The Purchasing Power of Money
By Irving Fisher
THE purpose of this book is to set forth the principles determining the purchasing power of money and to apply those principles to the study of historical changes in that purchasing power, including in particular the recent change in “the cost of living,” which has aroused world-wide discussion.If the principles here advocated are correct, the purchasing power of money–or its reciprocal, the level of prices–depends exclusively on five definite factors: (1) the volume of money in circulation; (2) its velocity of circulation; (3) the volume of bank deposits subject to check; (4) its velocity; and (5) the volume of trade. Each of these five magnitudes is extremely definite, and their relation to the purchasing power of money is definitely expressed by an “equation of exchange.” In my opinion, the branch of economics which treats of these five regulators of purchasing power ought to be recognized and ultimately will be recognized as an exact science, capable of precise formulation, demonstration, and statistical verification…. [From the Preface to the First Edition]
First Pub. Date
New York: The Macmillan Co.
Assisted by Harry G. Brown (Instructor in Political Economy in Yale U.) 2nd edition. Harry G. Brown, assistant.
The text of this edition is in the public domain.
- Preface to the First Edition
- Preface to the Second Edition
- Suggestions to Readers
- Chapter 1
- Chapter 2
- Chapter 3
- Chapter 4
- Chapter 5
- Chapter 6
- Chapter 7
- Chapter 8
- Chapter 9
- Chapter 10
- Chapter 11
- Chapter 12
- Chapter 13
- Appendix to Chapter II
- Appendix to Chapter III
- Appendix to Chapter V
- Appendix to Chapter VI
- Appendix to Chapter VII
- Appendix to Chapter VIII
- Appendix to Chapter X
- Appendix to Chapter XII
IN the last chapter it was shown that the quantity of bank deposits normally maintains a definite ratio to the quantity of money in circulation and to the amount of bank reserves. As long as this normal relation holds, the existence of bank deposits merely
magnifies the effect on the level of prices produced by the quantity of money in circulation and does not in the least
distort that effect. Moreover, changes in velocity or trade will have the same effect on prices, whether bank deposits are included or not.
But during periods of transition this relation between money (
M) and deposits (
M‘) is by no means rigid.
We are now ready to study these periods of transition. The change which constitutes a transition may be a change in the quantity of money, or in any other factor of the equation of exchange, or in all. Usually all are involved, but the chief factor which we shall select for study (together with its effect on the other factors) is quantity of money. If the quantity of money were suddenly doubled, the effect of the change would not be the same at first as later. The ultimate effect is, as we have seen, to double prices; but before this happens, the prices oscillate up and down. In this chapter we shall consider the
temporary effects during
the period of transition separately from the
permanent or ultimate effects which were considered in the last chapter. These permanent or ultimate effects follow after a new equilibrium is established,—if, indeed, such a condition as equilibrium may be said ever to be established. What we are concerned with in this chapter is the temporary effects,
i.e. those in the transition period.
The transition periods may be characterized either by rising prices or by falling prices.
Rising prices must be clearly distinguished from
high prices, and
low. With stationary levels, high or low, we have in this chapter nothing to do. Our concern is with rising or falling prices. Rising prices mark the transition between a low and a high level of prices, just as a hill marks the transition between flat lowlands and flat highlands.
Since the study of these acclivities and declivities is bound up with that of the adjustment of interest rates, our first task is to present a brief statement regarding the effects of rising and falling prices
the rate of interest. Indeed, the chief object of this chapter is to show that the peculiar behavior of the rate of interest during transition periods is largely responsible for the crises and depressions in which price movements end.
It must be borne in mind that although business loans are made in the form of money, yet whenever a man borrows money, he does not do this in order to hoard the money, but to purchase goods with it. To all intents and purposes, therefore, when A borrows one hundred dollars from B in order to purchase, say, one
hundred units of a given commodity at one dollar per unit, it may be said that B is virtually lending A one hundred units of that commodity. And if at the end of a year A returns one hundred dollars to B, but the price of the commodity has meanwhile advanced, then B has lost a fraction of the purchasing power originally loaned to A. For even though A should happen to return to B the identical coins in which the loan was made, these coins represent somewhat less than the original quantity of purchasable commodities. Bearing this in mind in our investigation of interest rates, let us suppose that prices are rising at the rate of 3 per cent each year. It is plain that the man who lends $100 at the beginning of the year must, in order to get 5 per cent interest in purchasing power, receive back both $103 (then the equivalent of the $100 lent) plus 5 per cent of this, or a total of $108.15. That is, in order to get 5 per cent interest in
actual purchasing power, he must receive a little more than 8 per cent interest in
money. The 3 per cent rise of prices thus ought to add approximately 3 per cent to the rate of interest. Rising prices, therefore, in order that the relations between creditor and debtor shall be the same during the rise as before and after, require higher money interest than stationary prices require.
Not only will lenders require, but borrowers can afford to pay higher interest in terms of money; and to some extent competition will gradually force them to do so.
*40 Yet we are so accustomed in our business dealings to consider money as the one thing stable,—to think of a “dollar as a dollar” regardless of the passage of time, that we reluctantly yield to this process of readjustment, thus rendering it very slow and imperfect. When prices
are rising at the rate of 3 per cent a year, and the normal rate of interest—
i.e. the rate which would exist were prices stationary—is 5 per cent, the actual rate, though it ought (in order to make up for the rising prices) to be 8.15 per cent, will not ordinarily reach that figure; but it may reach, say, 6 per cent, and later, 7 per cent. This inadequacy and tardiness of adjustment are fostered, moreover, by law and custom, which arbitrarily tend to keep down the rate of interest.
A similar inadequacy of adjustment is observed when prices are falling. Suppose that, by the end of a year, $97 will buy as much as $100 at the beginning. In that case the lender, in order to get back a purchasing power equivalent to his principal and 5 per cent interest, should get, not $105, but only $97 + 5 per cent of $97 or $101.85. Thus the rate of interest in money should in this case be 1.85 per cent, or less than 2 per cent, instead of the original 5 per cent. In other words, the 3 per cent fall of prices should reduce the rate of interest by approximately 3 per cent. But as a matter of fact, such a perfect adjustment is seldom reached, and money interest keeps far above 2 per cent for a considerable time.
We are now ready to study temporary or transitional changes in the factors of our equation of exchange. Let us begin by assuming a slight initial disturbance, such as would be produced, for instance, by an increase in the quantity of gold. This, through the equation of exchange, will cause a rise in prices. As prices rise, profits of business men, measured in money, will rise also, even if the costs of business were to rise in the same
proportion. Thus, if a man who sold $10,000 of goods at a cost of $6000, thus clearing $4000, could get double prices at double cost, his profit would be double also, being $20,000—$12,000, which is $8000. Of course such a rise of prices would be purely nominal, as it would merely keep pace with the rise in price level. The business man would gain no advantage, for his larger money profits would buy no more than his former smaller money profits bought before. But, as a matter of fact, the business man’s profits will rise more than this because the rate of interest he has to pay will not adjust itself immediately. Among his costs is interest, and this cost will not, at first, rise. Thus the profits
will rise faster than prices. Consequently, he will find himself making greater profits than usual, and be encouraged to expand his business by increasing his borrowings. These borrowings are mostly in the form of short-time loans from banks; and, as we have seen, short-time loans engender deposits. As is well known, the correspondence between loans and deposits is remarkably exact.
*42 Therefore, deposit currency (
M‘) will increase, but this extension of deposit currency tends further to raise the general level of prices, just as the increase of gold raised it in the first place.
*43 Hence prices, which were already outstripping the rate of interest, tend to outstrip it still further, enabling borrowers,
who were already increasing their profits, to increase them still further. More loans are demanded, and although nominal interest may be forced up somewhat, still it keeps lagging below the normal level. Yet nominally the rate of interest
has increased; and hence the lenders, too, including banks, are led to become more enterprising. Beguiled by the higher nominal rates into the belief that fairly high interest is being realized, they extend their loans, and with the resulting expansion of bank loans, deposit currency (
M‘), already expanded, expands still more. Also, if prices are rising, the money value of collateral may be greater, making it easier for borrowers to get large credit.
*44 Hence prices rise still further.
*45 This sequence of events may be briefly stated as follows:—
1. Prices rise (whatever the first cause may be; but we have chosen for illustration an increase in the amount of gold).
2. The rate of interest rises, but not sufficiently.
3. Enterprisers (to use Professor Fetter’s term), encouraged by large profits, expand their loans.
4. Deposit currency (
M‘) expands relatively to money (
5. Prices continue to rise, that is, phenomenon No. 1 is repeated. Then No. 2 is repeated, and so on.
In other words, a slight initial rise of prices sets in motion a train of events which tends to repeat itself. Rise of prices generates rise of prices, and continues to do so as long
as the interest rate lags behind its normal figure.
The expansion of deposit currency indicated in this cumulative movement abnormally increases the ratio of
M. This is evident if the rise of prices begins in a change in some element or elements in the equation other than the quantity of money; for if
M remains constant and
M‘ increases, the ratio
M must increase also. If
M increases in any ratio,
M‘ will increase in a greater ratio. If it increased only in the same ratio, prices would increase in that ratio (assuming velocities and quantities unchanged); and if prices increased in that ratio, loans (which being made to buy goods must be adjusted to the prices of goods) would have to be increased in that ratio in order to secure merely the same goods as before. But enterprisers, wishing to profit by the lag in interest, would extend the loans beyond this old or original point. Therefore, deposits based on loans would increase in a greater ratio. That is, the ratio
M would increase. In other words, during the period while
M is increasing,
M‘ increases still faster, thus disturbing the normal ratio between these two forms of currency.
This, however, is not the only disturbance caused by the increase in
M. There are disturbances in the
Q‘s (or in other words
V, and in
V‘. These will be taken up in order. Trade (the
Q‘s) will be stimulated by the easy terms for loans. This effect is always observed during rising prices, and people note approvingly that “business is good” and “times are booming.” Such statements represent the point of view of the ordinary business man who is an “enterpriser-borrower.” They do not represent the sentiments of the creditor, the salaried man, or the laborer, most of whom are silent but
long-suffering,—paying higher prices, but not getting proportionally higher incomes.
The first cause of the unhealthy increase in trade lies in the fact that prices, like interest, lag behind their full adjustment and have to be pushed up, so to speak, by increased purchases. This is especially true in cases where the original impetus came from an increase in money. The surplus money is first expended at nearly the old price level, but its continued expenditure gradually raises prices. In the meantime the volume of purchases will be somewhat greater than it would have been had prices risen more promptly. In fact, from the point of view of those who are selling goods, it is the possibility of a greater volume of sales at the old prices which gives encouragement to an increase of prices. Seeing that they can find purchasers for more goods than before at the previously prevailing prices, or for as many goods as before at higher prices, they will charge these higher prices.
But the amount of trade is dependent, almost entirely, on other things than the quantity of currency, so that an increase of currency cannot, even temporarily, very greatly increase trade. In ordinarily good times practically the whole community is engaged in labor, producing, transporting, and exchanging goods. The increase of currency of a “boom” period cannot, of itself, increase the population, extend invention, or increase the efficiency of labor. These factors pretty definitely limit the amount of trade which can be reasonably carried on. So, although the gains of the enterpriser-borrower may exert a psychological stimulus on trade, though a few unemployed may be employed, and some others in a few lines induced to work overtime, and although there may be some additional buying and selling
which is speculative, yet almost the entire effect of an increase of deposits must be seen in a change of prices. Normally the entire effect would so express itself, but transitionally there will be also some increase in the
We next observe that the rise in prices—fall in the purchasing power of money—will accelerate the circulation of money. We all hasten to get rid of any commodity which, like ripe fruit, is spoiling on our hands.
*46 Money is no exception; when it is depreciating, holders will get rid of it as fast as possible. As they view it, their motive is to buy goods which appreciate in terms of money in order to profit by the rise in their value. The inevitable result is that these goods rise in price still further. The series of changes, then, initiated by rising prices, expressed more fully than before, is as follows:—
1. Prices rise.
2. Velocities of circulation (
V‘) increase; the rate of interest rises, but not sufficiently.
3. Profits increase, loans expand, and the
4. Deposit currency (
M‘) expands relatively to money (
5. Prices continue to rise; that is, phenomenon No. 1 is repeated. Then No. 2 is repeated, and so on.
It will be noticed that these changes now involve all
the magnitudes in the equation of exchange. They are temporary changes, pertaining only to the transition period. They are like temporary increases in power and readjustments in an automobile climbing a hill.
Evidently the expansion coming from this cycle of causes cannot proceed forever. It must ultimately spend itself. The check upon its continued operation lies in the rate of interest. It was the tardiness of the rise in interest that was responsible for the abnormal condition. But the rise in interest, though belated, is progressive, and, as soon as it overtakes the rate of rise in prices, the whole situation is changed. If prices are rising at the rate of 2 per cent per annum, the boom will continue only until interest becomes 2 per cent higher. It then offsets the rate of rise in prices. The banks are forced in self-defense to raise interest because they cannot stand so abnormal an expansion of loans relatively to reserves. As soon as the interest rate becomes adjusted, borrowers can no longer hope to make great profits, and the demand for loans ceases to expand.
There are also other forces placing a limitation on further expansion of deposit currency and introducing a tendency to contraction. Not only is the amount of deposit currency limited both by law and by prudence to a certain maximum multiple of the amount of bank reserves; but bank reserves are themselves limited by the amount of money available for use as reserves. Further, with the rise of interest, the value of certain collateral securities, such as bonds, on the basis of which loans are made, begins to fall. Such securities, being worth the discounted value of fixed sums, fall
as interest rises; and therefore they cannot be used as collateral for loans as large as before. This check to loans is, as previously explained, a check to deposits also.
With the rise of interest, those who have counted on renewing their loans at the former rates and for the former amounts are unable to do so. It follows that some of them are destined to fail. The failure (or prospect of failure) of firms that have borrowed heavily from banks induces fear on the part of many depositors that the banks will not be able to realize on these loans. Hence the banks themselves fall under suspicion, and for this reason depositors demand cash. Then occur “runs on the banks,” which deplete the bank reserves at the very moment they are most needed.
*47 Being short of reserves, the banks have to curtail their loans. It is then that the rate of interest rises to a panic figure. Those enterprisers who are caught
must have currency
*48 to liquidate their obligations, and to get it are willing to pay high interest. Some of them are destined to become bankrupt, and, with their failure, the demand for loans is correspondingly reduced. This culmination of an upward price movement is what is called a crisis,
*49—a condition characterized by bankruptcies, and the bankruptcies
being due to a lack of cash when it is most needed.
It is generally recognized that the collapse of bank credit brought about by loss of confidence is the essential fact of every crisis, be the cause of the loss of confidence what it may. What is not generally recognized, and what it is desired in this chapter to emphasize, is that this loss of confidence (in the typical commercial crisis here described) is a consequence of a belated adjustment in the interest rate.
It is not our purpose here to discuss nonmonetary causes of crises, further than to say that the monetary causes are the most important
when taken in connection with the maladjustments in the rate of interest. The other factors often emphasized are merely effects of this maladjustment. “Overconsumption” and “over-investment” are cases in point. The reason many people spend more than they can afford is that they are relying on the dollar as a stable unit when as a matter of fact its purchasing power is rapidly falling. The bond-holder, for instance, is beguiled into trenching on his capital. He never dreams that he ought to lay by a sinking fund because the decrease in purchasing power of money is reducing the real value of his principal. Again, the stockholder and enterpriser generally are beguiled by a vain reliance on the stability of the rate of interest, and so they overinvest. It is true that for a time they are gaining what the bondholder is losing and are therefore justified in both spending and investing more than if prices were not rising; and at first they prosper. But sooner or later the rate of interest rises above what they had reckoned on, and they awake to the fact that they have embarked on enterprises which cannot pay these high rates.
Then a curious thing happens: borrowers, unable to get easy loans, blame the high rate of interest for conditions which were really due to the fact that the previous rate of interest was not high enough. Had the previous rate been high enough, the borrowers never would have overinvested.
The contraction of loans and deposits is accompanied by a decrease in velocities, and these conspire to prevent a further rise of prices and tend toward a fall. The crest of the wave is reached and a reaction sets in. Since prices have stopped rising, the rate of interest, which has risen to compensate the rise of prices,
should fall again. But just as at first it was slow to rise, so now it is slow to fall. In fact, it tends for a time to rise still further.
The mistakes of the past of overborrowing compel the unfortunate victims of these mistakes to borrow still further to protect their solvency. It is this special abnormality which marks the period as a “crisis.” Loans are wanted to continue old debts or to pay these debts by creating new ones. They are not wanted because of new investments but because of obligations connected with old (and ill-fated) investments. The problem is how to get extricated from the meshes of past commitments. It is the problem of liquidation. Even when interest begins to fall, it falls slowly, and failures continue to occur. Borrowers now find that interest, though nominally low, is still hard to meet. Especially do they find this true in the case of contracts made just before prices ceased rising or just before they began to fall. The rate of interest in these cases is agreed upon before the change in conditions takes place.
There will, in consequence, be little if any adjustment in lowering nominal interest. Because interest is hard to pay, failures continue to occur. There comes to be a greater hesitation in lending on any but the best security, and a hesitation to borrow save when the prospects of success are the greatest. Bank loans tend to be low, and consequently deposits (
M‘) are reduced. The contraction of deposit currency makes prices fall still more. Those who have borrowed for the purpose of buying stocks of goods now find they cannot sell them for enough even to pay back what they have borrowed. Owing to this tardiness of the interest rate in falling to a lower and a normal level, the sequence of events is now the opposite of what it was before:—
1. Prices fall.
2. The rate of interest falls, but not sufficiently.
3. Enterpriser-borrowers, discouraged by small profits, contract their borrowings.
4. Deposit currency (
M‘) contracts relatively to money (
5. Prices continue to fall; that is, phenomenon No. 1 is repeated. Then No. 2 is repeated, and so on.
Thus a fall of prices generates a further fall of prices. The cycle evidently repeats itself as long as the rate of interest lags behind. The man who loses most is the business man in debt. He is the typical business man, and he now complains that “business is bad.” There is a “depression of trade.”
During this depression, velocities (
V‘) are abnormally low. People are less hasty to spend money or checks when the dollars they represent are rising in purchasing power. The Q’s (or quantities in trade) decline because (1) the initiators of trade—the enterpriser-borrowers—are discouraged; (2) the inertia of
high prices can be overcome only by a falling off of expenditures; (3) trade against money which alone the
Q‘s represent gives way somewhat to barter. For a time there is not enough money to do the business which has to be done at existing prices, for these prices are still high and will not immediately adjust themselves to the sudden contraction. When such a “money famine” exists, there is no way of doing all the business except by eking out money transactions with barter. But while recourse to barter eases the first fall of prices, the inconvenience of barter immediately begins to operate as an additional force tending to reduce prices by inducing sellers to sell at a sacrifice if only money can be secured and barter avoided; although this effect is partly neutralized for a time by a decrease in the amount of business which people will attempt under such adverse conditions. A statement including these factors is:—
1. Prices fall.
2. Velocities of circulation (
V‘) fall; the rate of interest falls, but not sufficiently.
3. Profits decrease; loans and the
4. Deposit currency (
M‘) contracts relatively to money (
Prices continue to fall; that is, phenomenon No. 1 is repeated. Then No. 2 is repeated, and so on.
The contraction brought about by this cycle of causes becomes self-limiting as soon as the rate of interest overtakes the rate of fall in prices. After a time, normal conditions begin to return. The weakest producers have been forced out, or have at least been prevented from expanding their business by increased loans. The strongest firms are left to build up a new credit structure. The continuous fall of prices has
made it impossible for most borrowers to pay the old high rates of interest; the demand for loans diminishes, and interest falls to a point such that borrowers can at last pay it. Borrowers again become willing to take ventures; failures decrease in number; bank loans cease to decrease; prices cease to fall; borrowing and carrying on business become profitable; loans are again demanded; prices again begin to rise, and there occurs a repetition of the upward movement already described.
We have considered the rise, culmination, fall, and recovery of prices. These changes are abnormal oscillations, due to some initial disturbance. The upward and downward movements taken together constitute a complete credit cycle, which resembles the forward and backward movements of a pendulum.
*50 In most cases the time occupied by the swing of the commercial pendulum to and fro is about ten years. While the pendulum is continually seeking a stable position, practically there is almost always some occurrence to prevent perfect equilibrium. Oscillations are set up which, though tending to be self-corrective, are continually perpetuated by fresh disturbances. Any cause which disturbs equilibrium will suffice to set up oscillations. One of the most common of such causes is an increase in the quantity of money.
*51 Another is a shock to business confidence (affecting enterprise, loans, and deposits). A third is short crops, affecting the
Q‘s. A fourth is invention.
The factors in the equation of exchange are therefore
continually seeking normal adjustment. A ship in a calm sea will “pitch” only a few times before coming to rest, but in a high sea the pitching never ceases. While continually seeking equilibrium, the ship continually encounters causes which accentuate the oscillation. The factors seeking mutual adjustment are money in circulation, deposits, their velocities, the
Q‘s and the
p‘s. These magnitudes must always be linked together by the equation
SpQ. This represents the mechanism of exchange. But in order to conform to such a relation the displacement of any one part of the mechanism spreads its effects during the transition period over all parts. Since periods of transition are the rule and those of equilibrium the exception, the mechanism of exchange is almost always in a dynamic rather than a static condition.
It must not be assumed that every credit cycle is so marked as to produce artificially excessive business activity at one time and “hard times” at another. The rhythm may be more or less extreme in the width of its fluctuations. If banks are conservative in making loans during the periods of rising prices, and the expansion of credit currency is therefore limited, the rise of prices is likewise limited, and the succeeding fall is apt to be less and to take place more gradually. If there were a better appreciation of the meaning of changes in the price level and an endeavor to balance these changes by adjustment in the rate of interest, the oscillations might be very greatly mitigated. It is the lagging behind of the rate of interest which allows the oscillations to reach so great proportions. On this point Marshall well says: “The cause of alternating periods of inflation and depression of commercial activity… is
intimately connected with those variations in the real rate of interest which are caused by changes in the purchasing power of money. For when prices are likely to rise, people rush to borrow money and buy goods, and thus help prices to rise; business is inflated, and is managed recklessly and wastefully; those working on borrowed capital pay back less real value than they borrowed, and enrich themselves at the expense of the community. When afterwards credit is shaken and prices begin to fall, every one wants to get rid of commodities which are falling in value and to get hold of money which is rapidly rising; this makes prices fall all the faster, and the further fall makes credit shrink even more, and thus for a long time prices fall because prices have fallen.”
A somewhat different sort of cycle is the seasonal fluctuation which occurs annually. Such fluctuations, for the most part, are due, not to the departure from a state of equilibrium, but rather to a continuous adjustment to conditions, which, though changing, are normal and expected. As the autumn periods of harvesting and crop moving approach, there is a tendency toward a lower level of prices, followed after the passing of this period and the approach of winter by a rise of prices.
In the present chapter we have analyzed the phenomena characteristic of periods of transition. We have found that one such “boom” period leads to a reaction, and that the action and reaction complete a cycle of “prosperity” and “depression.”
It has been seen that rising prices tend towards a
higher nominal interest, and falling prices tend towards a lower, but that in general the adjustment is incomplete. With any initial rise of prices comes an expansion of loans, owing to the fact that interest does not at once adjust itself. This produces profits for the enterpriser-borrower, and his demand for loans further extends deposit currency. This extension still further raises prices, a result accentuated by a rise in velocities though somewhat mitigated by an increase in trade. When interest has become adjusted to rising prices, and loans and deposits have reached the limit set for them by the bank reserves and other conditions, the fact that prices no longer are rising necessitates a new adjustment. Those whose business has been unduly extended now find the high rates of interest oppressive. Failures result, constituting a commercial crisis. A reaction sets in; a reverse movement is initiated. A fall of prices, once begun, tends to be accelerated for reasons exactly corresponding to those which operate in the opposite situation.
The Rate of Interest, New York (Macmillan), 1907, Chapters V, XIV.
Statistical Studies in the New York Money Market (Macmillan), 1902, chart at end.
Jahrbücher für National-ökonomie, 1897 (Band 68), pp. 228-243, entitled “Der Bankzins als Regulator der Warenpreise.” This article, while not dealing directly with credit cycles as related to panics, points out the connection between the rate of interest on bank loans and changes in the level of prices due to the resulting expansion and contraction of such loans.
Money, New York (Macmillan), 1904, p. 223.
Journal de la Société de Statistique de Paris, April 1895, p. 143. The figures relate only to velocity of bank deposits. No corresponding figures for velocity of circulation of money exist. Pierre des Essars has shown that in European banks
V‘ reaches a maximum in crisis years almost without fail. The same I find true in this country as shown by the ratio of clearings to deposits in New York, Boston, and Philadelphia.
Yale Review, August, 1910, entitled “Typical Commercial Crises
versus a Money Panic.”
Rate of Interest, pp. 325, 326.
Des Crises Commerciales et de leur retour periodique en France en Angleterre et aux Etats-Unis. 2d ed., Paris (Guillaumin), 1889, pp. 4 and 5. See also translation of part dealing with the United States, by De Courcey W. Thom,
A Brief History of Panics in the United States, New York (Putnam), 1893, pp. 7-10.
Cours d’économie politique, Lausanne, 1897, pp. 282-284.
Rate of Interest, p. 336.
Principles of Economics, 5th ed., London (Macmillan), 1907, Vol. I, p. 594.
Notes for Chapter V