of money and the velocity of money.

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

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 this simple scenario. You provide a service for the government.

  1. The government decides to create $100 and pay you with it.
  2. You use that $100 to buy groceries.
  3. The grocery story uses that $100 it received from you to pay its suppliers.
  4. 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.

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 (V) directly, it can be determined from government statistics on the quantity of money (M) and the nominal GDP, 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:

M × V = P × Y = Nominal GDP



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.

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 the MZM money stock from January 1, 1959 - October 1,2017, with gray areas depicting periods of recession. MZM stands for Money Zero Maturity, which consists of currency and coins plus all financial assets that are redeemable at par on demand, including traveler's checks, demand deposits, other checkable deposits, savings deposits, all money market funds, but not time deposits. In other words, MZM money is M2 money minus time deposits. Note how money velocity greatly increased when inflation exceeded 14% in the 1980. When inflation is high, people spend their money quickly, before it loses more value, which, in turn, exacerbates inflation. Inflation finally declined substantially, when the Federal Reserve, under Paul Volcker, raised interest rates and slowed money growth. During the Great Recession in 2008 - 2009, money velocity dropped substantially and has fallen further during the low-inflation period from 2010 - 2017.
Graph of the velocity of the MZM money stock from January 1, 1959 - October 1,2017, with gray areas depicting periods of recession.

If money velocity is constant, then:

Money Growth = Real GDP Growth + Inflation

or, rearranged:

Inflation = Money Growth – Real GDP Growth


Inflation = ∆P = ∆M – ∆Y

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 exceeds real GDP growth.

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

Inflation = Money Growth


∆P = ∆M

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 increases aggregate demand, which increases prices.
Graph showing how changes in the money supply changes aggregate demand, which, in turn, changes average prices in the economy.

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.

What Is the Ideal Inflation Rate?

To facilitate consumer and business planning, the inflation rate should be low, study, and predictable. It should not be negative, because, otherwise, consumers and firms will hold money instead of spending it, thereby depressing the economy. Such was the state of Japan for many years. It is also the reason why Bitcoin and other cryptocurrencies with a defined quantity limit will never serve as the official currency.

Should the inflation rate be 0? If the inflation rate were 0, then central banks would have less leeway in stimulating the economy. Central banks can stimulate the economy by lowering the real interest rate (r), which is equal to the nominal interest rate (i) minus the inflation rate (π):

i = r + π, therefore r = i – π

If the inflation rate is 0, then the real interest rate will equal the nominal interest rate, so the real interest rate cannot be made lower than 0. By accepting some inflation, the real interest rate can be negative by setting the nominal interest rate below the inflation rate, which can be an effective tool for stimulating the economy.

Another benefit of a low, nonzero inflation rate is that it helps to lower taxes, since the government benefits directly from an expansion of the money supply. For instance, a government can use the new money supply as a source of revenue or as a means of decreasing the real interest rate on its debt securities. For instance, the United States government issues T-bills that often pay a lower interest rate than the inflation rate. Even the interest rates paid on 10-year Treasuries during the decade after the Great Recession was little more than the inflation rate.

Although inflation is also a form of tax, consumers and firms often find ways to lower their actual inflation of their money by finding other ways of saving or finding cheaper substitutes of what they usually buy.

Money Growth, Money Velocity, and Inflation