§ 2 (to Chapter II, § 5) The Concept of Velocity of Circulation

The velocity of circulation of money has been defined as a ratio of the money expended to the average money on hand, that is, as a rate of turnover. A rate of turnover differs from the popular concept of velocity. The latter regards velocity as the average number of times money changes hands from one person to another; whereas, the concept we have employed treats velocity as the average number of coins which pass through one man's hands, divided by the average amount held by him. The difference between the two concepts is very similar to that between two methods of obtaining the velocity of a railway train. One method is to follow the train for a certain number of miles, and note how long a time it takes to travel those miles. The other is to stand on a certain spot beside the track and note the time consumed by a given length of train in passing that spot. Following the train from place to place is like following a coin from person to person, while watching the train pass one point is like observing the rate of turnover of one person's purse. We may distinguish the two methods as the "coin-transfer" method and the "person-turnover" method. Both methods, if correctly employed, yield the same result. But in the coin-transfer method, an important distinction is usually overlooked, the distinction between the gross and net circulation of money. What is desired is the rate at which money is used for purchasing goods, not for "making change." The result is the difference between the number of times each piece changes hands against goods, and the number of times it changes hands with goods. If a $10 bill is transferred in purchase of goods and $2 is given back "in change," the actual money expended for goods is measured, not by $12, the gross transfer of money, nor yet by $10, the gross amount transferred against goods, but by $8, the net amount paid for goods.

If it is desired, in the coin-transfer method, to learn the average velocity of circulation of two pieces of money, such as a dollar and a ten-cent piece, we must not only find the net rate of turnover of each coin, but also take account of the discrepancy between the buying efficiencies of the two coins. Let it be assumed that during the year the dollar is passed 115 times against goods and 15 times with goods, so that its net velocity of circulation is 115 - 15 or 100. If we suppose the velocity of the ten-cent piece to be 290 - 90 or 200, the average velocity of the two must somehow take account of the different values of different denominations. A dollar is the equivalent of ten dimes. Its rapidity of circulation should therefore be "weighted" tenfold in order to get the real average, that is, the average of the service performed by the two. The net rate of circulation of 100 for the dollar is equivalent to a net velocity of circulation of 100 for each and every one of ten dimes. It follows that the average velocity of the two coins is, a result much closer to the velocity of the dollar than to that of the dime. With these two safeguards against error applied to the coin-transfer method, it is easy to see that the coin-transfer method will yield the same results as the person-turnover method.

There is yet another magnitude which should be considered in connection with the velocity of monetary circulation. This may be called the average time of turnover, i.e. the average amount of time consumed by all the given money, in being turned over once. This is the "reciprocal" of velocity. If money changes hands twenty times in a year, it turns over, on the average, once in 1/20 of a year, or once in somewhat over 18 days. This is its average time of turnover. If the average velocity of circulation or rate of turnover is forty times a year, then the average time of turnover is 1/40 of a year or about 9 days. Or, instead of considering all the given money directly, let us come at it through a component part of it. If a man having, on the average, $10 in his pocket every day, expends on the average $1 a day, he evidently turns over 1/10 of his money each day. Since to turn over 1/10 of his average stock each day is to turn over the whole of it 36½ times a year or once in 10 days, the time of turnover will be 10 days. If the man under consideration had a pocketbook arranged with a series of ten one dollar bills, and every day, as one was taken from the top to be expended, another were added at the bottom, evidently any and every bill would remain in his hands just ten days traveling from the bottom to the top of the pile.