The Theory of Interest

Fisher, Irving
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New York: The Macmillan Co.
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§1. Introduction


SINCE 1907, when The Rate of Interest was published, other students of the problem of interest have published their comments, objections, and criticisms. I have taken the opportunity to answer directly in various publications*74 most of the criticisms. It would serve no useful purpose to reprint these individual replies in this place. Rather, in this chapter, I shall state my understanding of the criticisms of my theory and shall offer replies where reply seems called for. This procedure will serve two purposes. First, it will present to the reader points of view and approaches to the problem of interest other than my own. Secondly, it will provide occasion for the statement of my position on the principal controversial problems in the theory of interest still remaining unsettled among economists.*75

§2. Income and Capital


Income, which, as I have stated before, is the most important factor in all economic theory and in interest theory in particular, resolves itself in final analysis into a flow of psychic enjoyments or satisfactions during a period of time. While this concept is the ideal, we can, for purposes of objectivity, approximate this ideal and at the same time impute to the income concept varying degrees of measurability by using in place of psychic income any of the following: real income, cost of living as a measure of real income, or money income.


One objection to the psychic concept of income as a basis for a theory of interest is that it is too narrow and restricted. It is held that the analysis of interest based on this concept "finds the cause of the changes in rates solely in the changed ratio between the stocks of present and of future consumption goods," while the "interest rate market is a funds market, not a machine or raw material or present consumables market." *76


"Nor is it entirely clear," continues this criticism, "why, in Fisher's view, the consumption perspective should read the law in point of interest rates to all equipment loan contracts, rather than, as Böhm-Bawerk sometimes appears to assert, the other way about. Why should not both sorts of demands be regarded as of equal title in causal effectiveness in the interest adjustment on final loans?"*77


I reply that I do not exclude "equipment loan contracts" from due consideration, but I do maintain that such intermediate loans are made for the purpose of securing larger incomes in the future, and larger incomes mean larger consumption. Production loans then are made only in contemplation of future consumption. Hence, though loans for the acquisition of intermediate goods do greatly preponderate in the loan markets, these loans have power to affect the interest rate only by changing the relative amount of future incomes compared to present incomes.


To the criticism that the consumption concept of income when used as the foundation of interest theory presents but a partial analysis of the supply and demand factors which are operative in determining interest rates, I make this reply: Interest rates are not a resultant of the supply of, and demand for, either capital goods or of capital values—sometimes conceived of as a loanable fund or funds, except as these signify the supply of and demand for income. An investment of capital, so called, is nothing more nor less than the sacrifice of income in anticipation of other, larger, and later income. It is a case of flexing the income stream, reducing it in the present or early future and increasing it in the remoter future. The income stream, so fundamental in the interest problem, includes incomes from all sources. It includes the value of the services of land, machines, buildings, and all other income-producing agents. Upon the value of these services, discounted at the prevailing rate of interest, the valuation of said land, machinery, buildings, and so on depends. What is properly called funds is this valuation of the income stream or portions of it. It should be evident that the approach to the problem of interest through the income stream and the supply of and demand for income gives to the problem the broadest possible basis.


The second indictment of narrowness of my concept of income denies my contention that savings are not income. One writer states this criticism as follows: "As a financial fact, there can be no saving and addition to capital value until there is first a property right to an income calculable in monetary terms (a financial present worth) to be saved. Hence to deny that monetary savings are monetary income is in simple common sense to deny a fait accompli; it is to assume the existence of the effect before its cause."*78


In so far as our disagreement here is a matter of words, it may be that my terminology is at fault. I used the term earnings to include capital gain and the term income in the sense of the value of services rendered by capital. There is little objection to changing this terminology, if we are willing to give up saying that capital value is the capitalized value of expected income. We could then maintain that capital gain is income. But if income includes only those elements on the anticipation of which the value of capital depends, then the increase in the value of capital is most emphatically not income.*79


In my reply to one critic,*80 I pointed out that this criticism seems to overlook, or omit, the mutual relations of discount and interest which constitute the raison d'être for the concepts which I have called capital and income. It is chiefly because savings do not enter into these discount relations on equal terms with other items of income that savings do not form a part of what I have called the income concept. I do not think there are reasons of terminology alone sufficient to justify the inclusion of savings in income. But, if savings are to be so included, some other term must be applied to take the place of what I have called income. The justification of these statements must rest on my books themselves and on later papers devoted to this subject.


But it is held that even aside from the relation of savings and income, a concept of income as services is quite useless. Services are both heterogeneous and incommensurable.*81 They cannot be summated to constitute a stock of services. They cannot be thrown together as if all were alike.


An examination of my The Nature Of Capital and Income (for example p. 121), will show that I do not treat all services as alike and capable of being added together. I have emphasized that miscellaneous services cannot be added together until each is multiplied by its price and all are thus reduced to a common denominator.


This criticism of my theory of income seems to overlook the fact that, while enjoyable services (psychic income) and objective services are themselves incommensurable, their values are not. Moreover, when the summation is completely carried out, the values of the physical elements cancel among themselves and leave as the net result only the values of the psychical elements.


It may be objected that, at one stage in this process, income appears to be more closely related to the expenditure of money than to its receipt and, as such, seems out of keeping with the ordinary idea of income. This seeming contradiction between money income and enjoyable income is readily resolved if we consider debits and credits. When money is spent, the expenditure itself is, it is true, outgo to be debited to the commodities bought with it. But these commodities afterward render a return in satisfactions. These satisfactions are certainly not expenditures, but receipts. Whether money spending is associated with outgo or income is entirely dependent on whether we fix attention on the loss of the money or the gain of the goods and services for which the money is spent.


These services, which constitute income, are related to capital in several ways. As income services, they flow from, or are produced by human beings and the physical environment. When I first came to the study of income and capital, I developed the concept of capital as a stock of wealth existing at an instant of time, and of income as a flow of wealth during a period of time, which concept I advanced in 1896.*82 I found it necessary in 1897 to modify my concept of income, and so stated.*83 Since then I have found no reason for further modification either of the concept of capital as a stock of wealth existing at an instant of time, or of the concept of income as a flow of services through a period of time, while the values of these are respectively capital value, and income value, often abbreviated into capital and income.


"It is not possible," it is objected, "to conceive of a literal stock of services at an instant of time; it is possible to conceive of their present worth as a financial fund at an instant of time. Services (taken in the sense of uses either of wealth or of human beings) may conceivably be delayed or hastened, but they are in their very nature a flow; they cannot be heaped up and constitute a stock of services. They can, at most, as they occur be 'incorporated' in durable forms of wealth. If this is so, then why this elaborate contrast between a flow of services, and a fund of something quite different? It is the vestigial remains of the older conception that Fisher has been obliged to discard."*84


While, however, I agree that these concepts of capital (as a fund of wealth) and income (as a flow of services) are not commensurate with the theory of interest, it would be a mistake to conclude from the emphasis placed on capital value, not capital goods, in the The Nature of Capital and Income, which was written as an introduction to the theory of interest, that the concept of capital goods emphasized by me in 1896 has been shelved as useless.


In the first place, the goods concept is itself a step in the formulation of the value concept, and secondly, The Nature of Capital and Income does not attempt to cover all of the four different relations between capital and income but only that one relation, income value to capital value, which is of importance to the theory of interest.


This valuation concept of capital, which in my view is necessary to the solution of the interest problem, does not distinguish between land and "produced means to further production." Some writers,*85 who hold this latter concept of capital, have contended that my treatment of land as typical of capital in general has led me to erroneous conclusions.


In particular, my criticism of the naïve productivity theories is said to fall down because of this consideration. But, as I have before written,*86 "my strictures on the ordinary productivity theories are not dependent on the putting forward of 'land' as typical of all forms of capital" or the particular definition of capital which I have used, but are, for the most part, merely a résumé of the strictures of Böhm-Bawerk, whose definition of capital excludes land. In other words, these criticisms hold true quite regardless of whether land is included in the capital concept or not.


However, while I recognize certain differences which exist between land and so-called artificial capital, these differences are of degree only, and do not carry the importance in most phases of economic theory which adherents of this concept of capital attribute to them. Professor J. B. Clark has presented *87 the similarities and dissimilarities of land and other durable agents so comprehensively and adequately that I shall not attempt to go over again this question at this point. However, one phase of this comparison is of importance. It is claimed by those*88 who hold land to be non-reproducible and, therefore, to lack a cost of production, that its value is governed by factors quite different from those determining the value of reproducible agents whose production does involve costs of production.


In brief, the contention is that the discount or capitalization principle of valuation upon which my theory rests is applicable only to land, since land value is not affected by cost of production. "If land, the limited gift of nature," one critic writes, "were truly representative of capital, then Fisher's reasoning would be unassailable." *89


But since land, it is implied, is not representative of capital in that it does not involve a cost of production, the valuation process which applies to land does not apply to those "produced means to further production" which do incur costs in their production. To a consideration of the relation of cost of production to capital value, therefore, we now turn.

§3. Cost of Production as a Determinant of Capital Value


The criticism that my views as to the relation of cost of production and capital value are invalid because of the use of land as typical of capital has been advanced by several writers.*90 In its most concrete form, it applies to the example which I presented of the case where an orchard was held to be worth $100,000 because this sum represented the discounted value of the expected income from the orchard of $5,000 per annum. But even if we change the orchard to machines, houses, tools, ships (that is, "produced means to further production") the principle that the value of anything is the discounted value of its expected income stands unrefuted. This is not to say cost of production does not have an influence. But past costs have no influence on the present value of a capital good, except as those costs affect the value of the future services it renders and the future costs. Future costs influence this value more directly by being themselves discounted at the current rate of discount. It is certainly true that if the reproduction cost of the capital goods is lowered, their production will be stimulated, the supply of services they render will be increased, the valuation of these services, i.e., the income from these capital goods per unit will be lowered, and, therefore, quite aside from any effect on the discount rate, the capitalization of this reduced income will tend to be lowered. Furthermore, this fall in the value of the capital goods will be brought down to a point, through the operation of the opportunity principle, where it is brought into conformity with the new cost of production of the capital good plus a margin to represent the amount of interest.


But, although it is true, it is objected, that under the supply and demand analysis, an increase in the supply of a single commodity will lower its value, the same does not follow when applied to all goods. "Exchange values and prices are relations among goods. Increase the supply of one good and the ratio at which it exchanges for others or for money will change to its disadvantage. If, however, you increase at the same time the supplies of all goods, including gold, the standard money material, you affect simultaneously both sides of all ratios of exchange and consequently the ratios should remain substantially as before. It is just such an increase of goods of all sorts and descriptions that is denoted by Böhm-Bawerk's phrase, 'the technical superiority of present over future goods', or by the more familiar phrase 'the productivity of capital'. Admitting the physical-productivity of capital (and Fisher does not question it), the value-productivity of capital or, more accurately, an increase in the total value product as a consequence of the assistance which capital renders to production seems to me to follow as a logically necessary consequence.... Since there is nothing in the assumption that the productivity of all instruments is doubled that involves any serious change in the expense of producing the instruments, the productivity theorist certainly would claim that under these conditions there must be, if not a doubling, certainly a very substantial increase in the rate of interest."*91


I can perhaps do no better than to repeat in part the reply which I made to this criticism in 1914.*92 "But the increased productivity of capital will entail a decreased price, or value per unit, of the products of that capital. And in addition there may be an increase in the expense of producing the capital, if, for instance, it is reproducible only under the laws of diminishing returns or increasing costs. Evidently it does not follow that the net return on capital-value will be permanently increased. In short, the expenses of production, on the one hand, and the price of the product of the capital multiplied by the increased product itself, on the other hand, will tend to adjust themselves to each other and to the rate of interest. But this rate of interest, according to my philosophy, instead of being permanently raised, will be ultimately lowered, for to double the productivity of capital will mean ultimately a much larger income to society than before, and this larger income tends to lower the rates of impatience of those who own it. So long as the rate of interest does not fall to correspond with the lower rates of impatience, there will continue to be profit in reproducing the productive capital until adjustment is attained—whether by decrease in the price of the products or by increase in the cost of the capital, or both, does not matter. In any case this adjustment must be by lowering and not by raising the rate of interest, for the rate of interest cannot be raised if the rates of impatience are not raised, and the rates of impatience cannot be raised if, as is assumed, the income stream is increased in size without being altered in other respects."


Very possibly, Professor Seager and I may have been arguing at cross purposes, for, of course, in the transition period while productivity is being doubled, the rate of interest may be raised. This is amply provided for in my theory. But even during the transition period something more is required than increased productivity in order that the rate of interest shall rise; the cost of making the change must be reckoned with and deducted from the income stream. Mere physical productivity will not suffice.


Having stated my views, it will serve to present clearly the difference of opinion to quote an illustration which Professor Harry G. Brown has furnished me of his views on the matter.

"Smith is a fisherman. His boat (capital necessary to his business) is wearing out and will last little longer. He catches, in general, 40 halibut a week, which he sells for $1 each, or $40 a week. He is also a good carpenter and can make himself a boat in a week's time. But to do so, he must give up the $40 worth of fish he could catch, or the $40 for which he could sell them. For him the cost of building a boat is $40. That is its cost in the sense of the sacrifice Smith must make in other products (fish) of his labor, if he builds the boat.

"Jones offers to sell him an exactly similar boat already built for $150. Smith refuses to pay over $40. Since other fishermen do the same, the demand for boats is such that Jones can't get $150. The fact is that the income Smith could get from his fish, which he expects to catch this week ($40) affects the price Jones can charge (value) for a boat (capital good) already built. This $40 worth of fish is not income from the boat we are about to value. It certainly is not the value of that income or its discounted value. And it is not a future cost of the to-be-valued boat.

"The cost you are thinking of as 'included' in your formulation (discount principle of capital value) is, for example, the expected cost (say 5 years hence) of replacing a worn-out or broken seat, broken oarlocks, etc., and the annual cost of painting. But the $40 which measures the cost to Smith of duplicating Jones' boat will make Smith unwilling to pay $150 even though your formulation, taken by itself, would let him—for he must have some boat. And Smith would have a curious mind if the $40 cost affected him only through first making him think of more plentiful and therefore less valuable future services. It has a direct effect on his price offer, not an effect consequent solely on a revaluation of expected future services.

"You can't make the psychology of the fisherman, Smith, fit into your formula. It's better to make a formula that fits what Smith's mind really does."


I accept all of Professor Brown's reasoning and conclusions except his application to me. His contention that the cost of duplicating existing capital will influence the value of that capital is perfectly correct, but so is the discount formula.


The two are not inconsistent. If they were, by the same logic, the generally accepted formula by which the value of a bond is calculated in every broker's office is contradicted every day whenever a cheaper bond is available. The first axiom in economics is, naturally, to get anything the cheapest way whether that way is to make it oneself, buy a substitute or otherwise, for in Professor Brown's reasoning it is solely the existence of an alternative cheaper way which makes the supposed disturbance.


The reasoning proves too much. Suppose Jones offers Smith a bond at one price and Smith refuses because he can get another just like it for less. He would choose the cheaper and he would have a "curious mind" if the cheaper cost affected him only through first making him think elaborately of the discount process. All he needs to know is that if Jones' bond is worth the price offered the cheaper one is even more clearly worth while. And Jones will sit up and take notice, possibly reducing his price.


The cheaper bargain thus has in Professor Brown's sense a "direct" effect on the price of Jones' bond, not an effect solely on a revaluation of expected services. But we cannot here conclude that the usual mathematical formula for the price of a bond was incorrect.


There is no more definite and universally accepted formula in the whole realm of economics and business than that referred to. It is used every day in brokers' offices. It gives the price of a bond in terms of the interest basis, the nominal interest and the time of maturity. It is the type, par excellence, of the capitalization principle both in theory and practice. It is not impaired by any undercutting of the market.


The boat is, economically, a sublimated bond. If Jones offers it to Smith for $150, while Smith can get it cheaper the discount principle is not invalidated. There is simply a readjustment in the boat as in the bond market. Moreover in an individual transaction where there is no marginal point reached by repeating the transaction—only one boat, not a series—there are wide limits within which the buyer gets his consumer's surplus and the seller his producer's surplus. Only when there is a series of successive boats or bonds do we have a full fledged example of the margin where consumer's rent disappears and an equality replaces inequalities.


In the isolated case we should be content to say that Smith will not pay more than the capitalized value. In the case of the conventional series of boats, the marginal boat will be such that the capitalization principle and the cost principle will both apply. The seventh boat, let us say, will cost Smith $100 whether to make or to buy. Jones and other boat owners will have reduced their price from $150 and Smith will have found that to make so many boats will have cost $100 instead of $40, to say nothing of the important fact that he would have to wait much more than a week.


All these points are covered in my presentation, for Professor Brown's example is only one of the myriad examples of alternative opportunities. Smith, like everybody else, will use the cheapest way in the sense of choosing the income stream of labor and satisfaction having the maximum present worth at the market rate of interest.


Professor Brown has his eyes on the opportunity part of the picture and no one has stressed that part more than I. But interwoven with it and consistent with it, in the analysis of a perfect market in which the individual is a negligible factor, is the principle that every article of capital is valued at the discounted value of its expected services and costs.


I do not intend to underestimate the importance of the cost concept. The importance it holds in my mind is not to be measured by the number of pages devoted to it in my books, the main purpose of which was to study capitalizations of income. I believe that the position on cost which was taken by Professor Davenport*93 is in general the correct one. What I attempted to point out was that those double-faced events, which I have called interactions, and which always have a double entry, a positive and negative entry, in social bookkeeping, are not ultimately cost any more than they are ultimately income. I also tried to emphasize that cost enters into capitalization on equal terms with income, when the cost is future. Past cost does not affect present valuations except indirectly, as it affects future expected income and cost.


No one would maintain that obsolete machinery, even in good condition, could be appraised on the basis of its cost. The only cases in which cost (with interest) is equal to value is where this value is also equal to the estimate of worth on the basis of future expectations; when, in other words, cost is superfluous as a determinant of value. That cost does influence value by limiting supply, thereby affecting the quantity and value of future services, cannot be questioned. It is natural that business men should not follow this roundabout relation, but connect directly cost with value. This, however, is no reason for economists to fail to analyze the relation in all its complications.

§4. Impatience as Determinant of the Interest Rate


Certain characteristics of The Rate of Interest led to the unfortunate deduction on the part of many readers*94 of that volume that I regarded impatience as the sole and complete determinant of the rate of interest. While I have tried in this book to forestall similar misinterpretations of my theory, and while it does not seem possible to me that any reader could now charge me with being a pure impatience theorist, it will serve a useful purpose to consider the various factors involved in this question.


We may draw upon Professor Fetter's writings for a clear statement of the issue between the productivity theory and the time preference theory of interest. He states positively that time preference is the sole cause of interest, although he assumes that physical productivity is essential to the emergence of value productivity.*95 He declares that his theory was new in assigning priority to capitalization over contract interest and in giving a "unified psychological explanation of all the phenomena of the surplus that emerges when undervalued expected incomes approach maturity, the surplus all being derived from the value of enjoyable (direct) goods, not by two separate theories, for consumption and production goods respectively."*96 [Italics mine.]


I have no criticism to make of this statement of the operation and effect of time preference so far as it goes. It seems to me to coincide sufficiently with the treatment which I have presented under the first approximation. There incomes were assumed to exist and to be rigidly fixed in amount and in time without our bothering to ask how they were produced. Nature offered no options to substitute one income stream for another. One could modify his income stream only by borrowing or lending. Under the hypothetical conditions so assumed, time preference would cause interest without help from any rate of return over cost. But such assumed conditions never do or can exist in the real world.


Of course a constant rigid physical productivity, yielding unchanging physical income streams, is contrary to the observed facts of life, just as unchanging time preference for each individual at all times and under all conditions is an absurdity. In real life men have the opportunity of choosing among many optional income streams. When such opportunities exist, time preference alone does not and cannot explain the emergence of interest. As a mathematical problem, the rate of interest would under the conditions of the second or third approximations be indeterminate without introducing the influence of the opportunity or productivity factor.*97


Productivity, that is, the possibility of increasing the present value of the income stream, introduces new variables which have to be determined as a part of the interest problem and every new variable requires a new equation or condition.


It happens that, for lack of applying this mathematical principle, writers have often thought themselves in greater disagreement on the explanation of interest than they really were. Wordy warfare has been waged among the various productivity theorists and the capitalization or time preference theorists. Each combatant seems to think that he and he alone has hit upon the correct and complete explanation and that, therefore, any other explanation is necessarily false. As a matter of fact, both productivists and time valuists are substantially right in their affirmations and wrong in their denials. Thus, theories which have been presented as antagonistic and mutually annihilatory are in reality harmonious and complementary.

§5. Productivity as a Determinant of Interest Rates


When the true nature of the income concept is grasped, it will be found that it includes within itself many special cases which have been advanced by various writers in explanation of the rate of interest. The relation of both impatience and opportunity to the rate of interest, in my opinion, can be comprehended accurately only by analyzing rigorously these concepts and determining the effect of each upon the income stream. By this procedure, we arrive at a fundamental explanation of the nature of impatience and of return on income invested and see how, by changes in the income stream, these rates are brought into conformity with the rate of interest.


I have always felt that John Rae came closer than any of the earlier writers to grasping all the elements of the interest problem. According to Rae, all instruments may be arranged in an order depending on the rate of return over cost. This amounts to saying that the formation of any instrument both adds to and subtracts from the preexisting income stream of the producer, its cost being the subtracted item and the return, the added one. The statement of Rae that for a certain cost of production an instrument will yield a certain return, is merely a form of my statement that a certain decrease of present income will be accompanied by a certain increase in future income. The relation between the immediate decrease and future increase will vary within a wide range, wherein the choice will fall at the point corresponding to the ruling rate of interest.


The same relationship was conceived by Adolphe Landry in his Intérêt du Capital. He states that one of the conditions determining the rate of interest is the "productivity of capital", in the peculiar sense which he gives to this phrase,*98 which is, in effect, the rate of return over cost.


It has seemed to me that much of the criticism, both favorable and unfavorable, of my book, The Rate of Interest, has been based on the erroneous assumption that the so-called productivity element found no place in my theory. Much of the misunderstanding of my theory may have been fostered by the lack, in my first book, of a good term with which to express this productivity factor in interest.


As a consequence, one critic, Professor Seager, writes that I refuse to admit that what Böhm-Bawerk calls the "technical superiority of present over future goods", and what other writers have characterized more briefly as "the productivity of capital" has any influence on the comparison between present gratifications and future gratifications in which, as he believes, the complete and final explanation of interest is to be sought.


"The most striking fact about this method of presenting his factors", this criticism continues, "is that he dissociates his discussion completely from any account of the production of wealth. From a perusal of his Rate of Interest and all but the very last chapters of his Elementary Principles (chapters which come after his discussion of the interest problem), the reader might easily get the impression that becoming rich is a purely psychological process. It seems to be assumed that income streams, like mountain brooks, gush spontaneously from nature's hillsides and that the determination of the rate of interest depends entirely upon the mental reactions of those who are so fortunate as to receive them.... The whole productive process, without which men would have no income streams to manipulate, is ignored, or, as the author would probably say, taken for granted."*99


My views are quite contrary to those here set forth. As I wrote in 1913:*100

"What Professor Seager calls the 'productivity' or 'technique' element, so far from being lacking in my theory, is one of its cardinal features and the one the treatment of which I flattered myself was most original! The fact is that my chief reason in writing the Rate of Interest at all arose from the belief that Böhm-Bawerk and others had failed to discover the true way in which the 'technique of production' enters into the determination of the rate of interest. Believing the 'technical' link in previous explanations unsound, and realizing as keenly as Professor Seager does the absolute necessity of such a link, I set myself the task of finding it. In the desirability of this I emphatically agree with Böhm-Bawerk."


I do not assume, except temporarily in the first approximation, that "income streams, like mountain brooks, gush spontaneously from nature's hillsides", and this is temporarily assumed, precisely as physicists temporarily assume a vacuum in studying falling bodies, or, to take a better but still imperfect analogy, precisely as, in treating supply and demand, we first assume a fixed supply before introducing the supply schedule or supply curve. This assumption gives place in the second approximation and the third approximation to the more complicated conditions of the actual world. My method of exposition is here, as usual, to take one step at a time, which means to introduce one set of variables at a time. All other things, for the time being, are assumed to remain equal. I realize that this is not the only method and that it may not be the best one, but it is at least a legitimate method.


On the other hand, it does not seem to me that the theory of interest is called upon to launch itself upon a lengthy discussion of the productive process, division of labor, utilization of land, capital, and scientific management. The problem is confined to discover how production is related to the rate of interest.


It should not, however, be assumed from what has been said that I regard all productivity theories as sound. Mention was made in Chapter III of the "naïve" productivity theories which hold that interest exists simply because nature, land and capital are productive.

§6. Technical Superiority of Present Goods


Böhm-Bawerk is among those who sensed the inadequacy of time preference or impatience as the sole determinant of the rate of interest. Yet he calls his theory the agio theory of interest, since he finds the essence of the rate of interest in the agio, or premium, on present goods when exchanged for future goods.


Böhm-Bawerk presented the agio theory, or what is here called the impatience or time preference theory, clearly and forcibly, and disentangled it from the crude and incorrect notions with which it had previously been associated. It was only when he attempted to explain the emergence of this agio by means of his special feature of "technical superiority of present over future goods" that, in my opinion, he erred greatly.


Böhm-Bawerk distinguishes two questions: (1) Why does interest exist? and (2) What determines any particular rate of interest?


In answer to the first question, he states virtually that this world is so constituted that most of us prefer present goods to future goods of like kind and number. This preference is due, according to Böhm-Bawerk, to three circumstances: (1) the "perspective underestimate" of the future, by which is meant the fact that future goods are less clearly perceived, and therefore less resolutely striven for, than those more immediately at hand; (2) the relative inadequacy (as a rule) of the provision for present wants as compared with the provision for future wants, or, in other words, the relative scarcity of present goods compared with future goods; (3) the "technical superiority" of present over future goods, or the fact, as Böhm-Bawerk conceives it, that the roundabout or capitalistic processes of production are more remunerative than those which yield immediate returns.


The first two of these three circumstances are undoubtedly pertinent, and are incorporated, under a somewhat different form, in this book. It is the third circumstance—the so-called technical superiority of present over future goods—which, as I shall try to show, contains fundamental errors.


My criticism of this third thesis, however, does not, as some have implied, consist in denying the existence or importance of the "technical" element in interest but in denying the soundness of the way in which Böhm-Bawerk applies it. It was for the purpose of presenting what in my view constitutes the true character of this element that I have placed so much emphasis on the opportunity principles given in Chapters VII, VIII, XI and XIII of this book.


According to Böhm-Bawerk, labor invested in long processes of production will yield larger returns than labor invested in short processes. In other words, labor invested in roundabout processes confers a technical advantage upon those who have command of that labor. In the reasoning by which Böhm-Bawerk attempts to prove this technical superiority, there are three principal steps. The first consists of postulating an "average production period," representing the length of the productive processes of the community; the second consists of the proposition that the longer this average production period, the greater will be the product; and the third consists in the conclusion that, in consequence of this greater productiveness of lengthy processes, present goods possess a technical superiority over future goods.


Although the first two of these three steps are of secondary importance, the following remarks concerning them are in point. The concept of an average production period is, I believe, far too arbitrary and indefinite to form a basis for the reasoning that Böhm-Bawerk attempts to base upon it. At best, it is a special, and very hypothetical, case not general enough to include the whole technical situation.


Böhm-Bawerk himself, in his reply to my original criticism, asserts his agreement with my contention concerning the second step that, while long processes are in general more productive than short processes, this is not a universal truth. Of the infinite number of possible longer processes only those which are more productive than shorter ones are chosen.*101 This is what was noted in Chapter XI when it was shown that the O curve is concave simply because the reëntrant parts are skipped!


It is the third step which is crucial to the theory of the technical superiority of present goods, namely, that the productiveness of long processes gives a special technical advantage to the possessor of present goods or present labor. This advantage produces, so Böhm-Bawerk asserted, a preference for present over future goods which is entirely apart from, and in addition to, the preference due to the underendowment of the present. Granting, for the moment, the validity of the concept of a production period, and that the longer the period, the greater its product, it may still be shown that no such technical superiority follows. Böhm-Bawerk regards this part of his theory as the most essential of all, and repeatedly states that the theory must stand or fall by the truth or falsity of that part.


Böhm-Bawerk supports his assertion of the existence of a technical superiority*102 by elaborate illustrative tables.*103 Each table is intended to show the investment possibilities of a month's labor available in any particular year. That longer processes are more productive than shorter ones, Böhm-Bawerk indicated by an increasing number of units of product for each successive year. The marginal utility of each year's yield when obtained is illustrated by a decreasing series, since the marginal utility of a stock of goods decreases as the number of units in the stock increases. Since the year 1888 was considered as the time of reference, or the first year in which the investment of labor was to be made, the numerical series representing the marginal utilities of the optional products as of the respective years of their production was reduced, by discounting, to a series of numbers representing the marginal utility of each year's yield as of the year 1888. The subjective value of each year's yield as of the year 1888, Böhm-Bawerk obtained by multiplying the number of units of each year's yield by its reduced marginal utility.


Of course, that investment of the month's labor available as of any particular year would be made which showed the maximum present value. When, however, the table of any one year is compared with that of any succeeding year, the maximum present subjective value selected is the greater the earlier the month's labor is available.


For example, a month's labor available in 1888 was shown to be most advantageously invested in the process which yielded the maximum present subjective value of 840 in 1890. But a month's labor available in 1889 yielded its maximum present value when invested so as to mature in 1893. In this latter case, however, the maximum was only 720 as compared with the maximum of 840 for a month's labor available in 1888.


Böhm-Bawerk therefore concludes that a month's labor available in 1888 is more productive than one available in 1889, 1890 or any succeeding year. In other words, entirely independent, according to him, of the perspective underestimate, and the under-endowment of the present, there inheres a technical superiority in present over future goods.


"This result", he writes,*104 "is not an accidental one, such as might have made its appearance in consequence of the particular figures used in our hypothesis. On the single assumption that longer methods of production lead generally to a greater output, it is a necessary result; a result which must have occurred, in an exactly similar way, whatever might have been the figures of quantity of product and value of unit in the different years."


But Böhm-Bawerk is mistaken in ascribing any part of this result to the fact that the longer processes are the more productive. In his tables he assumes the existence of one or both of the other two factors—the relative under-provision for the present as compared with the future, and the perspective undervaluation of the future, due to lack of intellectual imagination or emotional self-control. It is these elements, and these alone, which produce the advantage of present over future goods which the tables display.


That the result does not at all follow from "the single assumption that longer methods of production lead generally to a greater output" and has nothing whatever to do with that assumption, we can see clearly if we make the opposite assumption from that of Böhm-Bawerk, namely, that the longer the productive process the smaller will be the return. The very same result would still follow. The labor would still be invested at the earliest possible moment. In other words, let the figures representing units of product decrease instead of increase. The only difference would be that the month's labor available in 1888 would now be so invested as to bring returns in that year instead of being invested in a two years' process as before. If calculations are performed for each year and the results are compared, it will appear that the investment in 1888 yields the highest return, just as it did on the previous hypothesis.


Again, the same result would follow if the productivity increased and then decreased in all the tables, or if the productivity should first decrease and then increase. As long as the figure representing reduced marginal utility decreases, the "units of product" may be of any description whatever, without in the least affecting the essential result that the earlier the month's labor is available, the higher is its value.


On the other hand, if the conditions are reversed and the reduced marginal utility does not decrease, the earlier available labor will not have a higher value, whatever may be the character of the "units of product."


Böhm-Bawerk, however, specifically denies this:*105

"The superiority in value of present means of production, which is based on their technical superiority, is not one borrowed from these circumstances [i.e., the perspective underestimate of the future and the relative underendowment of the present]; it would emerge of its own strength even if these were not active at all. I have introduced the two circumstances into the hypothesis only to make it a little more true to life, or, rather, to keep it from being quite absurd. Take, for instance, the influence of the reduction due to perspective entirely out of the illustration."


In his table it is true that the month's labor available in the present is more highly valued than the same month's labor available at a later date. But Böhm-Bawerk carefully retained in his illustration one of the "two circumstances" which he told us could be discarded, namely, the relative overprovision for the future. To leave one of these two circumstances effective instead of both is merely to change slightly the series of "reduced marginal utility". The change in the particular numbers is quite immaterial so long as the series is still descending, and it does not matter whether the descent is due to perspective or to the relative underprovision for the present, or to both.


The only fair test of the independence of Böhm-Bawerk's third factor—the alleged technical superiority of present over future goods—would be to strike out both the other elements (underestimate and overprovision of the future) so that there should be no progressive decrease in marginal utilities; in other words, to make the numbers representing "reduced marginal utilities" all equal. Böhm-Bawerk, for some reason, hesitates to do this. He says:*106

"But if we were also to abstract the difference in the circumstances of provision in different periods of time, the situation would receive the stamp of extreme improbability, even of self-contradiction."


Even if this be true, and in my view it is not, it is no reason for refusing to push the inquiry to its limit. When this is done, however, the figures of present value of the various yearly products become absolutely alike; hence the maximum of the former, if there be a maximum, must be identical with the maximum of the latter.


Though Böhm-Bawerk did not consider this case in his tables, he speaks of it briefly in his text, but seems to be somewhat puzzled by it. He says:*107

"If the value of the unit of product were to be the same in all periods of time, however remote, the most abundant product would, naturally, at the same time be the most valuable. But since the most abundant product is obtained by the most lengthy and roundabout methods of production—perhaps extending over decades of years—the economic center of gravity, for all present means of production, would, on this assumption, be found at extremely remote periods of time—which is entirely contrary to all experience."


Böhm-Bawerk's confusion here is probably to be ascribed to his insistence on the indefinite increase of product with a lengthening of the production period. Practically we ought to assume that somewhere in the series the product decreases. We would then have a more practical illustration of the fact that the labor available this year and that available next year stand on a perfect equality.


The conclusion is that, if we eliminate the "other two circumstances" (relative underestimate of, and overprovision for, the future), we eliminate entirely the superiority of present over future goods. The supposed third circumstance of technical superiority, in the sense that Böhm-Bawerk gives it, turns out to be non-existent.


The fact is that the only reason any one does prefer the product of a month's labor invested today to the product of a month's labor invested next year is that today's investment will mature earlier than next year's investment.*108 If a fruit tree is planted today which will bear fruit in four years, the labor available today for planting it is preferred to the same amount of labor available next year for the reason that if the planting is deferred a year, the fruit will likewise be deferred a year, maturing in five instead of four years from the present. It does not alter this essential fact to speak of the possibility of a number of different investments. A month's labor today may, it is true, be spent in planting slow-growing or fast-growing trees, but so may a month's labor invested next year. It is from the preference for the early over the late fruition of any productive process that the so-called technical superiority of present over future goods, as conceived by Böhm-Bawerk, derives all its force.


Böhm-Bawerk, however, attempts to prove that his third circumstance—the alleged technical superiority of present goods—is really independent of the first two, by the following reasoning:*109

"...if every employment of goods for future periods is, not only technically, but economically, more remunerative than the employment of them for the present or near future, of course men would withdraw their stocks of goods, to a great extent, from the service of the present, and direct them to the more remunerative service of the future. But this would immediately cause an ebb-tide in the provision for the present, and a flood in the provision for the future, for the future would then have the double advantage of having a greater amount of productive instruments directed to its service, and those instruments employed in more fruitful method of production. Thus the difference in the circumstances of provision, which might have disappeared for the moment, would recur of its own accord.

"But it is just at this point that we get the best proof that the superiority in question is independent of differences in the circumstances of provision: so far from being obliged to borrow its strength and activity from any such difference, it is, on the contrary, able, if need be, to call forth this very difference.... We have to deal with a third cause of the surplus value, and one which is independent of any of the two already mentioned."


The argument here is that if "the other two circumstances" which produce interest, namely, underestimate of the future and underendowment of the present, are temporarily absent, they will be forced back into existence by the choice of roundabout processes. In other words, the technical superiority of present goods produces interest by restoring the other two circumstances. But this is tantamount to the admission that technical superiority actually depends for its force on the presence of these other two circumstances and is not independent. The essential fact is that the presence of technical superiority does not produce interest when the other two are absent.*110


Although Böhm-Bawerk devoted many pages in the third edition of his book and the Supplements (Exkurse) to answering my criticisms,*111 I can find nothing in his answers which affects the main argument as set forth above.*112 I have omitted certain of the less important of my original criticisms to which Böhm-Bawerk has replied.


Perhaps the most interesting point about Böhm-Bawerk's failure correctly to formulate the "technical" feature which he thus vainly sought is that it is really much simpler than he imagined. It does not require his elaborate tables and comparisons among their many columns. Merely the first column of his tables contains implicitly the true "technical" feature in one of its many forms of choosing from among optional income streams. This shows the successive amounts of product obtainable for a series of production periods of different lengths. This series is exactly analogous to the successive ordinates in Chart 16 showing the lumber to be obtained from a forest at different dates. There comes a point in such a series or such a curve, where a further lengthening of the time by one year will add to the product over the preceding year (i.e., will yield a rate of return over cost both reckoned in kind) at a rate harmonizing with the rate of interest. Oddly enough Böhm-Bawerk does not mention this derivative from his table. Another form, more nearly what Böhm-Bawerk apparently was groping for, could have been presented had his table been extended to include not merely one dose of 100 days labor but many such doses and if "labor" and "product" were reduced to a common denominator. Then the product of the marginal labor would be the return while the labor itself would be the cost from which return over cost could be derived. But the comparisons which Böhm-Bawerk actually employed are beside the point.

§7. Interest as a Cost


From the foregoing criticisms and discussion it will, I hope, be seen that I have given full recognition, in this book, to the elements of productivity, technique of production, and cost, and that my chief objections to their treatment by many other writers is either that their treatment is inadequate and leaves the problem of interest indeterminate, or simply that they do not reduce the problem to its simplest terms.


In particular, it has been noted that the ultimate economic cost is labor and that all money payments and industrial operations intervening between labor and satisfactions may, in the large view, be dropped out. I have endeavored, in this and in other ways, to articulate the theory of interest with sound accounting principles, even when no great damage would be done to interest theory, as such, if unsound accounting were allowed to enter.


The most flagrant case of unsound accounting injected into this discussion is, in my opinion, when waiting is regarded as a cost.


This grows out of the common tendency to account for all economic values in terms of cost. When we cannot find the cost, we invent it. We feel sure interest must be fully accounted for in terms of cost. When we find inadequate the cost of producing capital or the cost of managing it or of organizing it or of investing it, we fall back on waiting, abstinence, or labor of saving.


It is true that these words are used by some writers to mean nothing more than what I have included in the phrase impatience or time preference. In these cases the question is merely one of terminology. In a large number of instances, however, the abstinence or waiting theory seems to me to differ from the impatience theory not only in words but in essence. In this the assumption is made that abstinence or waiting exists as an independent item in the cost of production, to be added to the other costs and to be treated in all ways like them.


If abstinence or waiting or labor of saving is in any sense a cost, it is certainly a cost in a very different sense from all other items which have previously been considered as costs. An illustration will make clear the difference between true costs and the purely fictitious or invented cost of waiting. According to the theory that waiting is a cost, if planting a sapling costs $1 worth of labor, and in 25 years, without further expenditure of labor, or any other cost whatever (except waiting) this sapling becomes worth $3, this $3 is a mere equivalent for the entire cost of producing the tree. The items in this cost are, it is claimed, $1 worth of labor and $2 worth of waiting.


According to the theory of the present book, however, the cost of producing the tree is the $1 worth of labor, and nothing more. The value of the tree, $3, exceeds that cost by a surplus of $2, the existence of which as interest it is our business to explain. Labor cost and waiting are too radically different to be grouped together as though each were a cost in the same sense as the other.


The cost of waiting can neither be located in time, independently of the item waited for, nor can it, like any other item, be discounted, for it is itself the discounting. If we discount the discounting, we would have to discount the discounting of the discounting and repeat the process indefinitely.


If we insist on calling waiting or abstinence a cost we reduce to absurdity all our economic accounting. Among other things, the simplest, purest type of income, a perpetual annuity, will be found, by such accounting, to be no income at all.


An able critic and correspondent, after admitting this fact, says simply, "What of it?"

Well, perhaps nothing vital as to the theory of interest itself. And since that is, after all, the sole subject of this book I shall relegate to the Appendix the discussion of What of it? as to accounting.*113

§8. Empirical and Institutional Influences on Interest Rates


The problem of fully determining any specific market rate of interest is an intricate and baffling problem to solve just as is the problem of fully explaining any historical fact whatsoever. This volume makes no claim to being the monumental work necessary to analyze every possible influence that acts upon such a rate. The purpose of the book is rather to isolate the fundamental or basic forces which are operative in the interest problem.


The approach is theoretical, rational, or philosophic, if you like, as contrasted with the statistical, empirical, or quantitative approach. While it is true that in the discussion of the theoretical portions of the book, empirical evidence has been employed, this analysis is supplemental to rather than independent of the principles to be illustrated or tested.


The aim in view has therefore dictated the suppression of the innumerable secondary factors in order to focus the analysis upon the primary factors involved. It is these latter factors with which pure economic theory is concerned and this book is intended to be a study in pure theory.


As such, its ultimate objective is to explain how the rate of interest would be determined in vacuo or under the ideal operation of the assumptions. Outside this domain, there are literally thousands of forces which would have to be analyzed and allowed for before an adequate explanation of an actual market rate of interest could be made.


Thus, after presenting in Chapter II the theoretical relations of changes in the value of money to the rate of interest, we assume thereafter (until we reach Chapter XIX) a constant value of money and therefore the absence of any influence of a changing value of money. Yet we know that such an assumption is seldom realised in this actual world of incessant inflation and deflation.


Although this methodology of pure theory is at one with that employed in the whole range of scientific investigation, it may seem to some open to the criticism of being unreal and therefore presumably defective, if not useless, so far as practical affairs go.*114 While it is impossible, because of the divergent approaches, to express succinctly the criticisms which revolve about this point, certain examples may be given to set forth their general content and character.


Professor Thorstein Veblen, for example, asserted that interest did not come into existence until a high state of development had been reached in business and in money economy and credit economy. He argued that credit economy giving rise to interest economy has existed for "only a relatively brief phase of civilization that has been preceded by thousands of years of cultural growth during which the existence of such a thing as interest was never suspected" (p. 299).


"In short", Professor Veblen continued, "interest is a business proposition and is to be explained only in terms of business, not in terms of livelihood as Mr. Fisher aims to do" (p. 299). He admitted that business may be the chief or sole method of getting a livelihood, but asserted that business gains are not convertible with the sensations of consumption, as he thought my theory requires (pp. 299 and 300). Any argument for convertibility, or equivalence, is fallacious because "habitual modes of activity and relations have grown up and have by convention settled into a fabric of institutions" (p. 300).


If, at the start, we grant the postulate that the market rate of interest as set on money loans under a money economy or credit economy is the only interest rate existent, we are confronted with the problem of explaining why such a rate of interest exists. Institutions of themselves do not explain it. Institutions and conventions, like business, have been created by men, not from some inexplicable purpose unconnected with their living and feeling, but in order to add to the gratifications they obtain from living. Institutions cannot make men act or think other than as men. These man-made, man-operated institutions are merely tools devised by man to create for him gratifications more readily and more abundantly.


In my analysis, I find man's impatience to enjoy today and his desire to grasp the opportunities to invest so as to provide future enjoyments the fundamental causes which account for the emergence of incomes and of interest. To start with business institutions and attempt to explain the existence of interest as a phenomenon created by banks is like trying to explain value as something created by produce markets and stock exchanges.


Impatience and opportunity are working themselves out in the activities of business institutions, and men cannot avoid the dominance of these impulses and situations when engaged in any activity that demands a choice between present and future income. Interest, therefore, cannot be restricted to an explicit or contractual phenomenon but must be inherent in all buying and selling, and in all transactions and human activities which involve the present and the future.


While I cannot accept the view which would cast overboard theory because it is theory, I am keenly aware of the fact that theory as such does not tell the whole story about an actual rate of interest. Pure theory is not called upon so to do.


But after pure theory has said its last word, there is a broad field for empirical study of omitted factors. While we assumed that the unstable dollar remained stable and worked no interference with the fundamental forces determining the rate of interest, we know that in actual fact, the interference of a changing money value with these forces is tremendous—because of the "money illusion."


Laws, gold movements, stock exchange speculation, banking customs and policies, governmental finance, corporation practice, investment trusts and many other factors work their influences on the so-called money market where interest rates are determined. Practically, these matters are of equal importance with fundamental theory. While theory, in other words, assumes a waveless sea, actual, practical life represents a choppy one.

§9. Conclusion


In the study of such a complex and many-sided problem as that of the rate of interest, it is natural (and in fact, very desirable) that there should be many different approaches, views, and methods. Unfortunately, however, this latitude for individual interpretation and analysis has many times invited misunderstanding, confusion, and magnification of non-essential differences.


I have attempted to set forth and analyze in this chapter those matters contained in the criticisms of The Rate of Interest which, to my mind, are of major importance, and concerning which there still exists considerable disagreement among students of the interest problem.


Many of these questions seem to me to be based on misunderstandings of my theory of interest. I have been greatly helped by criticisms of this kind to see the shortcomings of my first attempt to expound that theory. I am hopeful that my present efforts to set forth in sharper relief and with greater clarity one solution of the problem of interest will succeed in subordinating these secondary matters to the more important issues of fundamental theory.


This done, I am confident that economic theorists will find that they are not so far apart on matters of fundamental theory as their writings would seem to indicate. When mutual understanding is achieved, they will undoubtedly find that their differences are often more apparent than real, consisting chiefly in the methods of approach and of analysis.

Notes for this chapter

For historical development and detailed criticisms of interest theories the reader is referred to Böhm-Bawerk, Capital and Interest. A brief historical résumé is given in Cassel, The Nature and Necessity of Interest, Chap. I, pp. 1-67.
These articles are included in the general bibliography at the end of the book.
References to the authors of the views which I am stating impersonally in the text will be made, where possible, in footnotes. It is hoped that this procedure will prevent the impression that I am attempting any exhaustive critique of the interest theory of others.
Davenport, H. J., Interest Theory and Theories. American Economic Review, Vol. XVII, No. 4, December, 1927, pp. 636-656.
Ibid., p. 650.
Fetter, Frank A., Clark's Reformulation of the Capital Concept. Economic Essays Contributed in Honor of John Bates Clark, pp. 151-152, footnote on p. 153; cf. also Flux, Irving Fisher on Capital and Interest, Quarterly Journal of Economics, Vol. XXIII, Feb., 1909, pp. 307-323.
See my articles: Are Savings Income? Journal of the American Economic Association, Vol. IX, No. 1, April, 1908, pp. 1-27; Professor Fetter on Capital and Income, Journal of Political Economy, Vol. XV, No. 7, July, 1907, pp. 421-434; Comment on Professor Plehn's Address, American Economic Review, Vol. XIV, No. 1, Mar., 1924, pp. 64-67; and The Concept of Income in the Light of Experience, English reprint from Wieser Festschrift, Vol. III.
A Reply to Critics, Quarterly Journal of Economics, Vol. XXIII, May, 1909, pp. 536-541.
Fetter, Interest Theories, Old and New, American Economic Review, Vol. IV, No. 1, March, 1914, pp. 68-92.
What is Capital? The Economic Journal, Vol. VI, Dec., 1896, pp. 509-534.
The Rôle of Capital in Economic Theory, The Economic Journal, Vol. VII, Dec., 1897, pp. 511-537.
Fetter, Clark's Reformulation of the Capital Concept. Economic Essays Contributed in Honor of John Bates Clark, p. 152.
Seager, The Impatience Theory of Interest, American Economic Review, Vol. II, No. 4, December, 1912, pp. 834-851; Brown, Economic Science and The Common Welfare.
The Impatience Theory of Interest, American Economic Review, Vol. III, No. 3, September, 1912, pp. 610-615.
Clark, Distribution of Wealth, pp. 338-344.
For example, Seager and Brown, cited above.
Seager, cited above, p. 844.
Seager, Brown, and Flux cited above; also Loria, Irving Fisher's Rate of Interest, Journal of Political Economy, Vol. XVI, Oct., 1908, pp. 331-332.
Seager, cited above, pp. 842-3, 847.
The Impatience Theory of Interest, American Economic Review, Vol. III, No. 3, September, 1913, pp. 614-615.
Davenport, Value and Distribution.
Cf. Seager and Flux, cited above, and particularly Fetter, Interest Theories Old and New, American Economic Review, Vol. IV, No. 1, March, 1914, pp. 69-72.
Fetter, Interest Theories Old and New, American Economic Review, March, 1914, pp. 74, 76, 77.
Ibid., p. 77.
As is always possible in solving simultaneous equations we can, if we wish, express certain of the variables, such as those relating to productivity, or opportunity, namely the rates of return over cost, in terms of the other variables and thus seem to eliminate them. In my first book I tried, for the most part, thus to present the rate of return over cost, or as I then called it, the rate of return on sacrifice as determined through the rate of preference. But we can just as well in like manner eliminate time preference and present it in terms of rate of return.
Landry, L'Intérêt du Capital, pp. 66-95.
Seager, The Impatience Theory of Interest, American Economic Review, Vol. II, No. 4, December, 1912, pp. 835-837.
The Impatience Theory of Interest. American Economic Review, Vol. III, No. 3, September, 1913, p. 610.
Positive Theorie des Kapitales. "Meine These schränkt vielmehr diese Wirkung ausdrücklich auf 'klug gewählte' Verlängerungen ein und lässt überdies, indem sie ihr Zutreffen nur 'in aller Regel' oder, wie ich in der ersten Auflage sagte, 'im grossen und ganzen' behauptet, das Vorkommen von Ausnahmen offen." Exkurs I, p. 3.

"Wenn Fisher hiemit nicht mehr in Abrede stellen wollte, als was ich oben auf S. 3 des Exkurse I selbst in Abrede gestellt habe, dass nämlich nicht alle längeren Produktionsumwege nur deshalb, weil sie länger sind, auch produktiver sein müssen, so wären wir in vollem Einklang." Exkurs IV, p. 105.

The Positive Theory of Capital, p. 266.
In The Rate of Interest there is presented an exhaustive analysis of the validity of the proof presented by these tables of the theory of technical superiority advanced by Böhm-Bawerk. While it does not seem advantageous to repeat here this analysis, since it is available in my previous book to any reader who may be interested, it is pertinent to present the conclusions drawn therefrom.
The Positive Theory of Capital, p. 268.
The Positive Theory of Capital, p. 268.
Positive Theory of Capital, p. 269.
Positive Theory of Capital, p. 269.
This is true under the assumption, implied in Böhm-Bawerk's tables, that the product is the same except as to the time of its availability, namely, that the series of figures called "units of product" are identical as shown in his tables.
Positive Theory of Capital, pp. 269 and 270.
See von Bortkiewicz, Der Kardinalfehler der Böhm-Bawerkschen Zinstheorie. Jahrbuch für Gesetzgebung, Verwaltung und Volkswirtschaft, 1906, pp. 61-90.

See also von Schaposchnicoff, Die Böhm-Bauerksche Kapitalzinstheorie. Jahrbücher für Nationalökonomie und Statistik. Verlag von Gustav Fischer, Jena, Dritte Folge, Bd. XXXIII (LXXXVIII), pp. 433-451.

Positive Theorie des Kapitales. Dritte Aufiage, and Exkurse zur Positive Theorie des Kapitales. See especially Exkurse IV and Exkurse XII.
Böhm-Bawerk claims that merely to find out the factors operative in a given problem is not the same thing as to explain those factors. He thinks that my theory of interest would be adequate only if the mathematical solution of the problem by means of simultaneous equations, and what he calls the "causal" solution were the same, or at least somewhat similar.

Of course, these two types of solution are not the same. The causal solution cannot be so simply conceived as to make one factor solely cause and another solely effect. The advance of all science has required the abandonment of such simplified conceptions of causal relationship for the more realistic conception of equilibrium.

Here, all factors are considered as variables. Any disturbance in one factor reacts on all the others, and the variations in these other factors react upon the factor of original disturbance. The mathematical solution of the problem of interest by means of simultaneous equations recognizes the mutual interdependence of all the factors in the interest problem and, at the same time, yields a determinate solution for the problem.

See Appendix to this Chapter, §1.
Veblen, Fisher's Rate of Interest, Political Science Quarterly, Vol. XXIV, June, 1909, pp. 296-303. Marget, The Loan Fund, a doctoral dissertation at Harvard University, 1926; Schumpeter, Theorie der Wirtschaftlichen Entwicklung, p. 363. Criticisms of a similar character have been received in private correspondence from several of those who read this book in manuscript, particularly Professors L. D. Edie, B. H. Beckhart, and C. O. Hardy.

Part IV, Chapter 21

End of Notes

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