Second, Professor Fisher ... seeks to establish a causal relation between the amount of money in circulation (M) and the amount of deposits (M´) which, in my judgment, is wholly unfounded. He has developed this in his paper in the Royal Statistical Journal. The error consists in supposing that a man's deposit account at any time varies with the amount of money in his possession. Rather, the deposit account varies with a man's wealth. The rich man does not carry much more money to pass from hand to hand than the man of moderate means. Monetary habits in the community require a certain level of circulation for all persons, but the deposits of an individual may soar above the common level without regard to the money he keeps in circulation. His bank deposits are rather a measure of the saleable goods he has sold, "coined into means of payment."
Third, I well recognize the high position Professor Fisher occupies in the mathematical school of Walras and others; but has he not made an error in stating the essence of the price relation in his mathematical symbols? So far as I understand him, he seems to deny the fundamental value-concept (on which there has hitherto been general agreement) that price is a ratio between goods and gold. In furtherance of that idea, he thinks that, before individual prices can be arrived at, the general price level must be ascertained. Now, in my exposition using the ratio-concept, I explained in detail how the general level of prices might be affected by causes affecting the gold side of the ratio. Therefore, I did not neglect to account for the general level and that too without doing violence to the accepted value-concept. But the ratio-concept (which Professor Fisher seems to deny) allows the forces acting on goods also to affect the general level of prices as I have shown. In my opinion, he wrongly works from a general level of prices to particular prices; while I hold that particular prices, or actual quotations, are the bases from which all averages, or price levels, are always and inevitably computed. Moreover, in his diagrams, the level of prices he used was the one computed from individual quotations. Hence his whole reasoning on the conformity of the statistics to the terms of his equation is vitiated. Indeed the better agreement he finds—after elaborate statistical computations—between the elements and their result on prices ...—is due, I think, to relying on an equation which is nothing more than a statement that the whole is equal to the sum of its parts....
Finally, when Professor Johnson suggests that I am wrong in stating that forces affecting the goods side of the price ratio have an influence on prices, he certainly cannot mean that conditions affecting the producing, marketing, and financing of goods have no effect on prices. How else, for instance, can we explain the rise of the prices of agricultural products? The special causes affecting them have little to do with the quantity of "money." Moreover, the term "money" itself is used so loosely and vaguely that we can come to agreement on price theories only by first agreeing upon what we mean by "money." In my paper, I have discussed the relations of goods, and their prices, to gold. But, in this country, we use gold little as a medium by which goods are exchanged. Thus the relation of the prices of goods to our media of exchange has been practically omitted. And yet the price-making process generally precedes the creation of the usual banking media of exchange by which most goods are exchanged.
Irving Fisher[77]: In connection with the statement and explanation of the equation of exchange it was shown (1) that prices vary directly as the quantity of money, provided the volume of trade and the velocities of circulation remain unchanged; (2) that prices vary directly as the velocities of circulation (if these velocities vary together), provided the quantity of money and the volume of trade remain unchanged, and (3) that prices vary inversely as the volume of trade, provided the quantity of money—and therefore deposits—and their velocities remain unchanged.
Let us now inquire how far these propositions are really causal propositions. An examination of the influence of each of the six magnitudes on each of the other five will afford answers to the objections which have been raised to the quantity theory of money.
To set forth all the facts and possibilities as to causation we need to study the effects of varying, one at a time, the various magnitudes in the equation of exchange.
Our first question is: given (say) a doubling of the quantity of money in circulation (M) what are the normal or ultimate effects on the other magnitudes in the equation of exchange, viz.: M´, V, V´, the p's and the Q's?
We have seen that normally the effect of doubling money in circulation (M) is to double deposits (M´) because under any given conditions of industry and civilization deposits tend to hold a fixed or normal ratio to money in circulation. Hence the ultimate effect of a doubling in M is the same as that of doubling both M and M´. We propose next to show that this doubling of M and M´ does not normally change V, V´ or the Q's, but only the p's. The equation of exchange of itself does not affirm or deny these propositions.
For aught the equation of exchange itself tells us, the quantities of money and deposits might even vary inversely as their respective velocities of circulation. Were this true, an increase in the quantity of money would exhaust all its effects in reducing the velocity of circulation, and could not produce any effect on prices. If the opponents of the "quantity theory" could establish such a relationship, they would have proven their case despite the equation of exchange. But they have not even attempted to prove such a proposition. As a matter of fact, the velocities of circulation of money and of deposits depend, as will be 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 depend on individual habits. Each person regulates his turnover to suit his convenience. A given rate of turnover for any person implies a given time of turnover—that is, an average length of time a dollar remains in his hands. He adjusts this time of turnover by adjusting his average quantity of pocket money, or till money, to suit his expenditures. He will try to avoid carrying too little lest, on occasion, he be unduly embarrassed; and on the other hand to avoid encumbrance, waste of interest, and risk of robbery, he will avoid carrying too much. Each man's adjustment is, of course, somewhat rough, and dependent largely on the accident of the moment; but, 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 very 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. These may change without any effect on velocity. If the quantities of money and deposits are doubled, there is nothing, so far as velocity of circulation is concerned, to prevent the price level from doubling. On the contrary, doubling money, deposits, and prices would necessarily leave velocity quite unchanged. Each individual would need to spend more money for the same goods, and to keep more on hand. The ratio of money expended to money on hand would not vary. If the number of dollars in circulation and in deposit should be doubled and a dollar should come to have only half its former purchasing power, the change would imply merely that twice as many dollars as before were expended by each person and twice as many kept on hand. The ratio of expenditure to stock on hand would be unaffected.