§ 3. —Together with the Rapidity of Circulation.

It might be supposed that there is always in circulation in a country a quantity of money equal in value to the whole of the goods then and there on sale. But this would be a complete misapprehension. The money laid out is equal in value to the goods it purchases; but the quantity of money laid out is not the same thing with the quantity in circulation. As the money passes from hand to hand, the same piece of money is laid out many times before all the things on sale at one time are purchased and finally removed from the market; and each pound or dollar must be counted [pg 298] for as many pounds or dollars as the number of times it changes hands in order to effect this object.

If we assume the quantity of goods on sale, and the number of times those goods are resold, to be fixed quantities, the value of money will depend upon its quantity, together with the average number of times that each piece changes hands in the process. The whole of the goods sold (counting each resale of the same goods as so much added to the goods) have been exchanged for the whole of the money, multiplied by the number of purchases made on the average by each piece. Consequently, the amount of goods and of transactions being the same, the value of money is inversely as its quantity multiplied by what is called the rapidity of circulation. And the quantity of money in circulation is equal to the money value of all the goods sold, divided by the number which expresses the rapidity of circulation.

This may be expressed in mathematical language, where V is the value of money, Q is the quantity in circulation, and R the number expressing the rapidity of circulation, as follows:

V = 1 / (Q × R).

The phrase, rapidity of circulation, requires some comment. It must not be understood to mean the number of purchases made by each piece of money in a given time. Time is not the thing to be considered. The state of society may be such that each piece of money hardly performs more than one purchase in a year; but if this arises from the small number of transactions—from the small amount of business done, the want of activity in traffic, or because what traffic there is mostly takes place by barter—it constitutes no reason why prices should be lower, or the value of money higher. The essential point is, not how often the same money changes hands in a given time, but how often it changes hands in order to perform a given amount of traffic. We must compare the number of purchases made by the money in a given time, not with the time itself, but with the goods sold in that same time. If each piece of [pg 299] money changes hands on an average ten times while goods are sold to the value of a million sterling, it is evident that the money required to circulate those goods is £100,000. And, conversely, if the money in circulation is £100,000, and each piece changes hands, by the purchase of goods, ten times in a month, the sales of goods for money which take place every month must amount, on the average, to £1,000,000. [The essential point to be considered is] the average number of purchases made by each piece in order to affect a given pecuniary amount of transactions.

“There is no doubt that the rapidity of circulation varies very much between one country and another. A thrifty people with slight banking facilities, like the French, Swiss, Belgians, and Dutch, hoard coin much more than an improvident people like the English, or even a careful people, with a perfect banking system, like the Scotch. Many circumstances, too, affect the rapidity of circulation. Railways and rapid steamboats enable coin and bullion to be more swiftly remitted than of old; telegraphs prevent its needless removal, and the acceleration of the mails has a like effect.” “So different are the commercial habits of different peoples, that there evidently exists no proportion whatever between the amount of currency in a country and the aggregate of the exchanges which can be effected by it.”229