Mises Wire

# Understanding Money Velocity and Prices

Frank Shostak

The yearly growth rate of US's "Austrian money supply" jumped by almost 80 percent in February 2020 (see chart). Given such massive increase in money supply, it is tempting to suggest that this lays the foundation for an explosive increase in the annual growth of prices of goods and services sometime in the future.

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Some experts are of the view that what matters for increases in the momentum of prices is not just increases in money supply but also the velocity of money—or how fast money circulates. The velocity of AMS fell to 2.4 in June this year from 6.8 in January 2008. In this way of thinking, a decline in money velocity is going to offset the strong increase in money supply. Hence, the effect on the momentum of goods prices is not going to be that dramatic. What is the rationale behind all this?

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#### The Popular View of What Velocity Is

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 might be used as follows: a baker, John, pays the 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 financed \$30 worth of transactions in that year. Now, if there are \$3 trillion 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 is used on average six times during the year (since 6*\$500 billion =\$3 trillion). Five hundred billion dollars by means of a velocity factor have effectively become \$3 trillion. 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 could 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 a 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 an unstable velocity implies an unstable demand for money, which makes it so much harder for the central bank to navigate the economy toward the path of economic stability.

#### Does the Concept of Money Velocity 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. But actually 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 kilograms 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 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 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 baker’s 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 were indeed been the means of funding or the means of payments. If this were the case, then poverty worldwide could have been erased a long time ago. If rising velocity is boosts effective funding, then it would be 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. But does not make any sense to argue that money circulates, as the popular thinking has it. It always belongs to somebody.

According to Ludwig von Mises, 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. (Human Action, p. 403).

#### Why Velocity Has Nothing to Do with the Purchasing Power of Money

Does velocity have anything to do with the prices of goods? According to 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 kilograms 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 kilograms 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 agreed that it is a good deal to exchange ten loaves of bread for ten dollars, for it will enable him to procure five kilograms 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 kilograms 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. Individuals' 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,

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

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 ten dollars equals ten dollars. 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 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 a half kilogram of potatoes, while in the third transaction the price was one kilogram 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 an individual’s goals, he/she may decide that at present it is to his/her benefit to hold less money. Sometime in the future, he/she might decide that raising his/her demand for money would serve better his/her goals. What could possibly be wrong with this? The same goes for any other goods and services—demand for them changes all the time.

#### Conclusions

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 offset the effect of increases in money supply on the momentum of prices of goods. In addition, velocity cannot strengthen the means of funding, as conveyed by the equation of exchange, which is religiously followed by most economists and economic commentators.

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