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PART IV, CHAPTER XXI: SUMMARY - Irving Fisher, The Theory of Interest, as determined by Impatience to Spend Income and Opportunity to Invest it 
The Theory of Interest, as determined by Impatience to Spend Income and Opportunity to Invest it (New York: Macmillan, 1930).
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PART IV, CHAPTER XXI
§1. Interest and Purchasing Power of Money
We have seen that, theoretically, the rate of interest should be subject to both a nominal and a real variation, the nominal variation being that connected with changes in the standard of value, and the real variation being that connected with the other and deeper economic causes.
As to the nominal variation in the rate of interest, we found that, theoretically, an appreciation of 1 per cent of the standard of value in which the rate of interest is expressed, compared with some other standard, will reduce the rate of interest in the former standard, compared with the latter, by about 1 per cent, and that, contrariwise, a depreciation of 1 per cent will raise the rate by that amount. Such a change in the rate of interest would merely be a change in the number expressing it, and not fundamentally a real change. Yet, in actual practice, for the very lack of this perfect theoretical adjustment, the appreciation or depreciation of the monetary standard does produce a real effect on the rate of interest, and that a most vicious one. This effect, in times of great changes in the purchasing power of money, is by far the greatest of all effects on the real rate of interest. This effect is due to the fact that the money rate of interest, while it does change somewhat according to the theory as described in Chapters II and XIX, does not usually change enough to fully compensate for the appreciation or depreciation. The inadequacy in the adjustment of the rate of interest results in an unforeseen loss to the debtor, and an unforeseen gain to the creditor, or vice versa as the case may be. When the price level falls, the interest rate nominally falls slightly, but really rises greatly and when the price level rises, the rate of interest nominally rises slightly, but really falls greatly. It is consequently of the utmost importance, in interpreting the rate of interest statistically, to ascertain in each case in which direction the monetary standard is moving and to remember that the direction in which the interest rate apparently moves is generally precisely the opposite of that in which it really moves.
It should also be noted that in so far as there exists any adjustment of the money rate of interest to the changes in the purchasing power of money, it is for the most part (1) lagged and (2) indirect. The lag, distributed, has been shown to extend over several years. The indirectness of the effect of changed purchasing power of money comes largely through the intermediate steps which affect business profits and volume of trade, which in turn affect the demand for loans and the rate of interest. There is very little direct and conscious adjustment through foresight. Where such foresight is conspicuous, as in the final period of German inflation, there is less lag in the effects.
§2. The Six Principles
But the more fundamental theory of interest presupposes a stable purchasing power of money so that the real and nominal rates coincide. In that case the rate is theoretically determined by six sets of equations or conditions: the two Opportunity Principles; the two Impatience Principles; and the two Market Principles. The last pair may be said to cover prima facie supply and demand.
(A) The market must be cleared—and cleared with respect to every interval of time. (B) The debts must be paid.
The other two pairs represent the two sets of forces, one objective and the other subjective, behind supply and demand. The subjective pair expresses the influence of human impatience or time preference.
(A) The rate of time preference depends on the character of the various individuals concerned and on each individual's prospective income, its size, time-shape and risk.(B) Each individual's rate of time preference tends, at the margin of choice, to harmonize with the market rate of interest. Human impatience to spend and enjoy income is crystallized into the market rate.
The objective pair expresses the influence of investment opportunities.
(A) Each individual is encompassed about by opportunities to change the character of his prospective income stream. (B) At the margin of choice, any additions to an individual's future income at the cost of more immediate income constitutes a return over that cost, the rate of which return over said cost is also crystallized into the market rate of interest.
So the rate of interest is the mouthpiece at once of impatience to spend income without delay and of opportunity to increase income by delay.
Thus both from the subjective and the objective field appear prototypes, one of each for every individual, of the market rate of interest.
That rate, i, is equal to every individual's degree of impatience or rate of time preference, f, and also to his investment opportunity rate or rate of return over cost, r.
Yet these equations are not enough to make the problem determinate without those of the other four sets of determining conditions (clearing the market, repaying debts and empirical dependence of impatience and investment opportunity).
Much less is it possible to determine the rate of interest from the subjective side alone, through time preference, or from the objective side alone, through investment opportunity, or "productivity", or "technique of production".
The full explanation requires both (as well as the market principles) in order that there may be as many independent equations as unknown variables in the problem. Moreover there is not merely one rate of interest; there are many, one for each interval of time. And even so the explanation is full only under the theoretical conditions presupposed. If we pass beyond the presuppositions in order to approximate closer to the actual world, we find that, to be determinate, the problem requires more and more equations of a more and more empirical nature. This is especially true as (1) we introduce risk with its innumerable and omnipresent ramifications, involving in particular a multiplicity of rates of interest even for the same period of time; and as (2) we extend our view to admit variations in all other prices besides the rates of interest, involving thereby the whole economic equilibrium, not only of the loan market but of all markets, each interacting on every other; and as (3) we extend our view from one theoretical market to the actual markets of the whole world, involving thereby all the relations of international trade; and as (4) we take account of any other factors which may not be included in the foregoing specifications so as to take account, in particular, of all "institutional" influences, laws, politics, banking practices, government finance and so on to the end.
In the economic universe, as in astronomy, every star reacts on every other. From a practical point of view we cannot ignore the many perturbations. But from the theoretical point of view we gain clearness, simplicity and beauty, if we allow ourselves to assume certain other things equal, and confine our laws to a little part of the whole, such as the solar system.
From such a point of view, the second approximation is the most instructive, rather than the first which rules out the important element of investment opportunity, or than the third which becomes too complicated and vague for any complete theoretical treatment.
§3. The Nature of Investment Opportunity
In the second approximation—which, as we have just noted, contains all that is most typical in the theory of the rate of interest—the distinctive factor is the rate of return over cost or the investment opportunity rate. This is also the most difficult factor to picture, isolate, and disentangle from the rate of interest which it helps determine. Therefore, it is a matter of great importance pedagogically to make that distinction clear. The investment opportunity rate is distinct from the market or loan rate of interest because an investment opportunity is distinct from a loan. Investment opportunity, as here used, does not include a mere loan at the market rate of interest nor any other purchase-and-sale transaction made merely on the basis of the market rate. The definition of investment opportunity is specially framed to exclude mere loans. It is any opportunity of an individual to modify his prospective income other than by merely lending or borrowing (or the equivalent, buying or selling) at the market rate of interest.
Under this definition and the assumptions employed in the theory there can never be any doubt as to whether a given proposed transaction is an investment opportunity or a market loan or purchase. In the case of a market loan or purchase the individual cannot vary the rate of interest by any act of his, such as varying the size of his transactions. Under our assumptions of a perfect market his influence on the market rate is not only unconscious but infinitesimal and therefore entirely negligible in our analysis in which his motivity is of the essence. In the case of an investment opportunity, on the other hand, he can vary the rate of return by varying the size of his operations.
This contrast between the theoretical constancy of the one and the variability of the other, in relation to individual action, is due to the fact that in the public market the individual is a negligible element, while an investment opportunity is more private and personal to him or his group. The former is typified by the purchase, say, of a Liberty bond, or other standard securities. The latter is typified by building a factory, improving a sales organization, deepening the shaft of a mine—cases where the marginal rate of return is under the control of the individual since he sets the margin.
Of course it is true that, in almost every such operation, there are elements of purchase and sale in which the market rate of interest is an implicit ingredient, but as long as the operation is not exclusively a mere market interest affair and contains other ingredients, the rate is subject to variation with the extent of the operation and so is to be called a rate of return over cost. We are here interested in those other ingredients which produce the variability and thus differentiate such a rate from the market rate of interest. They are the non-commercial or non-trading ingredients; they concern production and technique rather than trade. They deal not with the market place, but with nature, environment, and the refractory conditions which surround and hamper us in our efforts to secure income. They exist even when no market exists, when a Robinson Crusoe, a hermit, or an isolated ranchman battles with soil and the elements for his daily bread.
The rate of return over cost, under the law of diminishing returns, is thus far more elementary and primeval than the rate of interest, and however incrusted that rate of return may become with other elements which grow out of modern market conditions it is still the basic objective condition underlying our problem.
Thus the rate of return over cost is distinguished from the rate of interest (1) by varying with the extent of the individual's investment; (2) by being consciously recognized, as thus variable115 and controllable, by the individual; (3) by being, therefore, a personal and individual matter and not altogether a public market matter; (4) by being directly related to producing as contrasted with trading.
§4. Investment Opportunity for Society as a Whole
In modern society hermits and self-supporting ranches are so rare that we cannot find any important cases where investment opportunities exist in pure primitive form and apart from the alloy of trading. In fact, the most typical investment opportunities are not only full of such alloys but are tied up with market financing operations. Almost every big investment opportunity is married to a productive loan.
The best picture on a big scale of investment opportunity, divested so far as may be of all ancillary market features, is to be found by considering society as a whole instead of the individual.
Society as a whole cannot borrow or lend as an individual can. This world can, for instance, add nothing to this year's income by a loan from elsewhere and subtract this amount with interest from future income. Yet it can and does vary and control the total income stream according to investment opportunity.
This picture, in the large, of society arranging, modifying, adjusting its total income stream as between this year and later years is the most important picture we can draw of investment opportunity not only because it automatically leaves out borrowing and lending, or buying and selling, but also because it automatically reduces the picture of income to its fundamental terms of real or, as I prefer to call it, enjoyment income and its obverse, labor pain. We do not have to think so vividly, as we do in the case of an individual, of money items and intermediate processes. We can without difficulty fix our attention on the final consumption. Society is like Robinson Crusoe picking and eating his berries, however complicated may be the apparatus which intervenes between the labor of picking and the enjoyment of eating.
Society may add to or subtract from its income stream at will at any period, present or future. But beyond a certain point every addition at one period must be at the cost of a subtraction at some other period. If future income is added, the increment so added is a return on and at the cost of a decrement in less remote income. The rate of return over cost is thus a social phenomenon of great significance. There are two and only two ways in which society may effect the present cost and the future return. It may effect the present cost by exerting more present labor or by abstaining more from present consumption; and it may realize the future return over that cost either in the form of more future consumption or of less future toil.
Both the present and the future adjustments are effected by changing the use made of capital instruments including land and human beings. That is, the labor, land, and other capital of society may be used in many optional ways and in particular may be invested for the early or remote future.
If the capital instruments of the community are of such a nature as to offer a wide range of choice, we have seen that the rate of interest will tend to be steady. If the range of choice is narrow, the rate of interest will tend to be variable. If the range of choice is relatively rich in future income as compared with the more immediate income, the rate of interest will tend to be high. If the range of choice tends to favor immediate income as compared with more remote future income, the rate of interest will tend to be low.
Thus, for the United States during the last century, its resources were of such a character as to favor future income. This is true, for a time at least, in every undeveloped country, and, as we have seen, gives the chief explanation of the fact that the rate of interest in such localities is usually high. The same is true of countries recovering from war. Today, for instance, Germany resembles a pioneer country. Her present income is necessarily low, but her prospect of a higher and increasing income in a few years is very great. The range of choice is dominated by "low today and high tomorrow."
The range of choice in any community is subject to many changes as time goes on, due chiefly to one or more of three causes: first, a progressive increase or decrease in resources; second, the discovery of new resources or means of developing old ones; and third, change in political conditions.
Under the first head may be noted the impending exhaustion of the coal supply in England, as noted by Jevons and other writers. This will tend to make the income stream from that island decrease, at least in the remote future, and this in turn will tend to keep the rate of interest there low. Under the second head, the constant stream of new inventions, by making the available income streams rich in the future, at the sacrifice of immediate income, tends to make the rate of interest high. This effect, however, is confined to the period of exploitation of the new invention, and is succeeded later by an opposite tendency. During the last half century the exploitation of Stephenson's invention of the locomotive, by presenting the possibility of a relatively large future income at the cost of comparatively little sacrifice in the present, tended to keep the rate of interest high. As the period of extensive railroad building is drawing to a close, this effect is becoming exhausted, and the tendency of the rate of interest, so far as this particular influence is concerned, is to fall.
On the other hand, the invention of the automobile, and the inventions and discoveries in electricity and chemistry have succeeded the railroads as a field for investment and have required new sacrifices of immediate income for the sake of future income. Thus, as fast as the first effect of any one invention, tending to raise interest, wears off and is succeeded by its secondary effect in lowering interest, this secondary effect is likely to be offset by the oncoming of new inventions.
As to the third head, political conditions which affect the rate of interest, such as the insecurity of property rights which occurs during political upheaval, as in Russia recently, tend to make the pure or riskless rate of interest low. At the same time it adds an element of risk to most loans, thereby diminishing the number of safe and increasing the number of unsafe loans. Hence the commercial rate of interest in ordinary loans during periods of lawlessness is likely to be high. Reversely, during times of peace and security, the riskless rate of interest is comparatively high, while the commercial rate tends to be low.
§5. Time Preference
We turn now to the remaining factor, namely, the dependence of time preference of each individual on his selected income stream. We have seen that the rate of preference for immediate as compared with remote income will depend upon the character of the income stream selected, but the manner of this dependence is subject to great variation and change. The manner in which a spendthrift will react to an income stream is very different from the manner in which the shrewd accumulator of capital will react to the same income stream. We have seen that the time preference of an individual will vary with six different factors: (1) his foresight; (2) his self-control; (3) habit; (4) the prospective length and certainty of his life; (5) his love of offspring and regard for posterity; (6) fashion. It is evident that each of these circumstances may change. The causes most likely to effect such changes are: (1) training to foster a realization of the need to provide against the proverbial "rainy day"; (2) education in self-control; (3) formation of habits of frugality, avoiding parsimony on the one hand and extravagance on the other; (4) better hygiene and care of personal health, leading to longer and more healthful life; (5) incentives to provide more generously for offspring and for the future generations; (6) modification of fashion toward less wasteful and harmful expenditures for the purpose of ostentatious display.
These various factors may act and react upon each other, and may affect profoundly the rate of preference for present over future income, and thereby influence greatly the rate of interest. Where, as in Scotland, there are educational tendencies which instill the habit of thrift from childhood, the rate of interest tends to be low. Where, as in ancient Rome, at the time of its decline, there is a tendency toward reckless luxury, competition in ostentation, and a degeneration in the bonds of family life, there is a consequent absence of any desire to prolong income beyond one's own term of life, and the rate of interest tends to be high. Where, as in Russia, under the Czars, wealth tended to be concentrated and social stratification to be rigid, the great majority of the community, on the one hand, through poverty and the recklessness which poverty begets, tends to have a high rate of preference for present over future income, whereas, at the opposite end of the ladder, the inherited habit of luxurious living tends, though in a different way, in the same direction. In such a community, the rate of interest is likely to be unduly high.
From the foregoing enumeration, it is clear that the rate of interest is dependent upon very unstable influences many of which have their origin deep down in the social fabric and involve considerations not strictly economic. Any causes tending to affect intelligence, foresight, self-control, habits, the longevity of man, family affection, and fashion will have their influence upon the rate of interest.
§7. The Future
From what has been said it is clear that, in order to estimate the possible variation in the rate of interest, we may, broadly speaking, take account of the following three groups of causes: (1) the thrift, foresight, self-control, and love of offspring which exist in a community; (2) the progress of inventions; (3) the changes in the purchasing power of money. The first cause tends to lower the rate of interest; the second, to raise it at first and later to lower it; and the third to affect the nominal rate of interest, in one direction and the real rate of interest in the opposite direction.
Were it possible to estimate the strength of the various forces thus summarized, we might base upon them a prediction as to the rate of interest in the future. Such a prediction, however, to be of value, would require more painstaking study than has ever been given to this subject.
Without such a careful investigation, any prediction is hazardous. We can say, however, that the immediate prospects for a change in the monetary standard seem to be toward its stabilization; that this will tend toward a general prosperity, the main effects of which should be in the direction of lowering the rate of interest; that changes in thrift, foresight, self-control, and benevolence are for the most part likely to intensify these factors and thus to lower the rate of interest; and that the progress of discovery and invention shows now a tendency to increase in speed, the immediate result of which should be to raise the rate of interest but finally to lower it.
APPENDIX TO CHAPTER I
§1 (to Ch. I, § 1)
Rates of Interest in Relation to Annual Rates of Change in the Price Level, London, 1825-1927
|ANNUAL RATES OF|
CHANGE IN THE
|REAL INTEREST IN|
|REAL INTEREST IN|
Rates of Interest in Relation to Annual Rates of Change in the Price Level, New York, 1860-1927
|PRIME TWO NAME|
60-90 DAY COMMERCIAL
|ANNUAL RATES OF|
CHANGE IN THE PRICE LEVEL
|REAL RATE OF INTEREST IN|
Rates of Interest in Relation to Annual Rates of Change in the Price Level, Berlin, 1864-1912
|BANK||MARKET||ANNUAL RATES OF
CHANGE IN THE
|REAL INTEREST IN
|REAL INTEREST IN
Rates of Interest in Relation to Annual Rates of Change in the Price Level, Paris, 1872-1914
|BANK||MARKET||ANNUAL RATES OF|
CHANGE IN THE
|REAL RATE OF|
|REAL RATE OF|
Rates of Interest in Relation to Annual Rates of Change in the Price Level, Calcutta, 1861-1926, Tokyo, 1887-1926
|BANK||ANNUAL RATES OF
CHANGE IN THE
|REAL RATE OF
§2 (to Ch. XIX, § 6)
Tables of interest rates
Interest Rates on 15 Railroad Bonds, United States, 1900-1927
|YEAR||AVERAGE PER CENT||YEAR||AVERAGE PER CENT||YEAR||AVERAGE PER CENT|
SOURCE: The Statistical Bulletin of The Standard Statistics Company, Inc., 1929-1930, page 58.
The Wholesale Price Indexes used in making correlations are the indexes of the United States Bureau of Labor Statistics given in Table II.
APPENDIX TO CHAPTER XX
§1 (to Ch. XX, § 17)
Waiting as a Cost
IF waiting were a cost like other costs, it would be subject to the law of discount, according to which the capital-value of any article of wealth is equal to the discounted value of its expected income less the discounted value of its expected outgo. The value of the tree which has been mentioned, taken, say, at the end of 14 years, will actually be about $2, and this is the discounted value of the $3 of income which the tree will yield at the end of eleven more years. According to what I believe to be the correct theory, this $3 is the only future item involved in this example. But according to the theory here criticised, this is not the case. Besides this positive item of income, $3 due in eleven years, we have to deal with a series of eleven negative items called "waiting" distributed through these eleven years, and amounting to the interest—about 10 cents for the first year and gradually increasing to 15 cents for the last year. If the waiting-items were bona fide annual costs—like, for instance, actual labor-costs of pruning the trees—the process of discount would properly be applied to them. That is, if these waiting costs really exist, they ought to be discounted and their discounted value ought to be deducted from the discounted value of the $3 of expected income. But we should then have to assign as the value of the tree not the correct figure of $2 but an incorrect figure of much less. The fact that we cannot thus discount so-called "waiting" costs as we discount all true costs is a proof that the "cost of waiting" even if we insist on calling it such differs radically from true costs.7
If we are to have any logical, usable self-consistent theory of income and capital, all items of income, positive or negative—the negative ones being "costs"—must be discountable.
But, as an answer to this objection, it might be argued by the abstinence theorists (if I may ascribe to them the best argument I can think of) that while waiting-cost is certainly not a discountable cost, nevertheless its inclusion in the list of costs obviates the necessity of discounting the other items of cost or of income. If all income and all cost items, including waiting, are counted at full value—not discounted at all—the capital may be valued simply by taking their net sum. Thus, to count "waiting" as a cost appears as an alternative and plausible method of keeping accounts. By this system we could apparently get rid of discounting and merely add and subtract items regardless of their situation in time. While this procedure obviates the objection to the abstinence theory of cost, so far as its application to capital value is concerned, it leaves objections equally great to its application to income. If waiting is a genuine economic cost, it must certainly be included on the outgo side of the income account. To show how this would apply to the cost of the tree, the following table is presented.
|Income Account of Tree if Waiting is Cost|
|TRUE INCOME||ALLEGED OUTGO||ALLEGED NET INCOME||TRUE CAPITAL VALUE AT END OF YEAR|
|1st year||$0.00||Labor $1.00|
|2d year||0.00||" .05||1.10|
|3d year||0.00||" .05||1.15|
|* * * *||* * * * *||* * * *||* *||* * *|
|14th year||0.00||" .10||2.00|
|* * * *||* * * * *||* * * *||* *||* * *|
|25th year||3.00||" .15||3.00|
According to this method of accounting, we see that, during the year in which the sapling is planted, its cost consists of labor to the extent of $1, expended, let us say, at the beginning of the year, and 5 cents' worth of waiting suffered during the course of that first year. During the second year a waiting cost of about the same amount is incurred, and so on for each succeeding year, the cost of waiting gradually increasing, as the tables of compound interest would indicate, until in the fourteenth year it amounts to 10 cents, and in the twenty-fifth year to 15 cents. The total cost for the 25 years will then be $3, and the return to the planter at the end, from the sale of the tree, will also be $3. Consequently, if we take the whole period from the first application of labor to the final sale of the tree, the net income will be zero. This result is, to say the least, somewhat surprising, but not so much so as some other results of the same species of bookkeeping, as the following additional examples will show.
Suppose a person owns an annuity amounting to $100 a year for 10 years. According to the ordinary method of keeping accounts, his income consists of this $100 a year each year. But if we count the waiting as a cost, we shall find that the income for each year is less than $100. The owner of such an annuity will, during the first year, have to suffer "waiting" to the extent of $39, supposing interest is at 5 per cent; for this is the increase in value of his annuity during that year, due to his waiting for the future installments of income of which his annuity consists.8 His net income during that year, therefore, according to such accounting, is not $100, but $100 - $39, or $61. During the second year his income in this second year is somewhat greater, for the cost of "waiting" is only $35. His net income is, therefore, $100 - $35, or $65. Similar computations carried out for succeeding years are shown in the table on the following page.
|Income Account of Annuity if Waiting is Cost|
|TRUE INCOME||ALLEGED OUTGO||ALLEGED NET INCOME||TRUE CAPITAL VALUE AT BEGINNING OF YEAR|
|1st year||$100||Waiting $39||$61||$772|
|2d year||100||" 35||65||711|
|3d year||100||" 32||68||646|
|4th year||100||" 29||71||578|
|5th year||100||" 25||75||507|
|6th year||100||" 22||78||432|
|7th year||100||" 18||82||354|
|8th year||100||" 14||86||272|
|9th year||100||" 9||91||186|
|10th year||100||" 5||95||95|
Is it good bookkeeping to introduce a new and anomalous element of cost which results in making the net income of the annuitant not the $100 which he actually receives and which common sense recognizes as the income from the annuity but the queer sums given in the table, namely, $61, $65, $68, and so forth?9
To push this criticism to the limit, let us finally consider a perpetual annuity of $100 a year. In this case we shall find that the "cost of waiting" each year is the full $100, for the value of such an annuity, reckoned at 5 per cent, is $2000 reckoned at the beginning of each year, and $2100 reckoned at the end. If this annual $100 cost of waiting is to be regarded as a negative item of income and, like other costs, is to be subtracted from the positive income, we are forced to conclude that the owner of such a perpetual annuity receives each year no income whatever! For, if we deduct from the $100 of positive income the $100 cost of waiting, the remainder each year is zero! Yet a perpetual annuity is the simplest, purest case of income.
It should now be obvious that the theory which calls "waiting" a cost has worked out its own absurdity. If taken seriously and introduced into an accounting system it either interferes with the discount or capitalization principle or else distorts and even obliterates the income reckoning in its simplest, or most typical form, that of a perpetual annuity. It falsely simplifies the formula for valuing capital.
The idea that the value or price of an article should equal its cost seems to possess a certain fascination for many students of economics. That it is false has been sufficiently shown by Böhm-Bawerk through reasoning somewhat similar to the foregoing. That it is absurd when carried to its logical conclusion will be evident if we consider what happens if the same method of bookkeeping is carried out with respect to the future as well as the past. It is a poor rule which will not work both ways. This rule, applied to future expected income and outgo, yields the strange result that the capital value of any article instead of being less than its expected income is equal to it. Thus, to revert to the case of the tree, let us take its value at the end of 14 years. It is then worth $2, which, in the parlance of the abstinence theorists, is equal to its previous costs of production, consisting of $1 worth of labor plus $1 worth of waiting during the 14 years. It is also, in like manner, equal to the future income to be derived from it, which consists of $3 worth of actual receipts from the sale of the tree, due at the end of eleven more years, less the cost of waiting for those $3, which amounts to $1.
In the same way, the ten-year annuitant just considered has, at the beginning, property worth $772. This, according to proper bookkeeping, is the discounted value of the future income of $100 a year for 10 years, the total amount of which income is $1000. But, according to the abstinence theory, logically carried out, the income which the annuitant receives for the whole period is, as has been shown, not this $1000, but $772, which is just equal to the value of the property.10 Pursuing the method of limits, we find that, for the owner of a perpetual annuity, the same proposition would hold good. According to the true and ordinary method of reckoning, the total income from such an annuity is infinity, although its present capital value is only $2000. But according to the abstinence theorists the income itself is not infinite, but only $2000.
Those who are enamored of the alluring simplicity and neatness of the formula of the abstinence theorists, by which the capital value is not greater than past cost of production, but exactly equal to it, can scarcely be attracted by the exaggerated simplicity of the inverse theorem which is also involved, namely, that the capital value of any future expected income is not less than that income, but exactly equal to it also.
The fallacy of the abstinence theorists lies in the simple fact that waiting has no independent existence as a "cost." We can never locate it in time, nor estimate its amount, without first knowing some other more real and tangible costs. Waiting means nothing unless there is something to be waited for, and the cost of waiting can only be estimated in proportion to the magnitude of that which is so waited for. What is waited for is some payment or other event constituting income or outgo. But waiting for income or outgo is not itself income or outgo.
The mere accrual of value as we draw nearer the items constituting true income is neither income nor outgo but capital gain. The typical picture we should carry in our mind is of a saw-tooth curve consisting alternately of a gradual ascent along a discount curve, and a sudden drop as an income coupon is detached. The only income in this picture is the series of sudden drops, on which all the rest hangs. The gradual ascent in each saw tooth is not income; otherwise it would (largely) duplicate the true income. Nor is it outgo; otherwise it would (largely) negative the true income.
In the case of a bond selling at par these alternate ascents and drops are equal, and we carelessly speak of both as interest or as income. But the instant the bond sells above or below par we recognize the difference. If we follow this out we can scarcely go astray.
Even to those who do not formally accept any cost theory of interest, the interest itself will seem in some sense to be a cost, and in most books on economics, interest, however explained, is regarded as one of the costs of production. It is true that for a debtor who pays interest, the interest is, to him, a real cost, and is debited on his books. But we need only to be reminded of the debit and credit bookkeeping of the first chapter to see that this item is counterbalanced on the books of the creditor, to whom this interest is by no means a cost, but, on the contrary, an item of income. For society as a whole, therefore, even in the case of interest which is explicitly paid, it cannot be said that it constitutes a cost of production. In the case of a person who works with his own capital, the truth of this statement is even more evident. Economists who state that the independent capitalist must charge off interest as one of his costs of production seem to forget that such self-paid interest must be charged back again as income also. Labor sacrifice is quite different. It is a real cost and in no time bookkeeping can it be cancelled out. The fallacy of assuming that interest is a cost is doubtless due to the habit of regarding production from the point of view of the "enter priser." Since he usually pays interest, he comes to think of it purely as a cost.
I have devoted considerable space to the refutation of the abstinence theory so far as it is more than verbal, and collides with any workable theory of income, because its errors are so subtle and insidious as to beguile many of the best and most wary of economists.
I. WORKS ON INTEREST THEORY.
BÖHM-BAWERK, EUGEN VON. Capital and Interest. London, Macmillan and Co., 1890. xlv, 431 pp.
———. The Positive Theory of Capital. Translated by William Smart, London, Macmillan and Co., 1891. xl, 428 pp.
———. Recent Literature on Interest (1884-1889). New York, The Macmillan Co., 1903. xlii, 151 pp.
———. Positive Theorie des Kapitales. Dritte Auflage, Innsbrück, Wagner'schen Universitäts-Buchhandlung, 1912. xxiii, 652 pp. Also Exkurse, 477 pp.
———. Kleinere Abhanalungen über Kapital und Zins. Wien und Leipzig, Hölder-Pichler-Tempsky A. G., 1926. viii, 585 pp.
BROWN, HARRY GUNNISON. Economic Science and the Common Welfare. Columbia, Missouri. Lucas Brothers, 1926. xiii, 273 pp. Especially Part II, Chapters III and IV, pp. 76-170.
CARVER, THOMAS NIXON. The Distribution of Wealth. New York, The Macmillan Co., 1904. xvi, 290 pp.
CASSEL, GUSTAV. The Nature and Necessity of Interest. London, Macmillan and Co., 1903. xii, 188 pp.
———. The Theory of Social Economy. New York, Harcourt, Brace and Co., 1924. xiv, 654 pp.
CLARK, JOHN BATES. Distribution of Wealth. New York, The Macmillan Co., 1899. xxviii, 445 pp.
DAVENPORT, H. J. Value and Distribution. University of Chicago Press, 1908. xi, 582 pp.
FETTER, FRANK A. Economic Principles. New York, The Century Company, 1915. x, 523 pp.
FISHER, IRVING. The Rate of Interest. New York, The Macmillan Co., 1907. xxii, 442 pp.
GONNER, E. C. K. Interest and Savings. London, Macmillan and Co., 1906. xv, 172 pp.
HEINZE GERHARD. Statische oder Dynamische Zinstheorie? Leipzig, Dr. Werner Scholl, 1928. viii, 165 pp.
HOAG, CLARENCE GILBERT. A Theory of Interest. New York, The Macmillan Co., 1914. x, 228 pp.
JEVONS, W. STANLEY. Theory of Political Economy. 3rd edition, London, Macmillan and Co., 1888. lvi, 296 pp.
LANDRY, ADOLPHE. L'Intérêt du Capital. Paris, V. Biard and E. Brière, 1904. 367 pp.
PARETO, VILFREDO. Cours d'Économie Politique. Lausanne, F. Rouge, 1896 and 1897. Tome Premier, viii, 430 pp. Tome Second, 426 pp.
———. Manuel d'Économie Politique. Paris, V. Giard and E. Brière, 1909. 695 pp.
RAE, JOHN. The Sociological Theory of Capital. New York, The Macmillan Co., 1905. lii, 485 pp.
SAX, EMIL. Der Kapitalzins. Berlin, Julius Springer, 1916. viii, 249 pp.
WALRAS, LÉON. Éléments d'Économie Politique Pure. Lausanne, F. Rouge, 1900. xx, 491 pp.
ANSIAUX, M. Le Phénomène de L'Intérêt et son Explication. Revue de L'Institut de Sociologie. Deuxième Année, Tome I, Bruxelles, 1921-1922, pp. 47-57.
BILGRIM, H. Analysis of the Nature of Capital and Interest. Journal of Political Economy. Vol. XVI, March, 1908, pp. 129-151.
BÖHM-BAWERK, EUGEN VON. Capital and Interest. Quarterly Journal of Economics. Vol. xxi, November, 1906, pp. 1-21; February, 1907, pp. 247-282.
BORTKIEWICZ, L. VON. Der Kardinalfehler der Boehm-Bawerkschen Zinstheorie. Jahrbuch fuer gesetzgebung, Band 30, 1906, pp. 61-90, Leipzig, Duncker und Humblot, 1906.
CARVER, T. N. The Place of Abstinence in the Theory of Interest. Quarterly Journal of Economics, October, 1893, pp. 40-61.
CHAPMAN, S. J. Must Inventions Reduce the Rate of Interest? Economic Journal, Vol. XX, September, 1910, pp. 465-469.
DAVENPORT, H. J. Interest Theory and Theories. American Economic Review, Vol. XVII, No. 4, December, 1927, pp. 636-656.
DAVIES, G. R. Factors Determining the Interest Rate. Quarterly Journal of Economics, Vol. XXXIV, May, 1920, pp. 445-461.
FETTER, FRANK A. Interest Theories Old and New. American Economic Review, Vol. IV, No. 1, March, 1914, pp. 68-92.
———. Clark's Reformulation of the Capital Concept, in Economics Essays Contributed in Honor of John Bates Clark, pp. 136-156, New York, The Macmillan Co., 1927.
FISHER, IRVING. Professor Fetter on Capital and Income. Journal of Political Economy, Vol. XV, July, 1907, pp. 421-434.
———. Are Savings Income? Journal of the American Economic Association, Vol. IX, No. 1, April, 1908, pp. 1-27.
———. A Reply to Critics. Quarterly Journal of Economics, Vol. XXIII, May, 1909, pp. 536-541.
———. Capital and Interest. Political Science Quarterly, Vol. XXIV, No. 3, 1909, pp. 504-516.
———. Capital and Interest: Reply to Professor Veblen. Political Science Quarterly, Vol. XXIV, September, 1909, pp. 504-516.
———. The Impatience Theory of Interest. Scientia, Vol. IX, April 1, 1911, pp. 380-401.
———. The Impatience Theory of Interest. American Economic Review, Vol. III, No. 3, September, 1913, pp. 610-615.
FLUX, A. W. Irving Fisher on Capital and Interest. Quarterly Journal of Economics, Vol. XXIII, February, 1909, pp. 307-323.
GONNER, E. C. K. Considerations about Interest. Economic Journal, Vol. XVIII, March, 1908, pp. 42-51.
GRAZIANI, AUGUSTO. Capitale e Interesse. Società Real di Napoli, 1925, pp. 33-92.
LANDRY, ADOLPHE. Irving Fisher: The Rate of Interest. Revue d'Economie Politique, 23 Année, 1909, Bulletin Bibliographique, pp. 156-159. Paris, L. Larose and L. Tenin, 1909.
LORIA, A. Irving Fisher's Rate of Interest. Journal of Political Economy, Vol. XVI, October, 1908, pp. 331-332. Reply by Irving Fisher, same issue, pp. 532-534.
LOWRY, DWIGHT M. The Basis of Interest. American Academy of Political and Social Science, March, 1892, pp. 53-76.
SCHUMPETER, JOSEPH. Eine "Dynamische" Theorie des Kapitalzinses. Zeitschrift für Volkswirtschaft, Sozialpolitik und Verwaltung, 1913, pp. 599-639. Vienna, Manzche, K. U. K. Haf-Verlags und Universitätsbuchhandlung, 1913.
SHAPOSCHNICOFF, N. von. Die Böhm-Bawerksche Kapitalzinstheorie. Jahrbüchern für Nationalökonomie und Statistik, Dritte Folge, Bd. XXXIII (LXXXVIII), Jena, Gustav Fischer, pp. 433-451.
TAUSSIG, F. W. Capital, Interest and Diminishing Returns. Quarterly Journal of Economics, Vol. XXII, May, 1908, pp. 333-363.
VEBLEN, T. Fisher's Rate of Interest. Political Science Quarterly, Vol. XXIV, June, 1909, pp. 296-303.
II. OTHER WORKS DEALING WITH INTEREST.
ADLER, KARL. Kapitalzins und Preisbewegung. Leipzig, Duncker und Humblot, 1913. 48 pp.
BECKHART, BENJAMIN H. The Discount Policy of the Federal Reserve System. New York, Henry Holt and Co., 1924. xii, 604 pp.
BOUCHER, PIERRE B. Histoire de L'Usure. Paris, Chaigneau, 1806. 215 pp.
BROWN, MARY W. The Development of Thrift. New York, The Macmillan Co., 1900. x, 222 pp.
CANNING, JOHN B. The Economics of Accountancy. New York, The Ronald Press Company, 1929. viii, 367 pp.
DICK, ERNST. The Relation Between the Rate of Interest and the Level of Prices. Distributed by H. R. Scott, Kodaikanal, S. India, March, 1928. 83 pp.
EDIE, LIONEL D. Economics: Principles and Problems. New York, Thomas Y. Crowell Co., 1926. xx, 799 pp.
———. Money, Bank Credit, and Prices. New York, Harper & Brothers, 1928. xiv, 500 pp.
FETTER, FRANK A. Modern Economic Problems. New York, The Century Company, 1917. xi, 498 pp.
FISHER, IRVING. The Income Concept in the Light of Experience. English translation of article in Die Wirtschaftstheorie der Gegenwart, Vol. III of the Wieser Festschrift, Vienna, 1927. 29 pp., in translation.
———. The Nature of Capital and Income. New York, The Macmillan Co., 1927. xxi, 427 pp.
GIFFEN, ROBERT. The Growth of Capital. London, George Bell and Sons, 1889. 169 pp.
GRIMES, JOHN ALDEN and CRAIGUE, WILLIAM HORACE. Principles of Valuation. New York, Prentice Hall Inc., 1928. xvii, 274 pp.
KOCK, KARIN. A Study of Interest Rates. London, P. S. King, 1929. 264 pp.
MONTAGNE, JEAN. Le Capital. Paris, Albin Michel, 1919. 253 pp.
NORTON, JOHN P. Statistical Studies in the New York Money-Market. New York, The Macmillan Co., 1902. vi, 180 pp.
PALGRAVE, R. H. INGLIS. Bank Rate and the Money Market. New York, E. P. Dutton and Co., 1903. xxiii, 237 pp.
RABY, R. C. The Regulation of Pawnbroking. New York, Russell Sage Foundation, 1924. 63 pp.
RYAN, FRANKLIN W. Usury and Usury Laws. Boston, Houghton Mifflin Company, 1924. xxix, 249 pp.
WICKSELL, KNUT. Über Wert, Kapital und Rente. Jena, Gustav Fischer, 1893. xvi, 143 pp.
———. Geldzins und Güterpreise. Jena, Gustav Fischer, 1898. xi, 189 pp.
BIRCK, L. V. Moderne Scholastik. Eine Kritische Darstellung der Böhm-Bawerkschen Theorie. Weltwirtschaftliches Archiv., 24 Bd., October, 1926, Heft 2, pp. 198-227.
BONN, H. Geld und Kapitalmarkte im Jahre 1924. Wirtschaftsdienst, Vol. X, Feb. 6, 1925, pp. 247-248.
BURGESS, W. RANDOLPH. Factors Affecting Changes in Short Term Interest Rates. Journal of the American Statistical Association, Vol. XXII, New Series, No. 158, June, 1927, pp. 195-201.
CASSEL, GUSTAV. The Future of the Rate of Interest. Skandinaviska Kreditaktiebolaget, January, 1926. Stockholm, P. A. Norstedt & Söner, 1926, pp. 1-4.
———. The Rate of Interest, the Bank Rate, and the Stabilization of Prices. Quarterly Journal of Economics, Vol. XLII, August, 1928, pp. 511-529.
———. Discount Policy and Stock Exchange Speculation. Skandinaviska Kreditaktiebolaget, October, 1928. Stockholm, P. A. Norstedt & Söner, 1928, pp. 57-60.
CLEVELAND TRUST COMPANY. Business Bulletin, June 15, 1928, and August 15, 1928.
CONRAD, OTTO. Der Kapitalzins. Jena, Jahrbücher für Nationalökonomie und Statistik, 3 Folge, Band 35, 1908, pp. 325-359.
CRUM, W. L. Cycles of Rates on Commercial Paper. Review of Economic Statistics. Prel. Vol. V, No. 1, January, 1923, pp. 17-29.
FETTER, FRANK A. Recent Discussion of the Capital Concept. Quarterly Journal of Economics, Vol. XV, November, 1900, pp. 1-45.
FISHER, IRVING. Appreciation and Interest. Publications of the American Economic Association, Vol. IX, No. 4, August, 1896, pp. 331-442.
———. What Is Capital? Economic Journal, Vol. VI, December, 1896, pp. 509-534.
———. The Rôle of Capital in Economic Theory. Economic Journal, Vol. VII, December, 1897, pp. 511-537.
———. The Rate of Interest after the War. Annals of the American Academy of Political and Social Science, Vol. LXVIII, November, 1916, pp. 244-251.
———. Comment on President Plehn's Address. American Economic Review, Vol. XIV, No. 1, March, 1924, pp. 64-67.
FRIDAY, DAVID. Factors which Determine the Future of the Rate of Interest: Economic Principles of Supply and Demand. Trust Companies, Vol. XXIII, July, 1921, pp. 9-12.
GIBSON, A. H. The Future Course of High-Class Investment Values. Bankers', Insurance Managers', and Agents' Magazine, January, 1923, pp. 15-34.
GIFFEN, SIR ROBERT. Accumulations of Capital in the United Kingdom in 1875-85. The Journal of the Royal Statistical Association, Vol. LIII, 1890, pp. 1-35.
HARGER, C. M. Problems of Interest Rates. Financial World, Vol. XXXII, June 23, 1919, p. 19.
INOSTRANIETZ, M. L'Usure en Russie. Journal des Économistes, 1893, Ser. 5, Vol. XVI, pp. 233-243. Paris, Administration et Redaction, Librairie Guillaumin et C., 1893.
JAY, PIERRE. Call Money Market in New York City and the Interest Rates Charged Therein. Economic World, Vol. XIX, April 10, 1920, pp. 511-513.
KEMMERER, E. W. War and the Interest Rate. Economic World, Vol. XVI, November 2, 1918, pp. 616-619.
———. Rediscounting and the Federal Reserve Discount Rate. American Bankers' Association Journal, Vol. XII, April, 1920, pp. 582-584.
LEVY, R. G. Du Taux Actuel de L'Intérêt et de ses Rapports avec la Production des Métaux Précieux et les Autres Phénomènes Économiques. Journal des Économistes, March, 1899, p. 334; April, 1899, p. 28.
MAGEE, JAMES D. Call Rates and the Federal Reserve Board. American Economic Review, Vol. X, March, 1920, pp. 59-65.
MITCHELL, W. C. Interest Cost and the Business Cycle. American Economic Review, Vol. XVI, No. 2, June, 1926, pp. 209-221. [Original text reads "MITCHELL, W. F."—Econlib Ed.]
———. Supplementary Note on Interest Cost. American Economic Review, Vol. XVI, No. 4, December, 1926, pp. 660-663.
———. Interest Rates as Factors in the Business Cycle; with a Reply by J. E. McDonough. American Economic Review, Vol. XVIII, March, 1928, pp. 217-233.
MOURRE, BARON. Les Causes des Variations du Taux de L'Intérêt. Revue d'Economie Politique, 1924, pp. 45-64. Paris, Librairie de la Société du Recueil Sirey, Léon Tenin, Directeur, 1924.
PERSONS, WARREN M., and FRICKEY, EDWIN. Money Rates and Security Prices. Review of Economic Statistics, Vol. VIII, No. 1, January, 1926, pp. 29-46.
PERSONS, WARREN M. Money Rates, Bond Yields and Security Prices. Review of Economic Statistics, Vol. IX, No. 2, April, 1927, pp. 93-102.
PINSCHOF, C. L. The World's Return to Gold: the Ultimate Effect on Rates of Interest. Acceptance Bulletin of the American Acceptance Council, November 30, 1925, pp. 4-5.
PLEHN, CARL C. Notes Concerning the Rates of Interest in California. Quarterly Publication of the American Statistical Association, September, 1899, pp. 351-352.
PRICE, T. H. Do High Interest Rates Presage Deflation? Commerce and Finance, Vol. VIII, November 12, 1919, pp. 1511-1512.
REEVE, S. A. Interest and Dividends; Other Features of Interest; Irrevocability of Interest. Modern Economic Tendencies, 1921, pp. 204-231, 254-342.
RIST, CHARLES. La Hausse du Taux de L'Intérêt et la Hausse des Pris. Revue Économique Internationale, X Année, Vol. I, pp. 462-493. Bruxelles, Goemaere, 1913.
SCHMIDT, F. Die Abhaengigkeit der Wechselkurse von Zinsgeschaeften und die Marktzinsdifferenz. Schmollers Jahrbuch, 1919, pp. 339-365. München, Leipzig, Duncker und Humblot, 1919.
SEAGER, HENRY R. The Impatience Theory of Interest. American Economic Review, Vol. II, No. 4, December, 1912, pp. 834-851.
SMITH, J. G. Measurement of Time Valuation. American Economic Review, Vol. XVIII, June, 1928, pp. 227-247.
SNYDER, CARL. The Influence of the Interest Rate on the Business Cycle. American Economic Review, Vol. XV, No. 4, December, 1925, pp. 684-699.
———. Interest Rates and the Business Cycle. American Economic Review, Vol. XVI, No. 3, September, 1926, pp. 451-452.
Tables Showing: Rates on United States Treasury Certificates Issued During 1920-21; Rates of Discount Charged by the Bank of England and by the Open Market in London; Bank Rates of Discount Charged in Selected Money Markets; Changes in Central Bank Rates in World Monetary Centers. Review of Economic Statistics, March, 1921, pp. 70, 73.
WESTERFIELD, RAY B. Effect of Falling Prices and Interest on Foreign Loans and on War Debts. The Annalist, January 4, 1929, pp. 5-7.
WICKSELL, KNUT. Influence of the Rate of Interest on Prices. Economic Journal, Vol. XVII, June, 1907, pp. 213-220.
YOUNG, ALLYN A. An Analysis of Bank Statistics for the United States; III Regional Differences: 1901-1914. Review of Economic Statistics, Vol. VII, No. 2, 1905, pp. 86-104.
[115.] It is true that in the hard-tack case and some other extreme and hypothetical cases considered, it was assumed that for a certain interval the O curve was assumed to be straight. To include such a theoretical case, the statements in the text need a slight modification. But such extreme cases are not typical even in the theory and are probably never exemplified in practice.
[1.] American Economic Review, Vol. XIV, p. 64.
[2.] See any text book on the calculus, e.g. Wilson, E. B. Advanced Calculus. Boston, Ginn & Co., 1912, pp. 118-125.
[3.]The mathematical reader will note that the function F here representing total wantability W is vitally related to the function F in Chapters XII and XIII, representing the marginal rate of time preference f, since 1 + f is the ratio of the differential quotient of W relatively to this year's income to the corresponding differential quotient for next year's income.
[4.] Walras, Leon, Élements d'Économie Politique Pure.
[5.] Pareto, Vilfredo, Cours d'Economie Politique.
[6.] Cours d'Économie Politique, Vol. I, p. 314.
[7.] See Böhm-Bawerk, Recent Literature on Interest (1884-1899), p. 35.
[8.] This is evident, since the value of his annuity, capitalized at 5 per cent, reckoned at the beginning, is $772, whereas, reckoned at the end of the first year, before his $100 is paid, it is $811.
[9.] It may be of interest to note that this error is the inverse of, or complementary to, the more common one by which the net income is the $100 less the "depreciation." In the first year this would be $772 less $711, or $61, so that the "income" is $39. This sort of accounting, when, instead of depreciation, there is appreciation or savings, would make savings appear as income instead of capital. This savings, or depreciation, fallacy is especially discussed in Are Savings Income? American Economic Association Journal, April, 1908, and The Income Concept in the Light of Experience. It has been the subject of much controversy. Some economists who fall into this savings-are-income, depreciation-is-outgo fallacy in some parts of their system fall into the waiting-is-cost fallacy in other parts. Both cannot be right. Each exhibits the evil consequences which ensue from playing fast and loose with the concepts of capital and income. If we wish to indulge in such a metaphor as "I got it at the 'cost' of waiting," we can do so but only at the "cost" of inaccuracy. Neither of these so-called "costs" is more than a metaphor.
[10.] Lest the non-mathematical reader should be puzzled by this result, which seems to contradict the fact already brought out, that, under the pseudo-reckoning of the abstinence theorists, the net income is zero every year, it must be remembered that this zero income is repeated an infinite number of times, and that when we deal with infinity we can get reliable results only by the method of limits. The mathematical reader will find no difficulty in showing, by the method of limits, that there is a "remainder term" which will, in the supposed accounting, make the total income distributed through all eternity simply equal to the capital value, $2000.