Mises Wire

Money Velocity and Economic Growth

After rising to 2.198 in Q3 1997, the ratio of US Gross Domestic Product (GDP) to money supply M2 fell to 1.433 by Q3 2017. Since then the ratio has bounced slightly to 1.457 in Q1 2019. Economists label this ratio as the velocity of money.

Some experts regard the steep decline in the ratio as an ominous sign for the economy in the months ahead since it raises the likelihood of a sharp decline in the growth rate of prices.



This in turn raises the likelihood of price deflation and in turn of a severe economic slump. It is also held that a fall in the ratio raises the likelihood that monetary injections by the Fed are going to become ineffective in the event that the US central bank will attempt to revive the economy once it falls into an economic slump.

What is the rationale behind this way of thinking?

The Popular View of Money Velocity

According to popular thinking, the idea of velocity is straightforward. It is held that over any interval of time, such as a year, a given amount of money can be used repeatedly to finance people’s purchases of goods and services.

The money one person spends for goods and services at any given moment can be used later by the recipient of that money to purchase yet other goods and services. For example, during a year a particular ten-dollar bill can be used as follows: a baker John pays ten-dollars to a tomato farmer George. The tomato farmer uses the ten-dollar bill to buy potatoes from Bob who uses the ten-dollar bill to buy sugar from Tom. The ten-dollars here served in three transactions. This means that the ten-dollar bill was used three times during the year, its velocity is therefore three.

A $10 bill, which is circulating with a velocity of ‘3’ was used to finance $30 worth of transactions in that year. Now, if there are $3000 billion worth of transactions in an economy during a particular year and there is an average money stock of $500 billion during that year, then each dollar of money is used on average six times during the year (since 6*$500 billion =$3000).

Hence $500 billion by means of a velocity factor has effectively become $3000 billion. This implies that the velocity of money can boost the means of finance. From this it is established that,

Velocity = Value of transactions / stock of money

This expression can be also presented as,

V = P*T/M

Where V stands for velocity, P stands for the average price, T stands for the volume of transactions and M stands for the stock of money. This expression can be further rearranged by multiplying both sides of the equation by M. This in turn will give us the famous equation of exchange

M*V = P*T

This equation states that money multiplied by velocity equals the value of transactions. Many economists employ GDP instead of P*T thereby concluding that

M*V = GDP = P*(real GDP)

The equation of exchange appears to offer a wealth of information regarding the state of an economy. For instance, if one were to assume a stable velocity, then for a given stock of money one can establish the value of GDP. Furthermore, information regarding the average price or the price level allows economists to establish the state of the real output and its growth rate. Note that from the equation of exchange a fall in the velocity of money (V) for a given money (M) results in a decline in economic activity as depicted by GDP. In addition, for given money (M) and a given volume of transactions (T) a fall in velocity results in a decline in the average price (P).

For most economists the equation of exchange is regarded as a very useful analytical tool. The debates that economists have are predominantly with respect to the stability of velocity. If velocity is stable then money becomes a very powerful tool in tracking the economy.

The importance of money as an economic indicator however diminishes once velocity becomes less stable and hence less predictable. It is held that unstable velocity implies an unstable demand for money, which makes it so much harder for the central bank to navigate the economy towards the path of economic stability.

Does the concept of velocity of money make sense?

From the equation of exchange, i.e. M*V = GDP it would appear that for a given stock of money an increase in velocity helps to finance a greater value of transactions than money could have done by itself.

As logical as it sounds, neither money nor velocity have anything to do with financing transactions. Here is why.

Consider the following: a baker John sold ten loaves of bread to a tomato farmer George for ten dollars. Now, John exchanges the ten dollars to buy five kg of potatoes from Bob the potato farmer. How did John pay for potatoes? He paid with the bread he produced.

Note that John the baker had financed the purchase of potatoes not with money but with bread. He paid for potatoes with his bread using money to facilitate the exchange. Money fulfils here the role of the medium of exchange and not the means of payment. (John has exchanged bread for money and then money is exchanged for potatoes i.e. something is exchanged for something with the help of money).

The number of times money changed hands has no relevance whatsoever on the bakers’ ability to fund the purchase of potatoes. What matters here is that he possesses bread that serves as the means of payment for potatoes.

Imagine that money and velocity would have indeed been the means of funding or the means of payments. If this would have been the case then poverty worldwide could have been erased a long time ago. If rising velocity is supposed to boost effective funding then it would have been to everyone’s benefit to make sure that money circulates as fast as possible. This implies that anyone who holds on to money should be classified as menace to the society for he slows down the velocity of money and hence the creation of real wealth. In addition, it does not make any sense to argue that money circulates as popular thinking has it. It always belongs to somebody. According to Ludwig von Mises in Human Action, money never circulates as such,

Money can be in the process of transportation, it can travel in trains, ships, or planes from one place to another. But it is in this case, too, always subject to somebody’s control, is somebody’s property.

Why velocity has nothing to do with the purchasing power of money

Does velocity have anything to do with the prices of goods? From the equation of exchange for a given M and the volume of transactions (T) a fall in velocity V results in a decline in the average prices (P) i.e. P= (M/T)*V. This is erroneous.

Prices are the outcome of individuals’ purposeful actions. Thus, John the baker holds that he will raise his living standard by exchanging his ten loaves of bread for ten dollars, which will enable him to purchase five kg of potatoes from Bob the potato farmer. Likewise, Bob has concluded that by means of ten dollars he will be able to secure the purchase of ten kg of sugar, which he holds will raise his living standard.

By entering an exchange, both John and Bob are able to realize their goals and promote their respective well-being. John had agreed that it is a good deal to exchange ten loaves of bread for ten dollars for it will enable him to procure five kg of potatoes. Likewise, Bob had concluded that ten dollars for his five kg of potatoes is a good price for it will enable him to secure ten kg of sugar. Observe that price is the outcome of different ends, and hence the different importance that both parties to a trade assign to means. Individual’s purposeful actions determine the prices of goods and not velocity. The fact that so-called velocity is ‘3’ or any other number has nothing to do with goods prices and the purchasing power of money as such. According to Mises (again, in Human Action),

In analyzing the equation of exchange one assumes that one of its elements--total supply of money, volume of trade, velocity of circulation--changes, without asking how such changes occur. It is not recognized that changes in these magnitudes do not emerge in the Volkswirtschaft [political economy, or more loosely ‘economy’] as such, but in the individual actors’ conditions, and that it is the interplay of the reactions of these actors that results in alterations of the price structure. The mathematical economists refuse to start from the various individuals’ demand for and supply of money. They introduce instead the spurious notion of velocity of circulation fashioned according to the patterns of mechanics (Human Action p 399).

Velocity Does Not Have an Independent Existence

Contrary to popular way of thinking velocity is not an independent entity - it is always the value of transactions P*T divided into money M i.e. P*T/M. On this Rothbard wrote (Man Economy and State p 735),

But it is absurd to dignify any quantity with a place in an equation unless it can be defined independently of the other terms in the equation.

Given that V is P*T/M it follows that the equation of exchange is reduced to M*(P*T)/M = P*T, which is reduced to P*T = P*T, and this is not a very interesting truism. It is like stating that $10=$10. This tautology conveys no new knowledge of economic facts.

Since velocity is not an independent entity, it as such causes nothing and hence cannot offset the effects from money supply growth. Velocity also cannot increase the means of funding as the equation of the exchange implies.

Moreover, the average purchasing power of money cannot be even established. For instance, in a transaction the price of one dollar was established as one loaf of bread. In another transaction, the price of one dollar was established as half kg of potatoes, while in the third transaction the price is one kg of sugar. Observe that since bread, potatoes and sugar are not commensurable no average price of money can be established.

Now, if the average price of money cannot be established it follows that the average price of goods (P) cannot be established either. Consequently, the entire equation of exchange falls apart. Conceptually the whole thing is not a tenable proposition and covering it in mathematical clothing cannot make it more tenable.

Additionally, does so-called unstable velocity imply an unstable demand for money? The fact that people change their demand for money does not imply instability. Because of changes in individual’s goals, they may decide that at present it is to their benefit to hold less money. Sometime in the future, they might decide that raising their demand for money would serve better their goals. So what could possibly be wrong with this? It is the same that goes for any other goods and services — demand for them changes all the time.


A massive decline in the velocity of money M2 since Q3 1997 raises an alarm among some commentators that at some stage this could result in a visible price deflation. This in turn runs the risk of plunging the US economy into a severe economic slump. But, if this were to happen, the reason would be not a fall in the velocity of money, but a decline in the subsistence fund because of loose monetary policies. Contrary to popular thinking, the velocity of money does not have a life of its own. It is not an independent entity and hence it cannot cause anything, let alone price deflation.

Note: The views expressed on Mises.org are not necessarily those of the Mises Institute.
What is the Mises Institute?

The Mises Institute is a non-profit organization that exists to promote teaching and research in the Austrian School of economics, individual freedom, honest history, and international peace, in the tradition of Ludwig von Mises and Murray N. Rothbard. 

Non-political, non-partisan, and non-PC, we advocate a radical shift in the intellectual climate, away from statism and toward a private property order. We believe that our foundational ideas are of permanent value, and oppose all efforts at compromise, sellout, and amalgamation of these ideas with fashionable political, cultural, and social doctrines inimical to their spirit.

Become a Member
Mises Institute