V is defined,[206] not as the number of times a given dollar is exchanged in a given year (the "coin-transfer" notion), but as a social average based on the average number of coins which pass through each man's hands, divided by the average amount held by him (the "person-turnover" concept of velocity.) V´ is similarly defined. Fisher asserts that both concepts, if correctly employed, lead to the same result. I would point out one important difference between them here: if money is short-circuited, if, i. e., a part of the economic community loses its incomes, or finds its incomes reduced, then the "velocity of money," on the "coin-transfer" basis is reduced, provided the "person-turnover" average remains the same, while on the "person-turnover" basis the velocity will remain unchanged. It is clearly the "coin-transfer" concept which is fundamental, from the standpoint of the equation of exchange, and Fisher feels justified in using the other method only because he considers it an equivalent of the "coin-transfer" concept. I shall later show cases where the distinction between the two concepts is all-important, particularly in the case where T is reduced by the elimination of middlemen.[207]

The conception of velocity of circulation as a real, unitary entity, a cause, in the process of price-determination, is, I suppose, almost as old as the quantity theory itself. It is an essential part of the quantity theory. To me "velocity of circulation" seems to be a mere name, denoting, not any simple cause or small set of causes, which can exert a specific influence, but rather a meaningless abstract number, which is the non-essential by-product of a highly heterogeneous lot of activities of men, some of which work one way, and others of which work in another way, in affecting prices. It is at best a passive resultant of conflicting and divergent tendencies, and has, to my mind, no more causal significance than the average of the abstract numbers of yards gained by both sides, heights and weights of players, kick-offs, and minutes taken out for injuries, would have on the result of the Yale-Harvard game. The real causes of changes in prices lie deeper! I should expect V and V´ to be the most highly flexible factors in the equation of exchange, and should expect to be able to keep the equation straight, in a great variety of situations, by allowing the V's to vary.

Before undertaking detailed analysis of the causes governing V, I shall discuss Fisher's specific argument, typical of the quantity theory, that an increase of money cannot change the V's. "As a matter of fact, the velocities of circulation of money and deposits depend, as we have seen, on technical conditions, and bear no discoverable relation to the quantity of money in circulation. Velocity of circulation is the average rate of 'turnover,' and depends on countless individual rates of turnover. These, as we have seen, depend on individual habits. Each person regulates his turnover to suit his individual convenience.... In the long run, and for a large number of people, the average rate of turnover, or what amounts to the same thing, the average time money remains in the same hands, will be closely determined. It will depend on density of population, commercial customs, rapidity of transport, and other technical conditions, but not on the quantity of money and deposits nor on the price-level." (Italics mine.[208]) He proceeds to assume that money is doubled with a halving of the V's, instead of a doubling of P. Everybody now has on hand twice as much money and deposits as his convenience has taught him to keep on hand. He will then try to get rid of this surplus, and he can only do it by buying goods. But this will increase somebody else's surplus, and he will likewise try to get rid of it. This will raise prices. "Obviously this tendency will continue until there if found another adjustment of quantities to expenditures, and the V's are the same as originally."[209] The foregoing argument rests in part, it will be seen, on the assumption that a fixed ratio between M and M´ obtains, else the increase of money in everybody's hands would not mean a corresponding increase in their deposits. I have already criticised this doctrine. For the contention that the V's will finally be just the same as before, I find no specific argument at all—"obviously" presumably making that unnecessary.

As the point immediately at issue is that V's will be unchanged by the increase in M (otherwise P would not increase proportionately—let us see if considerations can be adduced which will make this a little less "obvious." First, it will be noticed that Fisher, in the foregoing, in one sentence speaks of the matter as resting on habit, and in the next sentence, on convenience. He speaks, also, of business custom. Now it is important to note that habit and custom, on the one hand, and considerations of convenience on the other, do not necessarily coincide. Many habits and customs are highly inconvenient. And it is not at all likely that habit and custom should govern so highly complex a thing as the ratio between cash on hand and the price-level. Rather, in so far as custom and habit rule, one would expect them to relate to a simpler matter, namely, the amount of cash on hand. If the amount of cash kept on hand should remain controlled by habit, while the amount of money is increased, then V, instead of remaining unchanged, would actually be increased, unless the habits should be broken in on. I shall show in a moment that considerations of convenience would probably lead to a reduced V, in so far as individual turnover is concerned. But which tendency will prevail? Well, that will depend on the degree to which custom and habit rule as compared with considerations of convenience—i. e., there would be no rule valid for all communities. That convenience would lead to a larger amount of money on hand—and I am following Fisher's temporary hypothesis that there has been no rise in prices prior to the movement to restore the V's to their old magnitudes—will appear from considerations like these. Few men have as much on hand as they would like to have, including both their cash in hand and their deposit balances. Most people have the tendency to hoard, though it is usually held in check by necessity. If money on hand be increased suddenly, without prices being increased, and without any prospect of increased incomes in the future—and there is nothing in Fisher's provisional hypothesis to call for increased incomes, as they could, in fact, come only from an increase in prices—why might not there be a considerable saving of money, with a corresponding reduction in V? If it be objected that people, in saving their money, will in considerable degree put it into the banks, and that the banks, with larger reserves, will increase loans and deposits, I would urge, that it is on the part of banks that this tendency to increase hoards in times of abundant money is particularly marked, and for proof would point to the figures quoted from Keynes[210] for the great banks and treasuries of Europe in the last fifteen years. It is not necessary for my purpose at this point to do more than show that there is reason to expect an increase in money to change the V's. Fisher's argument rests on the contention that the V's will be neither increased or reduced—otherwise an increase in money will not proportionately raise prices. The appeal to habit and custom in the matter is particularly unsatisfactory. Custom and habit could not possibly regulate things so complex as velocities of money and bank-deposits.

Whatever be the ultimate effect of an increase in money, the immediate effect is commonly to reduce the money-rates. Banks have less inducement to pay interest on deposits, and charge lower rates for loans. Now merchants, especially small merchants, are often embarrassed in making change for customers. The man who has tried to make payment with a ten dollar bill in a country store has not infrequently put the storekeeper to much inconvenience. To offer a ten dollar bill, or even a five dollar bill, to a storekeeper on Amsterdam Avenue in New York City may well mean that the one clerk in the establishment, or the proprietor's wife will run out with the bill to three or four neighboring stores before finding change with which to break it. If money is more abundant, if money-rates are easier, for a time, it may easily happen that many small merchants will experience the superior convenience of having a more adequate amount of change in the till, and will, even after the money-rates have risen—if they do rise again to the old figure—find a new reason for keeping more cash on hand. There is a marginal equilibrium between the interest on the capital invested in cash in the till, and the wages of the clerk,[211] whose active legs assist the velocity of money. Not only banks and small dealers, however, find it advantageous to increase their supply of ready funds, held idle for special occasions. The United States Steel Corporation has kept as much as $50,000,000.00 to $75,000,000.00 in idle cash or idle deposits, as a means of being independent of banks in times of emergency.[212] The motive for accumulating reserves and hoards, either of cash or deposit accounts, is at all times strong. In times of financial ease, it may easily find the difficulties which ordinarily repress it give way, and, by being gratified, grow stronger.

I conclude that there is positive reason for expecting an increase of money to reduce the velocity of money.

Horace White, in his Money and Banking, in the earlier editions, speaks of the velocity of money, "alias the state of trade." Is not this the truth? Is not money circulating rapidly, when business is active, and slowly when business is dull? Is not the velocity of circulation a highly flexible and variable average, a cause of nothing, and an index of business activity? Or, better, perhaps, are not the V's and T both governed, in large degree, by more fundamental causes which are largely the same for both? Fisher would admit something of this for transition periods. Even for normal adjustments, he admits that an increase in T, unaccompanied by an increase in M, leads to some increase in the V's, though he doesn't say how much.[213] He denies, however, that an increase in the V's will increase T.[214] In general, it is clear that he regards the V's and T as governed by different causes. The control of the V's by T is not the only or the chief control of the V's. The V's can increase greatly without an increase of T, in his scheme. That this is so, will appear from a comparison of the list of causes which he gives as governing the V's and T respectively:

Causes governing V's:

1. Habits of the individual.
(a) As to thrift and hoarding.
(b) As to book credit.
(c) As to use of checks.
2. Systems of payments in the community.
(a) As to frequency of receipts and disbursements.
(b) As to regularity of receipts and disbursements.
(c) As to correspondence between times and amounts of receipts and disbursements.
3. General causes.
(a) Density of population.
(b) Rapidity of transportation.

Compare this list with the causes governing T:[215]