The Magic of Money Velocity

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 had increased by 10 percent in a given year, while the price level—as measured by the consumer price index—has remained unchanged, it would mean that there must have been a slowing down of 10 percent in the velocity of money circulation.

If the quantity of money had remained unchanged, but there has been a 10 percent increase in the price level in a given period, it would mean that there must have been a 10 percent increase in the velocity of money circulation in that period. It would appear, therefore, that the velocity of money circulation is an important determinant of the purchasing power of money.

Velocity and the Mainstream View

For example, during a given year, a particular $10 bill may be used as follows: a baker, John, pays $10 to a tomato farmer, George. The tomato farmer uses the $10 bill to buy potatoes from Bob, who uses the $10 bill to buy sugar from Tom. The $10 here served in three transactions. This means that the $10 bill was used three times during the year; its velocity of circulation is therefore three. A $10 bill—circulating with a velocity of three—financed $30 worth of transactions in that year.

Let us say that $3 billion dollars’ worth of transactions took place during a particular year. During that year, the average money stock in the economy stood at $500 million dollars. Consequently, one could infer that each dollar was used, on average, six times during the year. From this it is established that,

Velocity = Value of transactions / Stock of money

This expression can be also presented as,

V = P*T/M

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 will give us the following equation, known as the equation of exchange:

M*V = P*T 

This equation states that money multiplied by velocity equals the value of transactions. Some economists employ GDP at current prices 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.

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?

Money fulfills the role of the medium of exchange and not the means of payment. On this Mises wrote,

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 has changed hands has no relevance. What matters is that users of money have goods and services demanded by others, not money itself.

Imagine that money and velocity would have indeed been the means of funding or the means of payments. If this had been the case, then poverty worldwide could have been erased a long time ago. If rising velocity is supposed to boost the 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 a menace to society for he slows down the velocity of money and hence the generation of wealth.

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.

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, people exchange in a value-for-value transaction. The price is the outcome of different ends, and hence, the different importance that both parties to a trade assign to means. The fact that velocity is three or any other number has nothing to do with goods prices and the purchasing power of money. Individual’s purposeful actions determine the prices of goods and not the velocity of money. Causes emanate from individuals and not various factors.

The Velocity of Money 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). 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.

Furthermore, the average purchasing power of money cannot be established. For instance, in a transaction, the price of $1 was charged for one loaf of bread. In another transaction, the price of $1 was established for five pounds of potatoes. In a third transaction, $1 is charged for one pound of sugar. Since bread, potatoes, and sugar are not commensurable, no average price of money can be established. An average of the numbers can be found, but it is meaningless. Hence, 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. On this Rothbard wrote,

Thus, any concept of average price level involves adding or multiplying quantities of completely different units of goods, such as butter, hats, sugar, etc., and is therefore meaningless and illegitimate.

Conclusion

The velocity of money doesn’t have a life of its own. It is not an independent entity and, hence, it can’t cause anything. Contrary to popular thinking, money does not circulate. Money always belongs to somebody.