Chapter XI · (continued 2)

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.

If it be objected that this assumes that with the doubling in M and M´ there would be also a doubling of prices, we may meet the objection by putting the argument in a slightly different form. Suppose, for a moment, that a doubling in the currency in circulation should not at once raise prices, but should halve the velocities instead; such a result would evidently upset for each individual the adjustment which he had made of cash on hand. Prices being unchanged, he now has double the amount of money and deposits which his convenience had taught him to keep on hand. He will then try to get rid of the surplus money and deposits by buying goods. But as somebody else must be found to take the money off his hands, its mere transfer will not diminish the amount in the community. It will simply increase somebody else's surplus. Everybody has money on his hands beyond what experience and convenience have shown to be necessary. Everybody will want to exchange this relatively useless extra money for goods, and the desire so to do must surely drive up the price of goods. No one can deny that the effect of every one's desiring to spend more money will be to raise prices. Obviously this tendency will continue until there is found another adjustment of quantities to expenditures, and the V's are the same as originally. That is, if there is no change in the quantities sold (the Q's), the only possible effect of doubling M and M´ will be a doubling of the p's; for we have just seen that the V's cannot be permanently reduced without causing people to have surplus money and deposits, and there cannot be surplus money and deposits without a desire to spend it, and there cannot be a desire to spend it without a rise in prices. In short, the only way to get rid of a plethora of money is to raise prices to correspond.

So far as the surplus deposits are concerned, there might seem to be a way of getting rid of them by cancelling bank loans, but this would reduce the normal ratio which M´ bears to M, which we have seen tends to be maintained.

We come back to the conclusion that the velocity of circulation either of money or deposits is independent of the quantity of money or of deposits. No reason has been, or, so far as is apparent, can be assigned, to show why the velocity of circulation of money, or deposits, should be different, when the quantity of money, or deposits, is great, from what it is when the quantity is small.

There still remains one seeming way of escape from the conclusion that the sole effect of an increase in the quantity of money in circulation will be to increase prices. It may be claimed—in fact it has been claimed—that such an increase results in an increased volume of trade. We now proceed to show that (except during transition periods) the volume of trade, like the velocity of circulation of money, is independent of the quantity of money. An inflation of the currency cannot increase the product of farms and factories, nor the speed of freight trains or ships. The stream of business depends on natural resources and technical conditions, not on the quantity of money. The whole machinery of production, transportation, and sale is a matter of physical capacities and technique, none of which depend on the quantity of money. The only way in which the quantities of trade appear to be affected by the quantity of money is by influencing trades accessory to the creation of money and to the money metal. An increase of gold money will, as has been noted, bring with it an increase in the trade in gold objects. It will also bring about an increase in the sales of gold mining machinery, in gold miners' services, in assaying apparatus and labor. These changes may entail changes in associated trades. Thus if more gold ornaments are sold, fewer silver ornaments and diamonds may be sold. Again the issue of paper money may affect the paper and printing trades, the employment of bank and government clerks, etc. In fact, there is no end to the minute changes in the Q's which the changes mentioned, and others, might bring about. But from a practical or statistical point of view they amount to nothing, for they could not add to nor subtract one-tenth of 1 per cent. from the general aggregate of trade. Only a very few Q's would be appreciably affected, and those few very insignificant.

We conclude, therefore, that a change in the quantity of money will not appreciably affect the quantities of goods sold for money.

Since, then, a doubling in the quantity of money: (1) will normally double deposits subject to check in the same ratio, and (2) will not appreciably affect either the velocity of circulation of money or of deposits or the volume of trade, it follows necessarily and mathematically that the level of prices must double. While, therefore, the equation of exchange, of itself, asserts no causal relations between quantity of money and price level, any more than it asserts a causal relation between any other two factors, yet, when we take into account conditions known quite apart from that equation, viz., that a change in M produces a proportional change in M´, and no changes in V, V´, or the Q's, there is no possible escape from the conclusion that a change in the quantity of money (M) must normally cause a proportional change in the price level (the p's).

While the equation of exchange is, if we choose, a mere "truism," based on the equivalence, in all purchases, of the money or checks expended, on the one hand, and what they buy, on the other, yet in view of supplementary knowledge as to the relation of M to M´, and the non-relation of M to V, V´, and the Q's, this equation is the means of demonstrating the fact that normally the p's vary directly as M, that is, demonstrating the quantity theory. To throw away contemptuously the equation of exchange because it is so obviously true is to neglect the chance to formulate for economic science some of the most important and exact laws of which it is capable.

We may now restate, then, in what causal sense the quantity theory is true. It is true in the sense that one of the normal effects of an increase in the quantity of money is an exactly proportional increase in the general level of prices.

I have no desire, as some one has humorously suggested, to hide behind an equation, but I do find it necessary to take refuge behind my book on the Purchasing Power of Money. So many new questions have been asked that, in the few moments at my disposal, I could not answer them all satisfactorily. I believe they have all been answered in the book referred to. For instance, a chapter has been devoted to transition periods in which it has been shown, as Professor Taussig has suggested, that during transition periods an increase in T may cause an increase in M´.

The Testimony of Ricardo

[78]Let us suppose that the circulation of all countries were carried on by the precious metals only, and that the proportion which England possessed were one million; let us further suppose, that, at once, half of the currencies of all countries, excepting that of England, were suddenly annihilated, would it be possible for England to continue to retain the million which she before possessed? Would not her currency become relatively excessive compared with that of other countries? If a quarter of wheat, for example, had been both in France and England of the same value as an ounce of coined gold, would not half an ounce now purchase it in France, whilst in England it continued of the same value as one ounce? Could we by any laws, under such circumstances, prevent wheat or some other commodity (for all would be equally affected) from being imported into England, and gold coin from being exported? If ... the exportation of bullion were free, gold might rise 100 per cent.; and for the same reason, if 35 Flemish schillings in Hamburgh had before been of equal value with a pound sterling, 17-1/2 schillings would now attain that value. If the currency of England only had been doubled, the effects would have been precisely the same.

Suppose, again, the case reversed, and that all other currencies remained as before, while half that of England was retrenched. If the coinage of money at the mint was on the present footing, would not the prices of commodities be so reduced here that cheapness would invite foreign purchasers, and would not this continue till the relative proportions in the different currencies were restored?

If such would be the effects of a diminution of money below its natural level, and that such would be the consequences the most celebrated writers on political economy are agreed, how can it be justly contended that the increase or diminution of money has nothing to do either with the foreign exchanges, or with the price of bullion?

Now, a paper circulation, not convertible into specie, differs in its effects in no respect from a metallic currency, with the law against exportation strictly executed.

Supposing, then, the first case to occur whilst our circulation consisted wholly of paper, would not the exchanges fall, and the price of bullion rise in the manner which I have been representing; and would not our currency be depreciated, because it was no longer of the same value in the markets of the world as the bullion which it professed to represent? The fact of depreciation could not be denied, however the Bank Directors might assure the public that they never discounted but good bills for bona fide transactions; however they might assert that they never forced a note into circulation; that the quantity of money was no more than it had always been, and was only adequate to the wants of commerce, which had increased and not diminished;[79] that the price of gold, which was here at twice its mint value, was equally high, or higher, abroad, as might be proved by sending an ounce of bullion to Hamburgh, and having the produce remitted by bill payable in London bank notes; and that the increase or diminution of their notes could not possibly either affect the exchange or the price of bullion. All this, except the last, might be true, and yet would any man refuse his assent to the fact of the currency being depreciated?

Could the symptoms which I have been enumerating proceed from any other cause but a relative excess in our currency? Could our currency be restored to its bullion value by any other means than by a reduction in its quantity, which should raise it to the value of the currencies of other countries; or by the increase of the precious metals, which lower the value of theirs to the level of ours?

FOOTNOTES: