Reprinted from Mises.org
For most financial commentators an important factor that either reinforces or weakens the effect of changes in money supply on economic activity and prices is a velocity of money.
It is alleged that when the velocity of money rises, all other thing being equal, the buying power of money declines (i.e., the prices of goods and services rise). The opposite occurs when velocity declines.
If, for example, it was found that the quantity of money had increased by 10% 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 about 10% in the velocity of circulation.
The mainstream 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 again and again 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 have been used as following: 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 3 times during the year, its velocity is therefore 3.
A $10 bill, which is circulating with a velocity of ‘3’ financed $30 worth of transactions in that year. Consequently, 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 6 times during the year (since 6*$500 billion =$3000).
The $500 billion of money is boosted by means of a velocity factor to become effectively $3000 billion. From this it is established that
Velocity = Value of transactions / supply of money
This expression can be summarized as
V = P*T/M
Where V stands for velocity, P stands for average prices, T stands for volume of transactions and M stands for the supply of money. This expression can be further rearranged by multiplying both sides of the equation by M. This in turn will give the famous equation of exchange
M*V = P*T
This equation states that money times velocity equals 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 the 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 real output and its rate of growth.
Most economists take the equation of exchange very seriously. The debates that economists have are predominantly with respect to the stability of velocity. Thus 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 an unstable velocity implies an unstable demand for money, which makes it so much harder for the central bank to navigate the economy along the path of economic stability.
Why velocity has nothing to do with the purchasing power of money
But does velocity have anything to do with the prices of goods? Prices are the outcome of individuals’ purposeful actions. Thus the baker John believes that he will raise his living standard by exchanging his ten loaves of bread for $10 which will enable him to purchase five kg of potatoes from Bob the potato farmer. Likewise, Bob has concluded that by means of $10 he will be able to secure the purchase of ten kg of sugar, which he believes will raise his living standard.
By entering an exchange, both John and Bob are able to realize their goals and thus promote their respective well-being. John had agreed that it is a good deal to exchange 10 loaves of bread for $10 for it will enable him to procure 5kg of potatoes. Likewise Bob had concluded that $10 for his 5kg of potatoes is a good price for it will enable him to secure 10kg 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.
It is individuals’ purposeful actions that determine the prices of goods and not some mythical velocity.
Indeed, according to Mises in Human Action, the whole concept of velocity is hollow;
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.
Furthermore, 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.
Consequently, the fact that so-called velocity is ‘3’ or any other number has nothing to do with average prices and the average purchasing power of money as such. Moreover, the average purchasing power of money cannot even be 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 0.5kg 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 can’t be established it means that the average price of goods can’t be established either. Consequently, the entire equation of exchange falls apart. Conceptually the whole thing is not a tenable proposition and covering a fallacy in mathematical clothing cannot make it less fallacious.
According to Rothbard in Man, Economy, and State:
The only knowledge we can have of the determinants of price is the knowledge deduced logically from the axioms of praxeology. Mathematics can at best only translate our previous knowledge into relatively unintelligible form.
Even if we were to accept that the essential service of money is its speed of circulation there is no way that this characteristic of money could explain the purchasing power of money. On this Mises explains in Human Action:
Even if this were true, it would still be faulty to explain the purchasing power — the price — of the monetary unit on the basis of its services. The services rendered by water, whisky, and coffee do not explain the prices paid for these things. What they explain is only why people, as far as they recognize these services, under certain further conditions demand definite quantities of these things.