# The velocity of money circulation myth

By Dr Frank Shostak

For most economists the velocity of money circulation is an important factor in determining the prices of goods and services.

If, for example, it was found that the quantity of money increased by ten percent in a given year, while the price level has remained unchanged it would mean that there must have been a decline of about ten percent in the velocity of money circulation.

If the quantity of money remained unchanged but there has been a ten percent increase in the price level in a given period, it would mean that there must have been an increase in the velocity of money circulation of ten percent in that period.

According to popular thinking, the idea of the velocity of money circulation is straightforward.  For example, during a given year a particular ten-dollar bill may 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-dollar here served in three transactions. This means that the ten-dollar bill was used three times during the year, its velocity of circulation is therefore three.

A ten-dollar bill, which is circulating with a velocity of three financed thirty-dollar worth of transactions in that year. Now, if there are three billion dollars’ worth of transactions in an economy during a particular year and the average money stock is five hundred million dollars during that year, then each dollar of money is used on average six times during the year. Five hundred million dollars of money by means of a velocity factor has effectively become three billion dollars. This implies that the velocity of money circulation 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. Some 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, for a given velocity and a given stock of money one can establish the value of GDP. 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.

Furthermore, information regarding the average price or the price level allows economists to establish the state of the real output.

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 the velocity of money circulation. It is held that 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 the velocity of circulation of money becomes less stable and hence less predictable.

On this way of thinking, an unstable velocity of the circulation of money implies an unstable demand for money, which makes it harder for the central bank to navigate the economy towards the path of economic stability.

Does the concept of velocity of money circulation make sense?

From the equation of exchange, it would appear that for a given stock of money an increase in its velocity of circulation helps to finance a greater value of transactions than money could have done by itself. However, does it make sense? Consider the following: a baker John sold the 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 the bread that he produced using money to facilitate the exchange. Money fulfils here the role of the medium of exchange and not the means of payment.  According to Mises,

Commodities, says Say, are ultimately paid for not by money, but by other commodities. Money is merely the commonly used medium of exchange; it plays only an intermediary role. What the seller wants ultimately to receive in exchange for the commodities sold is other commodities.

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.

Now, being the medium of the exchange money does not circulate it always belongs to somebody it is always somebody’s property. According to Mises,

There is no fraction of time in between in which the money is not a part of an individual’s or a firm’s cash holding, but just in circulation. It is unsound to distinguish between circulating and idle money.

Also according to Mises,

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.

The velocity of money circulation and goods prices

Does the velocity of money circulation have anything to do with the prices of goods? Prices are the outcome of individuals’ purposeful actions.

By entering an exchange, both John and Bob are able to realize their goals and promote their respective well-being. John had concluded 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 the ten dollars for his five kg of potatoes is a good price for it will enable him to secure the 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. The fact that so-called velocity is three or any other number has nothing to do with goods prices and the purchasing power of money as such. Individual’s purposeful actions determine the prices of goods and not velocity.

The velocity of money circulation does not have an independent existence

Contrary to mainstream economics velocity is not an independent entity – it is always the value of transactions P*T divided into money M i.e. P*T/M.  According to Rothbard,

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 becomes M*(P*T)/M = P*T, which is reduced to P*T = P*T, and this is not very interesting truism. It is like stating that \$10=\$10 this conveys no new knowledge of economic facts.

Also, 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 0.5 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.  The whole thing is not a tenable proposition and covering it in mathematical clothing cannot make it more tenable.

Additionally, does a so-called unstable velocity of money circulation 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, he may decide that at present it is to his benefit to hold less money. Sometime in the future, he might decide that raising his demand for money would serve better his 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.

Conclusion

Contrary to popular thinking, money does not circulate. Money always belongs to somebody.

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