# The Purchasing Power of Money/chapter 8

CHAPTER VIII
INFLUENCE OF QUANTITY OF MONEY AND OTHER FACTORS ON PURCHASING POWER AND ON EACH OTHER
§ 1 VIII.1 THE chief purpose of the foregoing chapters is to set forth the causes determining the purchasing power of money. This purchasing power has been studied as the effect of five, and only five, groups of causes. The five groups are money, deposits, their velocities of circulation, and the volume of trade. These and their effects, prices, we saw to be connected by an equation called the equation of exchange, MV + M'V' = SpQ. The five causes, in turn, we found to be themselves effects of antecedent causes lying entirely outside of the equation of exchange, as follows: the volume of trade will be increased, and therefore the price level correspondingly decreased by the differentiation of human wants; by diversification of industry; and by facilitation of transportation. The velocities of circulation will be increased, and therefore also the price level increased by improvident habits; by the use of book credit; and by rapid transportation. The quantity of money will be increased, and therefore the price level increased correspondingly by the import and minting of money, and, antecedently, by the mining of the money metal; by the introduction of another and initially cheaper money metal through bimetallism; and by the issue of bank notes and other paper money. The quantity of deposits will be increased, and therefore the price level increased by extension of the banking system and by the use of book credit. The reverse causes produce, of course, reverse effects.
VIII.2 Thus, behind the five sets of causes which alone affect the purchasing power of money, we find over a dozen antecedent causes. If we chose to pursue the inquiry to still remoter stages, the number of causes would be found to increase at each stage in much the same way as the number of one's ancestors increases with each generation into the past. In the last analysis myriads of factors play upon the purchasing power of money; but it would be neither feasible nor profitable to catalogue them. The value of our analysis consists rather in simplifying the problem by setting forth clearly the five proximate causes through which all others whatsoever must operate. At the close of our study, as at the beginning, stands forth the equation of exchange as the great determinant of the purchasing power of money. With its aid we see that normally the quantity of deposit currency varies directly with the quantity of money, and that therefore the introduction of deposits does not disturb the relations we found to hold true before. That is, it is still true that (1) 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.
§ 2 VIII.3 It is proposed in this chapter to inquire how far these propositions are really causal propositions. We shall study in detail the influence of each of the six magnitudes on each of the other five. This study will afford answers to the objections which have often been raised to the quantity theory of money.
VIII.4 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. We shall in each case distinguish between the effects during transition periods and the ultimate or normal effects after the transition periods are finished. For simplicity we shall in each case consider the normal or ultimate effects first and afterward the abnormal or transitional effects.
VIII.5 Since almost all of the possible effects of changes in the elements of the equation of exchange have been already set forth in previous chapters, our task in this chapter is chiefly one of review and rearrangement.
VIII.6 Our first question therefore 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?
VIII.7 We have seen, in Chapter III, 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.
VIII.8 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 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 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.
VIII.9 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.
VIII.10 So far as the surplus deposits are concerned, there might seem to be a way of getting rid of them by canceling bank loans, but this would reduce the normal ratio which M' bears to M, which we have seen tends to be maintained.
VIII.11 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.
VIII.12 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. Probably no one will deny this, but some objectors might claim that, though technique of production and trade determine most of these things, nevertheless the Q's—the actual quantities of goods exchanged for money and deposit currency—might conceivably vary according as barter is or is not resorted to. If barter were as convenient as sale-and-purchase, this contention would have force. There would then be little need of distinguishing between money as the generally acceptable medium of exchange and other property as not generally acceptable. If all property were equally acceptable, all property would be equally money; or if there were many kinds of property nearly as exchangeable as money, resort to barter would be so easy that some of the goods sold for money could be almost equally well bartered for something else. But as long as there were any preference at all for the use of money, resort to barter would be reluctantly made and as a temporary expedient only. We have seen this when studying transition periods. Under normal conditions and in the long run only a negligible fraction of modern trade can be done through barter. We conclude, therefore, that a change in the quantity of money will not appreciably affect the quantities of goods sold for money.
VIII.13 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).
VIII.14 One of the objectors to the quantity theory attempts to dispose of the equation of exchange as stated by Newcomb, by calling it a mere truism. 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. "Truisms" should never be neglected. The greatest generalizations of physical science, such as that forces are proportional to mass and acceleration, are truisms, but, when duly supplemented by specific data, these truisms are the most fruitful sources of useful mechanical knowledge. 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.
VIII.15 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.*1
VIII.16 To deny this conclusion requires a denial of one or more of the following premises upon which it rests:—
(1) The equation of exchange, MV + M'V' = SpQ. (2) An increase of M normally causes a proportional increase of M'. (3) An increase of M does not normally affect V, V', or the Q's.
VIII.17 If these three premises be granted, the conclusion must be granted. If any of the premises be denied, the objector must show wherein the fallacy lies. Premise (1) has been justified in Chapter II and Chapter III, and mathematically demonstrated in the Appendices to Chapters II and III. Premise (2) has been shown to be true in Chapter III and premise (3) in the present chapter.
VIII.18 So much pains has been taken to establish these premises and to emphasize the results of the reasoning based on them because it seems nothing less than a scandal in Economic Science that there should be any ground for dispute on so fundamental a proposition.
VIII.19 The quantity theory as thus stated does not claim that while money is increased in quantity, other causes may not affect M', V, V', and the Q's, and thus aggravate or neutralize the effect of M on the p's. But these are not the effects of M on the p's. So far as M by itself is concerned, its effect on the p's is strictly proportional.
VIII.20 The importance and reality of this proposition are not diminished in the least by the fact that these other causes do not historically remain quiescent and allow the effect on the p's of an increase in M to be seen alone. The effects of M are blended with the effects of changes in the other factors in the equation of exchange just as the effects of gravity upon a falling body are blended with the effects of the resistance of the atmosphere.
VIII.21 Finally, it should be noted that, in accordance with principles previously explained, no great increase of money (M) in any one country or locality can occur without spreading to other countries or localities. As soon as local prices have risen enough to make it profitable to sell at the high prices in that place and buy at the low prices elsewhere, money will be exported. The production of gold in Colorado and Alaska first results in higher prices in Colorado and Alaska, then in sending gold to other sections of the United States, then in higher prices throughout the United States, then in export abroad, and finally in higher prices throughout the gold-using world.
§ 3 VIII.22 We have emphasized the fact that the strictly proportional effect on prices of an increase in M is only the normal or ultimate effect after transition periods are over. The proposition that prices vary with money holds true only in comparing two imaginary periods for each of which prices are stationary or are moving alike upward or downward and at the same rate.
VIII.23 As to the periods of transition, we have seen that an increase in M produces effects not only on the p's, but on all the magnitudes in the equation of exchange. We saw in Chapter IV on transition periods that it increases M' not only in its normal ratio to M, but often, temporarily, beyond that ratio. We saw that it also quickened V and V' temporarily.
VIII.24 As previously noted, while V and V' usually move in sympathy, they may move in opposite directions when a panic decreases confidence in bank deposits. Then people pay out deposits as rapidly as possible and money as slowly as possible—the last-named tendency being called hoarding.
VIII.25 We saw also that an increase of M during a period of rising prices stimulated the Q's. Finally we saw that a reduction in M caused the reverse effects of those above set forth, decreasing V and V', decreasing M' not absolutely only, but in relation to M, and decreasing the Q's partly because of the disinclination to sell at low money prices which are believed to be but temporary, partly because of a slight substitution of barter for sales; for if M should be very suddenly reduced, some way would have to be found to keep trade going, and barter would be temporarily resorted to in spite of its inconvenience. This would bring some relief, but its inconvenience would lead sellers to demand money whenever possible, and prospective buyers to supply themselves therewith. The great pressure to secure money would enhance its value—that is, would lower the prices of other things. This resultant fall of prices would make the currency more adequate to do the business required, and make less barter necessary. The fall would proceed until the abnormal pressure, due to the inconvenience of barter, had ceased. Practically, however, in the world of to-day, even such temporary resort to barter is trifling. The convenience of exchange by money is so much greater than the convenience of barter, that the price adjustment would be made almost at once. If barter needs to be seriously considered as a relief from money stringency, we shall be doing it full justice if we picture it as a safety-valve, working against a resistance so great as almost never to come into operation and then only for brief transition intervals. For all practical purposes and all normal cases, we may assume that money and checks are necessities for modern trade.
VIII.26 The peculiar effects during transition periods are analogous to the peculiar effects in starting or stopping a train of cars. Normally the caboose keeps exact pace with the locomotive, but when the train is starting or stopping this relationship is modified by the gradual transmission of effects through the intervening cars. Any special shock to one car is similarly transmitted to all the others and to the locomotive.
VIII.27 We have seen, for instance, that a sudden change in the quantity of money and deposits will temporarily affect their velocities of circulation and the volume of trade. Reversely, seasonal changes in the volume of trade will affect the velocities of circulation, and even, if the currency system is elastic, the quantity of money and deposits. In brisk seasons, as when "money is needed to move the crops," the velocity of circulation is evidently greater than in dull seasons. Money is kept idle at one time to be used at another, and such seasonal variations in velocity reduce materially the variations which otherwise would be necessary in the price level. In a similar way seasonal variations in the price level are reduced by the alternate expansion and contraction of an elastic bank currency. In this case temporarily, and to an extent limited by the amount of legal tender currency, money or deposits or both may be said to adapt themselves to the amount of trade. In these two ways, then, both the rise and fall of prices are mitigated.*2 Therefore the "quantity theory" will not hold true strictly and absolutely during transition periods.
VIII.28 We have finished our sketch of the effects of M, and now proceed to the other magnitudes.
§ 4 VIII.29 As to deposits (M'), this magnitude is always dependent on M. Deposits are payable on demand in money. They require bank reserves of money, and there must be some relation between the amount of money in circulation (M), the amount of reserves (μ), and the amount of deposits (M'). Normally we have seen that the three remain in given ratios to each other. But what is a normal ratio at one state of industry and civilization may not be normal at another. Changes in population, commerce, habits of business men, and banking facilities and laws may produce great changes in this ratio. Statistically, as will be shown in Chapter XII, the ratio M'/M has changed from 3.1 to 4.1 in fourteen years.
VIII.30 Since M' is normally dependent on M, we need not ask what are the effects of an increase of M'; for these effects have been included under the effects of M. But, since the ratio of M' to M may change, we do need to ask what are the effects of this change.
VIII.31 Suppose, as has actually been the case in recent years, that the ratio of M' to M increases in the United States. If the magnitudes in the equations of exchange in other countries with which the United States is connected by trade are constant, the ultimate effect on M is to make it less than what it would otherwise have been, by increasing the exports of gold from the United States or reducing the imports. In no other way can the price level of the United States be prevented from rising above that of other nations in which we have assumed this level and the other magnitudes in the equation of exchange to be quiescent. While the ultimate effect then is to increase the volume of circulating media, this increase is spread over the whole world. Although the extension of banking is purely local, its effects are international. In fact, not only will there be a redistribution of gold money over all gold countries, but there will be a tendency to melt coin into bullion for use in the arts.
VIII.32 The remaining effects are the same as those of an increase in M which have already been studied. That is, there will be no (ultimate) appreciable effect on V, V', or the Q's, but only on the p's, and these will rise, relatively to what they would otherwise have been, throughout the world. In foreign countries the normal effect will be proportional to the increase of money in circulation which they have acquired through the displacement of gold in the United States. In the United States the effect will not be proportional to the increase in M', since M has moved in the opposite direction. It will be proportional to the increase in M + M' if V and V' are equal, and less than in that proportion if V is less than V', as is the actual fact.
VIII.33 In any case the effect on prices is extremely small, being spread over the whole commercial world. Taking the world as a whole, the ultimate effect is, as we have seen, to raise world prices slightly and to melt some coin. The only appreciable ultimate effect of increasing the ratio of M' to M in one country is to expel money from that country into others. All of these effects are exactly the same as those of increasing the issue of bank notes, so long as they continue redeemable in gold or other exportable money. An issue beyond this point results in isolating the issuing country and therefore in rapidly raising prices there instead of spreading the effect over other countries. This is what happened in the United States during the Civil War.
VIII.34 As to transitional effects, it is evident that, before the expulsion of gold from the United States, there must be an appreciable rise in prices there, of which traders will then take advantage by selling in the United States, shipping away money, and buying abroad. During the period of rising prices all the other temporary effects peculiar to such a period, effects which have been described at length elsewhere, will be in evidence.
VIII.35 Exactly opposite effects of course follow a decrease of M' relatively to M.
§ 5 VIII.36 We come next to the effects of changes in velocities (V and V'). These effects are closely similar to those just described. The ultimate effects are on prices, and not on quantity of money or volume of trade. But a change in the velocity of circulation of money in any country, connected by international trade with other countries, will cause an opposite change in the quantity of money in circulation in that country. There will be a redistribution of money among the countries of the world and of money metal as between money and the arts.
VIII.37 The normal effect, then, of increasing V or V' in any country is to decrease M by export, to decrease M' proportionally, and to raise prices (p's) slightly throughout the world. There is no reason to believe that there will, normally, be any effects on the volume of trade. It is quite possible that a change in one of the two velocities will cause a corresponding change in the other, or, at any rate, that most of the causes which increase one will increase the other. Increased density of population, for instance, in all probability quickens the flow both of money and checks. Unfortunately, however, we have not sufficient empirical knowledge of the two sorts of velocity to assert, with confidence, any relations between them.
VIII.38 During transition periods the effects of changes in velocities are doubtless the same as the effects of increased currency.
§ 6 VIII.39 Our next question is as to the effects of a general increase or decrease in the Q's, i.e. in the volume of trade.
VIII.40 An increase of the volume of trade in any one country, say the United States, ultimately increases the money in circulation (M). In no other way could there be avoided a depression in the price level in the United States as compared with foreign countries. The increase in M brings about a proportionate increase in M'. Besides this effect, the increase in trade undoubtedly has some effect in modifying the habits of the community with regard to the proportion of check and cash transactions, and so tends somewhat to increase M' relatively to M; as a country grows more commercial the need for the use of checks is more strongly felt.*3
VIII.41 As to effects on velocity of circulation, we may distinguish three cases. The first is where the change in volume of trade corresponds to a change in population, as when there is an increase in trade from the settling of new lands, without any greater concentration in previously settled areas, and without any change in the per capita trade or in the distribution of trade among the elements of the population. Under such conditions no reason has been assigned, nor apparently can be assigned, to show why the velocity of circulation of money should be other for a condition in which the volume of trade is large than for a condition in which it is small.
VIII.42 The second case is where the increase in volume of trade corresponds to an increased density of population, but no change in per capita trade. In this case, the closer settlement may facilitate somewhat greater velocity.
VIII.43 The third case is where the change in the volume of trade does affect the per capita trade or the distribution of trade in the population.
VIII.44 There are then several ways in which the velocity of circulation may conceivably be affected. First, any change in trade, implying a change in methods of transportation of goods, will imply a change in methods of transportation of money; quick transportation means usually more rapid circulation.
VIII.45 Secondly, a changed distribution of trade will alter the relative expenditures of different persons. If their rates of turnover are different, a change in their expenditures will clearly alter the relative importance or weighting of these rates in the general average, thus changing that average without necessarily changing the individual rates of turnover. For instance, an increased trade in the southern states, where the velocity of circulation of money is presumably slow, would tend to lower the average velocity in the United States, simply by giving more weight to the velocity in the slower portions of the country.
VIII.46 Thirdly, a change in individual expenditures, when due to a real change in the quantity of goods purchased, may cause a change in individual velocities. It seems to be a fact that, at a given price level, the greater a man's expenditures the more rapid his turnover; that is, the rich have a higher rate of turnover; that the poor. They spend money faster, not only absolutely but relatively to the money they keep on hand. Statistics collected at Yale University of a number of cases of individual turnover show this clearly.*4 In other words, the man who spends much, though he needs to carry more money than the man who spends little, does not need to carry as much in proportion to his expenditure. This is what we should expect; since, in general, the larger any operation, the more economically it can be managed. Professor Edgeworth*5 has shown that the same rule holds in banking. When two banks are consolidated, the reserve needed is less than the sum of the two previous reserves.
VIII.47 We may therefore infer that, if a nation grows richer per capita, the velocity of circulation of money will increase. This proposition, of course, has no reference to nominal increase of expenditure. As we have seen, a doubling of all prices and incomes would not affect anybody's rate of turnover of money. Each person would need to make exactly twice the expenditure for the same actual result and to keep on hand exactly twice the money in order to meet the same contingencies in the same way. The determinant of velocity is real expenditure, not nominal. But a person's real expenditure is only another name for his volume of trade. We conclude, therefore, that a change in the volume of trade, when it affects the per capita trade, affects velocity of circulation as well.
VIII.48 We find then that an increase in trade, unlike an increase in currency (M and M') or velocities (V and V') has other effects than simply on prices—effects, in fact, of increasing magnitudes on the opposite side of the equation, V and V', and (though only indirectly by affecting business convenience and habit) M' relatively to M. If these effects increase the left side as much as the increase in trade itself (the Q's) directly increases the right side, the effect on prices will be nil. If the effect on the left side exceeds that on the right, prices will rise. Only provided the effect on the left side is less than the increase in trade will prices fall, and then not proportionately to the increase in trade.
VIII.49 In a former chapter, it was shown that a change in trade, provided currency (M and M') and velocities (V and V') remained the same, produced an inverse change in prices. But now we find that the proviso is inconsistent with the premise; currency and velocities can remain the same only by the clumsy hypothesis that the various other causes affecting them shall be so changed as exactly to neutralize the increase in trade. If these various other causes remain the same, then currency and velocities will not remain the same.
VIII.50 This is the first instance in our study where we have found that normally, i.e. apart from temporary or transitional effects, we reach different results by assuming causes to vary one at a time, than by assuming the algebraic factors in the equation to vary one at a time. The "quantity theory" still holds true—that prices (p's) vary with money (M)—when we assume that other causes remain the same, as well as when we assumed merely that other algebraic factors remain the same; and all the other theorems stated algebraically were found to hold causationally, excepting only the theorem as to variation in trade. While the main purpose of this chapter is to justify the "quantity theory" as expressing a causal as well as an algebraic relation, it is important to point out that causal and algebraic theorems are not always identical.
VIII.51 As to the transitional effects of a change in the volume of trade, these depend mainly on one of the two possible directions in which prices move. If they move upward, the transitional effects are similar to those we are already familiar with for periods of rising prices; if downward, they are similar to those incident to such a movement.
§ 7 VIII.52 We have now studied the effects of variations in each of the factors in the equation of exchange (save one) on the other factors. We have found that in each case except in the case of trade (the Q's) the ultimate effect was on prices (the p's). The only group of factors which we have not yet studied as cause are the prices (p's) themselves. Hitherto they have been regarded solely as effects of the other factors. But the objectors to the quantity theory have maintained that prices should be regarded as causes rather than as effects. Our next problem, therefore, is to examine and criticize this proposition.
VIII.53 So far as I can discover, except to a limited extent during transition periods, or during a passing season (e.g. the fall), there is no truth whatever in the idea that the price level is an independent cause of changes in any of the other magnitudes M, M', V, V', or the Q's. To show the untenability of such an idea let us grant for the sake of argument that—in some other way than as the effect of changes in M, M', V, V', and the Q's—the prices in (say) the United States are changed to (say) double their original level, and let us see what effect this cause will produce on the other magnitudes in the equation.
VIII.54 It is clear that the equality between the money side and the goods side must be maintained somehow, and that if the prices are raised the quantity of money or the quantity of deposits or their velocities must be raised, or else the volume of business must be reduced. But examination will show that none of these solutions is tenable.
VIII.55 The quantity of money cannot be increased. No money will come from abroad, for we have seen that a place with high prices drives money away. The consequence of the elevation of prices in the United States will be that traders will sell in the United States where prices are high, and take the proceeds in money and buy abroad where prices are low. It will be as difficult to make money flow into a country with high prices as to make water run up hill.
VIII.56 For similar reasons money will not come in via the mint. Since bullion and gold coin originally had the same value relatively to goods, after the supposed doubling of prices, gold coin has lost half its purchasing power. No one will take bullion to the mint when he thereby loses half its value. On the contrary, as we saw in a previous chapter, the result of high prices is to make men melt coin.
VIII.57 Finally, the high prices will not stimulate mining, but on the contrary they will discourage it, nor will high prices discourage consumption of gold, but on the contrary they will stimulate it. These tendencies have all been studied in detail. Every principle we have found regulating the distribution of money among nations (the distribution of money metal as between money and the arts or the production and consumption of metals) works exactly opposite to what would be necessary in order to bring money to fit prices instead of prices to fit money.
VIII.58 It is equally absurd to expect high prices to increase the quantity of deposits (M'). We have seen that the effect would be to diminish the quantity of money in circulation (M); but this money is the basis of the deposit currency (M'), and the shrinkage of the first will entail the shrinkage of the second. The reduction of M and M' will not tend to favor, but on the contrary will tend to pull down the high prices we have arbitrarily assumed.
VIII.59 The appeal to the velocities (V and V') is no more satisfactory. These have already been adjusted to suit individual convenience. To double them might not be a physical possibility, and would certainly be a great inconvenience.
VIII.60 There is left the forlorn hope that the high prices will diminish trade (the Q's). But if all prices including the prices of services are doubled, there is no reason why trade should be reduced. Since the average person will not only pay, but also receive high prices, it is evident that the high prices he gets will exactly make him able to stand the high prices he pays without having to reduce his purchases.
VIII.61 We conclude that the hypothesis of a doubled price level acting as an independent cause controlling the other factors in the equation of exchange and uncontrolled by them is untenable. Any attempt to maintain artificially high prices must result, as we have seen, not in adjusting the other elements in the equation of exchange to suit these high prices, but on the contrary in arousing their antagonism. Gold will go abroad and into the melting pot, will be produced less and consumed more until its scarcity as money will pull down the prices. The price level is normally the one absolutely passive element in the equation of exchange. It is controlled solely by the other elements and the causes antecedent to them, but exerts no control over them.
VIII.62 But though it is a fallacy to think that the price level in any community can, in the long run, affect the money in that community, it is true that the price level in one community may affect the money in another community. This proposition has been repeatedly made use of in our discussion, and should be clearly distinguished from the fallacy above mentioned. The price level in an outside community is an influence outside the equation of exchange of that community, and operates by affecting its money in circulation and not by directly affecting its price level. The price level outside of New York City, for instance, affects the price level in New York City only via changes in the money in New York City. Within New York City it is the money which influences the price level, and not the price level which influences the money. The price level is effect and not cause. Moreover, although the price level outside of New York is a proximate cause of changes of money in New York, that price level in turn is cause only in a secondary sense, being itself an effect of the other factors in the equation of exchange outside of New York City. For the world as a whole the price level is not even a secondary cause, but solely an effect—of the world's money, deposits, velocities, and trade.
VIII.63 We have seen that high prices in any place do not cause an increase of the money supply there; for money flows away from such a place. In the same way high prices at any time do not cause an increase of money at that time; for money, so to speak, flows away from that time. Thus if the price level is high in January as compared with the rest of the year, bank notes will not tend to be issued in large quantities then. On the contrary, people will seek to avoid paying money at the high prices and wait till prices are lower. When that time comes they may need more currency; bank notes and deposits may then expand to meet the excessive demands for loans which may ensue. Thus currency expands when prices are low and contracts when prices are high, and such expansion and contraction tend to lower the high prices and raise the low prices, thus working toward mutual equality. We see then that, so far from its being true that high prices cause increased supply of money, it is true that money avoids the place and time of high prices and seeks the place and time of low prices, thereby mitigating the inequality of price levels.
VIII.64 What has been said presupposes that purchasers have the option to change the place and time of their purchases. To the extent that their freedom to choose their market place or time is interfered with, the corrective adjustment of the quantity of money is prevented. The anomalous time of a panic may even be characterized by necessity to meet old contracts which afford no choice of deferring the payment. There may then be a "money famine" and a feverish demand for emergency currency needed to liquidate outstanding contracts which would never have been entered into if the situation had been foreseen. That such anomalous conditions do not negative the general thesis that prices are the effect and not the cause of currency (including deposit currency) is shown statistically by Minnie Throop England.*6
§ 8 VIII.65 Were it not for the fanatical refusal of some economists to admit that the price level is in ultimate analysis effect and not cause, we should not be at so great pains to prove it beyond cavil. It is due our science to demonstrate its truths. The obligation to do this carries with it the obligation to explain if possible why so obvious a truth has not been fully accepted.
VIII.66 One reason has already been cited, the fear to give aid and comfort to the enemies of all sound economists,—the unsound money men. Another may now receive attention, viz. the fallacious idea that the price level cannot be determined by other factors in the equation of exchange because it is already determined by other causes, usually alluded to as "supply and demand." This vague phrase has covered multitudes of sins of slothful analysts in economics. Those who place such implicit reliance on the competency of supply and demand to fix prices, irrespective of the quantity of money, deposits, velocity, and trade, will have their confidence rudely shaken if they will follow the reasoning as to price causation of separate articles. They will find that there are always just one too few equations to determine the unknown quantities involved.*7 The equation of exchange is needed in each case to supplement the equations of supply and demand.
VIII.67 It would take us too far afield to insert here a complete statement of price-determining principles. But the compatibility of the equation of exchange with the equations which have to deal with prices individually may be brought home to the reader sufficiently for our present purposes by emphasizing the distinction between (1) individual prices relatively to each other and (2) the price level. The equation of exchange determines the latter (the price level) only, and the latter only is the subject of this book. It will not help, but only hinder the reader to mix with the discussion of price levels the principles determining individual prices relatively to each other. It is amazing how tenaciously many people cling to the mistaken idea that an individual price, though expressed in money, may be determined wholly without reference to money. Others, more open-minded but almost equally confused, see the necessity of including the quantity of money among the causes determining prices, but in the careless spirit of eclecticism simply jumble it in with a miscellaneous collection of influences affecting prices, with no regard for their mutual relations. It should be clearly recognized that price levels must be studied independently of individual prices.
VIII.68 The legitimacy of separating the study of price levels from that of prices will be clearly recognized, when it is seen that individual prices cannot be fully determined by supply and demand, money cost of production, etc., without surreptitiously introducing the price level itself. We can scarcely overemphasize the fact that the "supply and demand" or the "cost of production" of goods in terms of money do not and cannot completely determine prices. Each phrase, fully expressed, already implies money. There is always hidden somewhere the assumption of a general price level. Yet writers, like David A. Wells,*8 have seriously sought the explanation of a general change in price levels in the individual price changes of various commodities considered separately. Much of their reasoning goes no farther than to explain one price in terms of other prices. If we attempt to explain the money price of a finished product in terms of the money prices of its raw materials and other money costs of prices of production, it is clear that we merely shift the problem. We have still to explain these antecedent prices. In elementary textbooks much emphasis is laid on the fact that "demand" and "supply" are incomplete designations and that to give them meaning it is necessary to add to each the phrase "at a price."But emphasis also needs to be laid on the fact that "demand at a price" and "supply at a price" are still incomplete designations, and that to give them meaning it is necessary to add "at a price level." The demand for sugar is not only relative to the price of sugar, but also to the general level of other things. Not only is the demand for sugar at ten cents a pound greater than the demand at twenty cents a pound (at a given level of prices of other things), but the demand at twenty cents at a high level of prices is greater than the demand at twenty cents at a low level of prices. In fact if the price level is doubled, the demand at twenty cents a pound will be as great as the demand was before at ten cents a pound, assuming that the doubling applies likewise to wages and incomes generally. The significance of a dollar lies in what it will buy; and the equivalence between sugar and dollars is at bottom an equivalence between sugar and what dollars will buy. A change in the amount of what dollars will buy is as important as a change in the amount of sugar. The price of sugar in dollars depends partly on sugar and partly on dollars,—that is, on what dollars will buy—that is, on the price level. Therefore, beneath the price of sugar in particular there lies, as one of the bases of that particular price, the general level of prices. We have more need to study the price level preparatory to a study of the price of sugar than to study the price of sugar preparatory to a study of the price level. We cannot explain the level of the sea by the height of its individual waves; rather must we explain in part the position of these waves by the general level of the sea. Each "supply curve" or "demand curve" rests upon the unconscious assumption of a price level already existing. Although the curves relate to a commodity, they relate to it only as compared with money. A price is a ratio of exchange between the commodity and money. The money side of each exchange must never be forgotten nor the fact that money already stands in the mind of the purchaser for a general purchasing power. Although every buyer and seller who bids or offers a price for a particular commodity tacitly assumes a given purchasing power of the money bid or offered, he is usually as unconscious of so doing as the spectator of a picture is unconscious of the fact that he is using the background of the picture against which to measure the figures in the foreground. As a consequence, if the general level changes, the supply and demand curves for the particular commodity considered will change accordingly. If the purchasing power of the dollar is reduced to half its former amount, these curves will be doubled in height; for each person will give or take double the former money for a given quantity of the commodity. If, through special causes affecting a special commodity, the supply and demand curves of that commodity and their intersection are raised or lowered, then the supply and demand curves of some other goods must change in the reverse direction. That is, if one commodity rises in price (without any change in the quantity of it or of other things bought and sold, and without any change in the volume of circulating medium or in the velocity of circulation), then other commodities must fall in price. The increased money expended for this commodity will be taken from other purchases. In other words, the waves in the sea of prices have troughs. This can be seen from the equation of exchange. If we suppose the quantity of money and its velocity of circulation to remain unaltered, the left side of the equation remains the same, and therefore the right side must remain unaltered also. Consequently, any increase in one of its many terms, due to an increase of any individual price, must occur at the expense of the remaining terms.
VIII.69 It is, of course, true that a decrease in the price of any particular commodity will usually be accompanied by an increase in the amount of it exchanged, so that the product of the two may not decrease and may even increase if the amount exchanged increases sufficiently. In this case, since the right side of our equation remains the same, the effect of the increase in some terms will necessarily be a decrease in others; and the remaining terms of the right side must decrease to some extent. The effect may be a general or even a universal lowering of prices. Even in this case the reduction in the price level has no direct connection with the reduction in the price of the particular commodity, but is due to the increase in the amount of it exchanged.*9
VIII.70 The reactionary effect of the price of one commodity on the prices of other commodities must never be lost sight of. Much confusion will be escaped if we give up any attempt to reason directly from individual prices. Improvements in production will affect price levels simply as they affect the volume of business transacted. Any rational study of the influence of improvements in methods of production upon the level of prices should, therefore, fix attention, first, on the resulting volume of trade, and should aim to discover whether this, in turn, carries prices upwards or downwards.
VIII.71 One of the supposed causes of high prices to-day, much under discussion at the present time, is that of industrial and labor combinations. From what has been said, it must be evident that, other things remaining equal, trusts cannot affect the general level of prices through manipulating special commodities except as they change the amounts sold. If prices for one commodity are changed without a change in the number of sales, the effect on the price level will be neutralized by compensatory changes in other prices. If trade unions seek to raise prices of labor while trusts raise prices of commodities, the general level of everything may rise or fall; but it can rise only by a general decrease in the quantities of commodities, labor, etc., sold, or by an increase of currency, or by an increase in velocities of circulation. If there is neither an increase nor decrease in volume of business, and if the quantity and velocity of circulation of money and its substitutes remain unchanged, the price level cannot change. Changes in some parts of the price level may occur only at the expense of opposite changes in other parts.
VIII.72 We have seen that the price level is not determined by individual prices, but that, on the contrary, any individual price presupposes a price level. We have seen that the complete and only explanation of a price level is to be sought in factors of the equation of exchange and whatever antecedent causes affect those factors. The terms "demand" and "supply," used in reference to particular prices, have no significance whatever in explaining a rise or fall of price levels. In considering the influence affecting individual prices we say that an increase in supply lowers prices, but an increase in demand raises them. But in considering the influences affecting price levels we enter upon an entirely different set of concepts, and must not confuse the proposition that an increase in the trade (the Q's) tends to lower the price level, with the proposition that an increase in supply tends to lower an individual price. Trade (the Q's) is not supply—in fact is no more to be associated with supply than with demand. The Q's are the quantities finally sold by those who supply, and bought by those who demand.
VIII.73 We may here state a paradox which will serve to bring out clearly the distinction between the causation of individual prices relatively to each other and the causation of the general level of prices. The paradox is that although an increased demand for any individual commodity results in a greater consumption at a higher price, yet an increased general demand for goods will result in a greater trade (the Q's) at lower prices.
VIII.74 We cannot, therefore, reason directly from particular to general prices; we can reason only indirectly by reference to the effects on quantities. Sometimes the rise in an individual price raises and at other times lowers the general price level.*10 To draw a physical parallel let us suppose that a thousand piles have been driven in a quicksand and that the owner wishes to raise their level a foot. He gets hoisting apparatus and planting it on the piles pulls one of them up a foot. He then pulls up another and continues until he has pulled up each of the thousand. But if every time he has pulled one up a foot he has pushed down 999 over 1/999 of a foot, when he has finished, he will find his thousand piles lower than when he began. Each time a pile has risen, the average level of all has fallen.
VIII.75 The proposition that a general increase in demand, resulting in an increase in trade, tends to decrease and and not to increase the general level of prices, may be regarded as a sort of pons asinorum to test one's knowledge of the fundamental distinction between those influences affecting the general price level and those affecting the rise and fall of a particular price with respect to that level.
§ 9 VIII.76 We have seen that the various factors represented in the equation of exchange do not stand on the same causal footing. Prices are the passive element and their general level must conform to the other factors. The causal propositions we have found to be true normally, i.e. after transitions are completed, are in brief as follows:—
VIII.77 1. An increase in the quantity of money (M) tends to increase deposits (M') proportionally, and the increase in these two (M and M') tends to increase prices proportionally.
VIII.78 2. An increase in the quantity of money in one country tends to spread to others using the same money metal, and to the arts, as soon as the price levels or the relative value of money and bullion differ enough to make export or melting of the money metal profitable and to raise slightly world prices.
VIII.79 3. An increase in deposits (M') compared with money (M) tends likewise to displace and melt coin, and to raise world prices.
VIII.80 4. An increase in velocities tends to produce similar effects.
VIII.81 5. An increase in the volume of trade (the Q's) tends, not only to decrease prices, but also to increase velocities and deposits relatively to money and through them to neutralize partly or wholly the said decrease in prices.
VIII.82 6. The price level is the effect and cannot be the cause of change in the other factors.
VIII.83 7. Innumerable causes outside the equation of exchange may affect M, M', V, V', and the Q's and through them affect the p's. Among these outside causes are the price levels in surrounding countries.
VIII.84 8. The causation of individual prices can only explain prices as compared among themselves. It cannot explain the general level of prices as compared with money.
VIII.85 9. Some of the foregoing propositions are subject to slight modification during transition periods. It is then true, for instance, that an increase in the quantity of money (M) besides having the effects above mentioned will change temporarily the ratio of M' to M and disturb temporarily V, V', and the Q's, making a credit cycle.
VIII.86 In general, then, our conclusion as to causes and effects is that normally the price level (the p's) is the effect of all the other factors in the equation of exchange (M, M', V, V', and the Q's); that among these other factors, deposits (M') are chiefly the effect of money, given the normal ratio of M' to M; that this ratio is partly the effect of trade (the Q's); that V and V' are also partly the effects of the Q's; and that all of the magnitudes, M, M', V, V', and the Q's are the effects of antecedent causes outside the equation of exchange, ad infinitum.
VIII.87 The main conclusion is that we find nothing to interfere with the truth of the quantity theory that variations in money (M) produce normally proportional changes in prices.

## Endnotes

1. Cf. Albert Aupetit, Essai sur la théorie générale de la monnaie, Paris (Guillaumin), 1901.
2. Cf. Hildebrand, Theorie des Geldes, Chapter XI, who, though seemingly unconscious of its bearing on the velocity of circulation, calls attention to the difference between two communities having the same expenditures, but one having a uniform trade and the other a trade "bunched" in certain seasons—say the crop seasons.
3. This is very far from asserting as Laughlin does that "The limit to the increase in legitimate credit operations is always expansible with the increase in the actual movement of goods"; see the Principles of Money, New York (Scribner), 1903, p. 82. We have seen, in Chapter IV, that deposit currency is proportional to the amount of money; a change in trade may indirectly, i.e. by changing the habits of the community, influence the proportion, but, except for transition periods, it cannot influence it directly.
4. See § 1 of Appendix to (this) Chapter VIII.
5. "Mathematical Theory of Banking,", Journal of the Royal Statistical Society, March, 1888.
6. "Statistical inquiry into the influence of credit upon the level of prices," University Studies (University of Nebraska), January, 1907, pp. 41-83.
7. Cf. Irving Fisher, "Mathematical Investigations in the Theory and Value of Prices," Transactions of the Connecticut Academy of Arts and Sciences, Vol. IX, 1892, p. 62.
8. Recent Economic Changes, New York (Appleton), 1890, Chapter IV.
9. For further discussion, see § 2 of Appendix to (this) Chapter VIII.
10. For further discussion, see § 2 of Appendix to (this) Chapter VIII.