AN APPROXIMATE FORMULA FOR DETERMINING THE VELOCITY OF THE CIRCULATION OF MONEY

[324]For the purpose of tracing the circulation of money, and measuring it by bank records,[325] we may classify the persons who use money in purchase of goods into three groups:

1. Commercial depositors, i. e., all engaged in business—firms, companies, and others—who have bank deposits mainly or wholly apart from personal accounts.

2. All other depositors, chiefly private persons.

3. All who, like most wage earners, are not depositors at all.

These three classes we shall distinguish as "Commercial depositors," "Other depositors," and "Nondepositors," or C, O, and N. The money in the possession of "Commercial depositors" we shall call "till money," and the rest "pocket money."

The three groups necessarily include all in the community who circulate money. By circulating money is meant expending it in exchange, not for some other circulating medium, as checks, but for goods....

... The category of "commercial depositors" coincides for all practical purposes with the category of business establishments.

"Other depositors" include most proprietors, professional, and salaried persons. Almost no wage earners are included, and almost no business establishments or business men in a business capacity....

... Although "other depositors" include most proprietors and professional and salaried persons, yet some proprietors and professional men, especially in rural communities, and some salaried persons, chiefly small clerks, are "Nondepositors."...

... "Nondepositors" consist chiefly of those who are classed in statistics as wage earners. While there are some wage earners who are depositors,[326] they are rare: and while there are some "nondepositors" who are not wage earners, especially (as just indicated) the agricultural proprietors (farmers) and small clerks, the amount of money circulated by them is small in comparison with the total circulation. While the line separating wages and salaries is not definitely marked in theory, it is usually easily recognised in practice....

We may now picture concretely the main currents of the monetary flow, including the circulation of money in exchange for goods.... [The figure here given] illustrates the three principal types.

The corners of the triangle, C, O, and N, represent the three groups of "commercial depositors," "other depositors," and "nondepositors," and the B's represent banks. The arrows represent the flow of money from each of these four categories to the others. Thus B_o represents the annual withdrawals from banks by "other depositors," O_c the spending of this withdrawn money by "other depositors" among "commercial depositors," and C_b the return of the money from the "commercial depositors" to the banks. This circuit (B_o O_c C_b) of three links is very common. A second type of circuit is represented by a chain of four arrows (B_o O_n N_c C_b). It is illustrated by private depositors drawing money (B_o), and paying wages (O_n) to servants who in turn spend the money (N_c) among tradesmen who finally deposit it (C_b). A third type of circuit, also fourfold, is represented by the arrows B_c C_n N_c C_b. It is illustrated by commercial firms cashing their checks at banks (B_c) for pay rolls, with the cash so obtained paying wages (C_n) to workmen who spend it (N_c) among other tradesmen who redeposit it in banks (C_b). These three types are not the only ones, but they are so much more important than any others that they merit out undivided attention before a completer study is undertaken.... [The accompanying figure] has been constructed for the purpose of exhibiting them uncomplicated by other details.

It will be noted that not all of the flows described are examples of the circulation of money. As already indicated, money may be said to circulate only when it passes in exchange for goods. Its entrance into and exit from banks is a flow, but not a circulation against goods. In the diagram the horizontal arrows represent such mere banking operations, not true circulation. On the other hand, the arrows along the sides of the triangle represent actual circulation. The diagram shows four such arrows, representing the four chief types of circulation: O_c payments of money from "other depositors" to "commercial depositors" in the purchase of goods; O_o payments from "other depositors" to "nondepositors," as when a housewife pays wages; C_n payments from "commercial depositors" to "nondepositors," as when a firm pays wages; and N_c payments from "nondepositors" to "commercial depositors," as when a wage earner buys goods of a merchant.

There four types of circulation of money occur in the three circuits already described, being sandwiched between the flows from and to the banks. The first, O_c, is contained within the circuit B_o O_c C_b and, since no "nondepositors" intervene, represents money changing hands once between its withdrawal from bank and its redeposit there. The remaining types (O_n, C_n, and N_c) are contained within the two other circuits (B_o O_n N_c C_b and B_c C_n N_c C_b), and, owing to the fact that "nondepositors" intervene, represent money circulating twice between withdrawal and redeposit.

In short, one of the three circuits (B_o O_c C_b) shows money circulating once out of bank. Both the others pass through N, and show money circulating twice out of bank. The diagram, then, represents all circulating money as springing from and returning to the banks; all of it as circulating at least once in the interim; and that portion handled by "nondepositors" as circulating once in addition. Therefore, the total circulation exceeds the total flow from and to banks by the amount flowing through "nondepositors." In other words, the total circulation in the diagram is simply the sum of the annual money flowing from and to banks and the money handled by "nondepositors." The quotient of this sum divided by the amount of money in circulation will give approximately the velocity of circulation of money....