Part I: Criticism

3 4 THE RATE OF INTEREST [CHAP•.! " cost" to the producer, such as the cost of the capitalist's personal exertion in controlling capital, or the "cost of waiting"; or that it constitutes a species of legalized plun der perpetrated by the employer on the employed. . Be fore the correct theory of interest can be securely implanted in any mind, these ideas must first be eradicated. To accomplish this is the object of the present and of the next three chapters. 1 § 2 An objection, formerly common, to the practice of taking interest was that interest is "unnatural." The word em ployed among the Greeks to signify interest or usury was 7'6"o~, "offspring"; and Aristotle declaimed against the taking of interest, on the ground that money could not have" offspring," -a curious instance of the influence of terminology on thought. Interest-taking between Jews was forbidden by the Mosaic laws, and similarly, in Rome, interest-taking be tween Romans was prohibited. Many biblical texts show the hostile attitude of the writers, both in the Old and New Testaments, toward the practice, and the Church Fathers through the Middle Ages for over a thousand years waged a ceaseless but fruitless war against interest-taking. St.

Thomas Aquinas stated that interest was an attempt to extort a price for the use of things which had already been used up, as for instance, grain and wine.2 He also declared that interest constituted a payment for time, and that time was a free gift of the Creator to which all have a natural right. 3 1 These chapters for the most part may be said to be a brief epit ome, under a changed classification, of Bohm-Bawerk's exhaustive Capital and Interest. 2 This criticism against the legitimacy of interest is very nearly re vived by Bohm-Bawerk in his criticism of the modern" use" theory of interest. Ope cit., Chap. VIII. a This theory is not unlike one of the objections made to land-rent by the single-tax advocates; namely, that space is a free gift of nature.

SEC. 2] CRUDE THEORIES 5 The unpopularity of interest-taking increased until the thirteenth century; but the practice persisted, and as business operations increased in importance, certain exemp tions and exceptions from its general prohibition were secured. Pawnshops, banks, and money-lenders were . specially licensed, and permission was granted for buying annuities, and taking land on mortgage for money loaned. One of the subterfuges by which the allowance of interest was excused suggests the true idea of interest as an index of the relative preference for present over future goods. It was conceded that, whereas a loan should be nominally without interest, yet when the debtor delayed payment, he should be fined for his delay (mora),and the creditor should receive compensation in the form of "interesse." Through this loophole it became common to mal{e an understanding in advance, by which the payment of a loan should be " de layed" year after year, and with every such postponement a "fine" should become payable.

Some of the Protestant reformers, while not denying that interest-taking was wrong, admitted that it was impossi ble to suppress it, and that it should therefore be tolerated. This toleration was in the same spirit as that in which many reformers -to-day defend the licensing of vicious institutions, such as saloons, racetracks, lotteries, and houses of prostitution. In the sixteenth century interest-taking began to find some definite champions. Calvin attempted to discrimi nate between interest-taking which was right and interest taking which was wrong. Among the wrong kinds he classed the taking of interest from the poor and from those in urgent need, and the taking of illterest in excess of a legal maximum. In order to defend interest, its champions began to con struct theories to account for the phenomenon. Most of these early. theories were little more than a shifting of the problem. It was seen that capital earned income whether it was lent or not. The income which a lender obtains 6 THE RATE OF INTEREST [CHAP. I through a loan contract may be called explicit interest,. but it was clear that the borrower was enabled to pay this interest because the capital which he borrowed earned it for him. The income which capital thus earns may be called implicit interest. The earliest attempt to construct a theory of interest merely explained explicit interest in terms of implicit interest. Salmasius and Locke, both in the seventeenth century, attempted thus to explain in terest. They tried to justify the taking of interest in a loan on the ground that an equivalent to that interest was obtained by the borrower from the capital he borrowed, and might have been obtained by the lender of the capital had he retained it. If, they said, a man lends $1000, he is entitled to interest upon it because, had he used it in business himself, he could have made profits by means of it. But beyond the bare statement that unlent capital yields income, these theories did not go. The re'al prob lem-" why capital yields income to the user" -was left untouched.

§3 The theories just described are for the most part obsolete to-day; yet we have a number of other theories almost equally crude. If a modern business man is asked what determines the rate of interest, he may usually be expected to answer, "the supply and demand of loanable money." But "supply and demand" is a phrase which has been too often forced into service to cover up difficult problems. Even economists have been prone to employ it to describe economic causation which they could not unravel. It was once wittily remarked of the early writers on economic problems, "Catch a parrot and teach him to say 'supply and demand,' and you have an excellent economist." Prices, wages, rent, interest, and profits were thought to be fully "explained" by this glib phrase. It is true that every ratio of exchange is due to the resultant of causes SEC. 4] CRUDE THEORIES 7 operating on the buyer and seller, and we may classify these as "demand" and" supply." But this fact does not relieve us of the necessity of examining specifically the two sets of causes, including lilility in its effect on demand, and ....cost in its effect on supply':- Consequently, when we say that the rate of interest is due to the supply and demand of "capital" or of "money" or of "loans," we are very far from having an adequate explanation. It is true that when merchants seek to discount bills at a bank in large numbers and for large amounts, the rate of interest will tend to be high, and that when merchants do not apply in large numbers and for large amounts, the rate of interest will tend to be low. But we must inquire for what purposes and from what causes merchants thus apply to a bank for the discount of loans, and why it is that some apply to, the bank for loans and others supply the bank with the funds to be loaned. The real problem is: What· causes make the demand for loa.ns,and wha.t ca.nsesmake the Sl1PP]~ This question is not answered by the summary "supply and de mand" theory. The explanation is not simply that those who have much capital supply the loans and those who have little capital demand them. In fact,.the contrary is quite often the case. The depositors in savings banks are the lenders, and they are usually poor, whereas those to whom the savings bank in turn lends the funds are rela tively rich.

§4 There is another phrase often employed by business men to, explain the rate of interest or, at all events, its existence. It is often said that interest is the price paid for the "use of money." As an explanation this is almost as superficial as "supply and demand"; for it is clear that the "use" of money is to facilitate exchange, and that, ex cept in rare instances (as when a bank borrows a chest of gold to reinforce its cash reserve), the money borro~ed \ 8 THE RATE OF INTEREST [CHAP. I does not remain long in the hands of the borrower.. If interest is a payment for use, it is payment for the use, not of the borrowed money, but of that for which the borrowed money is expended.. For this reason the final explanation of the rate of interest is not to be sought in anymonetary cause. A special version of the theory that interest depends on the "use of money" is found in the very persistent belief that the quantity of money in circulation governs the rate of interest, - that the' rate is high when money is scarce, and low when money is plentiful. The shallowness of this theory has been exposed repeatedly by economists from the time of Hume to the present. It requires only a little reflec tion to see that, although an increase of the quantity of money in circulation will increase the supply of loans, it will also equally increase the demand. For instance, a piano dealer who borrows $10,000 in order that he may add to his stock in trade 50 pianos costing $200 apiece would, if the supply of money were doubled, require a loan of double the amount; for such an inflation of the currency would double the cost of his stock, and in order to obtain 50 pianos - costing now $400 apiece instead of $200 he would have to borrow $20,000 instead of $10,000.

In spite of such reasoning, showing that an inflation of the currency must act on the demand for loans as surely as upon the supply, the theory that an abundance of money lowers the rate of interest is nevertheless widely accepted even among intelligent business men. Yet facts do not, any more than a priori reasoning, lend support to this belief.1 The probable reason for the persistence, among business men, of the opinion that an abundance of money reduces the rate of interest is the observed fact that the rate of interest is high when the reserves in banks are low, and vice versa, and that the rate in a loan center can be materi ally reduced by bringing to that center a supply of actual 1 A statistical discussion is contained in Chap. XVI, infra.

SEC. 4] CRUDE THEORIES 9 money to relieve the" stringency." This is true, and it is not denied that money plays a part in determining the rate of interest. But the part which it plays is chiefly as a puppet of other and mightier factors. The funda mental causes at work in a "money" market are not mone tary at all, but economic. The economic causes operate through money and seldom show themselves save under a money disguise; but, generally speaking, money is only their instrument, not an independent factor. If money is plentiful for loan purposes, it is because its owners decide to apply it for these rather than for other purposes, and not because money in general is plentiful. The owners of money determine the purpose to whichit shallbe applied. To understand the real causes at work in the loan market, we must go back of the money itself and learn the· reasons for bringing it into that market instead of spending it in other markets, - the meat, fish, fruit, or grocery markets, for instance. The abundance or scarcity of money for loan purposes is merely a sign or symptom of those more fundamental causes operating upon the rate of interest.

A full consideration of the manner in which money in loan centers is related to the rate of interest must, however, be deferred to Chapters V, XIV, and XVloi In the present chapter we are content merely to point out that the theories of which it treats are crude and superficial. They contain a modicum of truth, but they do not reach the root causes of interest. It Js true that explicit interest is dependent upon implicit interes1;._.. but this being so, the questIon still remains, What determines implicit interest? Again, it is true that the rate of interest, like every other ratio of exchange, depends on It supply and demand"; but the question ,is, What constitutes the supply and demand? And again, it is true that interest varies with loanable funds; but what causes the variation of those funds? To answer these ulterior questions, more careful and elaborate theories have been constructed. These will be considered in the three following chapters..

CHAPTER II PRODUCTIVITY THEORIES §1 IN the previous chapter it was shown that the problem of interest is not confined to contract or explicitinterest, but includes the much broader field of natural or implicit interest. The existence of implicit as distinct from ex plicit interest needs emphasis, for the reason that, to most persons, the "rate of interest" means simply the explicit rate of interest in a loan contract. When a personal note, mortgage, or corporation bond is issued, the "rate of in terest" is explicitly named in it and agreed upon by the contracting parties. But after its issue and before matur ity, this note or bond may change hands; and as the price of sale is seldom exactly par, the investor evidently "real izes" a "rate of interest" on his investment different from the rate named in the written instrument. This rate is not explicit, but implicit. It is implied by the price of the note or bond, and can be ascertained from bond tables.1 This implicit rate of interest is such that when it is used for calculating the present values of the future payments of the bond (the "principal" and U interest"), the sum of those present values will be the price of the bond.

It is evident that not bonds and notes alone, "but all se curities, imply in their price and their expected returns a rate of interest. There is thus an implicit rate of interest in stocks as well as in bonds. In the case of stocks the element of chance enters also; but while this adds some what to the intricacy of the calculation, it still requires the 1 See The Nature of Capital and Income, New York (Macmillan), 1906, Chap. XIII. 10 SEC .. 2] PRODUCTIVITY THEORIES 11 employment of a rate of interest. 1 In the same way all instruments of wealth, such as land, imply a rate of interest. This is recognized when land is sold on the basis of a num ber of "years' purchase." In like manner, machinery, dwellings, furniture, and, in fact, all articles of wealth,. as was shown in The Natureo! Capital and Income, are valued by discounting expected income; and all discounting of income can be calculated only by means of a "rate of interest." There is thus an "implicit rate of interest" in the value of every capital-good. It is, to be sure, often difficult to work out this rate definitely, on account of the elusive element of chance; but it has an existence in all capital. From this it is clear that the extent and impor tance of the interest problem cannot be grasped until implicit interest is recognized; and, as a matter of history, it was only after implicit interest was in some degree thus recognized that any theory of interest worthy of the name was evolved.

§2 The first writer who attempted to explain ··natural or implicit interest, as distinct from contractual or explicit interest, appears to have been Turgot. His explanation consisted simply in shifting the onus of the problem on to land. He explained that interest must be obtainable from the use of capital in general, because it is obtainable from the use of land in particular. He reasoned that, were it not likewise obtainable from other capital, everyone would invest in land. A man with $1000 worth of other goods would, if he received no increase, prefer to sell these goods and buy $,1000 worth of land, from which he could obtain say $50 a year. Land, he explained, evidently yields interest because it yields a perpetual series of crops, the land being bought for so many!" years' purchase" of those crops. This number of years' purchase, he said, was del See The Nature of Capital and Income, Chap. XVI.

12 THE RATE OF INTEREST [CHAP.II termined by lC snpply and demand"; but back of this convenient phrase he did not penetrate. Turgot's shifting the problem to land might naturally have revealed the true theory of interest as lying in the preference for present over future goods; for when one asks why land does not have an infinite value, equal to the entire value of its infinite future crops, the answer becomes at once obvious, namely, that no one would prize crops to accrue a million years hence on an equal footing with crops of to-day. Yet this explanation was never made. Turgot's theory may be regarded as a particular species of the numerous productivity theories, differing from the others chiefly in that he took his starting-point from the productivity of a particular form of capital, instead of from the productivity of capital in general. At the basis of all the thought of Turgot, as of other physiocrats, is the idea that land is the source of all human revenue.

§ 3 This idea few share to-day; yet there are many who, consciously or unconsciously, ascribe the phenomena of interest to the productivity of capital in general. When the rate of interest is 5 per cent., nothing at first sight seems more obvious than that this is so because capital will yield 5 per cent. Since capital is productive, it seems self-evident that an investment of $100 in produc tive land, machinery, or any other form of capital will receive a rate of interest proportionate to its productivity. Yet a very slight examination will suffice to show the in adequacy of this explanation. The productivity theory in its simplest or "naive" form, as Bohm-Bawerk calls it, confuses what we have distin guished 1 as physical-productivity and value~return. It takes no account of the great gap between the physical1 See The Nature of Capital and Income, Chap. XI.

SEC. 3] PRODUCTIVITY THEORIES 13 productivity of a factory - the ratio of its output to the size of the plant - and its value-return - the ratio of the value of the output to the value of the factory.l It is evident that if an orchard of ten acres yields 100 barrels of apples a year, the physical-productivity, ten barrels per acre, does not of itself give any clew to what rate of return on its value the orchard yields. To obtain the value-return, we must reduce both incQme and capital to a common standard of value. If the net annual crop of apples is worth $1000 and the orchard is worth $20,000, the ratio of the former to the latter, or 5 per cent., is a rate of value-return; -and if this rate is maintained without depreciation of the value of the orchard, this rate of value return is also the rate of interest. It seems at first sight very easy to pass from quantities to values, - to translate the ten acres of orchard and the 100 barrels of apples into dollars. But this apparently simple step begs the whole question. The important fact, and the one lost sight of in the-productivity theory, is that the value of the orchard depends upon the value of its crops; and in this dependence lurks implicitly the rate of interest itself. The statement that "capital produces income" is true only in the physical sense; it is not true in the value sense. That is to say, .-£apital-value does not produce in- ( wne-val:ue. On· the contrary, income-value produces .

E,.apital-value. It is not because the orchard is worth~ $20,000 that the annual crop will Qe worth $1000, blft it is because the annual crop is worth $1000 that the orchard will be worth $20,000. The $20,000 is the discounted value of-the expected income of $1000 per annum; and in the process of discounting, a rate of interest of 5 per cent. is implied. In general, it is not because a man has $100 worth of property that he will get $5 a year, but it is because 1 Certain theories, which Bohm-Bawerk calls "indirect produc tivity theories," have taken account in some degree of the distinc ,tion between the relation of quantity and value of income to quan tity and value of capital, and have attempted to bridge the chasms between them, but, as Bohm-Bawerk has shown, without success.

14 THE RATE OF INTEREST [CHAP. II he will get that $5 a year that his property is worth $100. In short, when capital and income are measured in value, their causal connection is the reverse of that which holds true when they are measured in quantity. The orchard produces the apples; but the value of the apples produces the value of the orchard. §4 We see, then, that present capital-wealthproduces future income-services 7· but future income-value produces present capital-value. The order to be observed in the study of capital and income is consequently as follows: (1) quantity of capital, or capital-wealth, (2) quantity of income, or income-services, (3) value of income, (4) value of capital. This order is shown in the following scheme: PRESENT CAPITAL FUTURE INCOME Quantities Values Capital-wealth -4-Income-services ~ Capital-value ~ Income-value This scheme signifies that (1) any capital-wealth, such, for instance, as land, railways, factories, dwellings, or food, is the means for obtaining income-services, whether these be preparatory services like production of crops, trans portation, and manufacturing transformations, or final services like shelter and nourishment. This first step in the sequence pertains to the study of the "technique"

of production and involves no rate of interest. (2) The in come-services are next reduced to a single denomination, such as dollars of gold. This step pertains to the study of prices, and, when applied to the final services, such as shel ter and nourishment, does not directly involve any rate of interest. (3) From the income-value thus obtained is com puted the value of the original capital by the process of SEC. 5] PRODUCTIVITY THEORIES 15 discounting. This final process introduces the element of interest. It is clearly with this last process that we are concerned in the study of interest. The paradox that, when we come to the value of capital, it is income which produces capital, and not the reverse, is,'then, the stumbling-block of the productivity theorists. It is clear, of course, in any ordinary investment, that, the selling value .of a stock or bond is dependent on its expected income. And yet business men, although they are constantly employing this discount process in eyery specific case, usually cherish the illusion that they do so because their money could be " productively invested"

elsewhere. They fail to observe that the principle of discounting the future is universal, and applies to any investment whatsoever, and that in such a discount process there is necessarily' involved a rate of interest. Consequently, any attempt to deduce the rate of interest from the ratio of the income from capital to the value of that capital is a petitio principii. § 5 The futility of the ,ordinary productivity theory may be further illustrated by observing the effect of a change of productivity. If an orchard could' in some way be made to yield double its original crop, the productivity of that capital in the physical sense would be doubled, but its yield in the sense of the rate of interest would not necessarily be affected at all, certainly not doubled. For the orchard whose yield of apples should increase from $1000 worth to $2000 worth would itself correspondingly increase in value from, say, $20,000 to something like $40,000, and the ratio of the income to the capital-value would remain about as before, namely, 5 per cent. To raise the rate of interest by raising the productivity of capital is, therefore, like trying to raise one's self by one's boot-straps.

16 THE RATE OF INTEREST [CHAP. II One cannot escape this conclusion (as has sometimes been attempted) by supposing the increasing produc tivity to be universal. It has been asserted, in substance, that though an increase in the productivity of one orchard would not appreciably affect the total productivity of capital, and hence would not appreciably affect the rate of interest, yet if the productivity of all the capital of the world could be doubled, the rate of interest would be doubled. It is true that doubling the productivity of the world's capital would not be entirely without effect upon the rate of interest; but this effect would not be in the simple direct ratio supposed. Indeed, an increase of the productivity of capital would probably result in a decrease, instead of an increase, of the rate of interest. To double the productivity of capital might more than double the value of the capital. That it would fail to do so has not been shown by the productivity theorists, much less that capital would remain unchanged in value.

§6 The same objections which have been indicated in relation to the productivity theory apply to what B6hm Bawerk calls the "use theories." These, in fact, are a special and improved form of the productivity theory. The ordinary productivity theory regards capital as producing an unspecified something called its "product," whereas the use theory regards that something specifically as a use or service. This accords to some extent with a correct theory of services, but nevertheless it is still subject to the objections which have just been made to the other produc tivity theories. If a machine renders a service or use of which the annual value is reckoned at $100, and the life'of the machine is ten years, this $1000 of services distributed over a decade gives, of itself, no intimation as to the rate of interest. Here, again, we must first know the rate of SEC. 6] PRODUCTIVITY THEORIES 17 interest itself in order to know the value of the machine.

Suppose that the rate of interest, on the basis of which the machine is valued, is 5 per cent. Then the value of the machine, when new, would be $772, this being the dis counted value, at 5 per cent., of the income above speci fied. This capital-value is, of course, derived from the expected income, and not vice versa. If, for any reason, the services of. the machine are doubled in quantity,and the price of these services remains unchanged, their value will rise and become $200 a year for each of the ten years. But the effect will not be to double the rate of interest; it will rather be to double.the capital-valueof the machine, and instead of being worth $772, which is the discounted value, at 5 per cent., of $100 a year for ten years, it will now be worth $1544, which is the discounted value, at 5 per cent., of $200 a year for ten years. Actually, of course, the doubling of the income-services performedby the machinewill lower the price of those ser vices and affect the manufacture of the machine which performs them. When the effects are complete, the resultant income-value of the services of the machine may rise above, fall short of, or remain stationary at $200 a year, according to the extent of the fall in the price of the services. As a consequence of such a changed income-value, the capital value of the machine may also change in either direction, or remain stationary. The capital-value follows the rate of interest, not the reverse. Whatever the effect on the rate of interest involved in these events, it is not the simple one, imagined by the use theorists, of a rise or fall proportionate to a rise or fall in inconle-services, or even to a rise or fall of income-value.

The objections which have been urged to the produc tivity and use theories apply with still greater force in cases 'where the depreciation of capital is offset so as to "stand ardize" 1 the income. It is sometimes said that interest is the income which capital yields beyond what is neces1 See The Nature of Capital and Income, Chap. XIV. c 18 THE RATE OF INTEREST [CHAP. II sary to replace the capital. But in the cost of replacement which maintains the capital there lurks again the very rate of interest to be explained. Let us examine the case of a factory plant of ten machines, each like the one just described. Suppose that these ten machines are evenly distributed through the years, as to wear -that, for instance, the life of each machine is ten years and that, accordingly, the cost of renewal is the cost of one machine annually. Let us imagine a man buying these ten machines for $4556. Knowing that the cost of each machine is $772 and its annual use is $100, he will calculate that he is "making 5 per cent. on his capital,"

because he will receive 10 x $100 or $1000 a year in service from his machines, and will spend each year for replace ment $772. This leaves a net income of $228, which, divided by the capital invested, $4556, makes just 5 per cent. If asked why the rate of interest is 5 per cent., this owner is likely to answer, because outfits like his yield 5 per cent. on their cost, over and above the cost of replace ment. A little reflection, however, will show that the rate of interest is implicitly assumed in his calculation. Not only the $4556 of capital, but even the $228 of income, are calculated on the assumption of a rate of interest of 5 per cent. That this is true of the capital, $4556, is evident by re peating, with reference to the entire ten machines, the calculations already explained for one. Each machine is valued by discounting its future annual services of $100 for its lifetime. One of the machines is new and has a life of ten years; consequently, it is worth, as already seen, $772, this being the discounted value of ten annual instal ments of $100 each, on the assumption of a 5 per cent.

interest rate as the basis for the calculation. The life of the next machine is only nine years, making, by a similar reck oning, a present value of $711; the life of the third machine, eight years, making its value $646, and so on. Thus the total for the ten machines is $772 + $711 + $646 + $578 SEC. 6] PRODUCTIVITY THEORIES 19 + $508 + $433 + $355 +$272 + $186 + $95, or $4556. It is clear that this item and each of the ten sums of which it is composed are calculated only by the aid ofa rate ofinterest. So much for the capital; now let us turn to the net in come of $228. The gross income is $100 per machine for ten machines, or $1000, and from this is deducted the cost of replenishing one machine.. This cost is $772, leaving $228 as net income. But this cost of replacement, $772, is the capital-value of a machine, and is obtained by means of a rate of interest, namely, 5 per cent. The reason, then, that the $4556 yields $228, or 5 per cent., is not because of the productivity of the machines, but because 5 per cent.

is assumed in the calculation both of the $4556 and of the $228. The 5 per cent. emerges at the end only because it was put in at the beginning.1 Were the productivity the source of the rate of interest, we should expect a double productivity to double the rate of interest. But the reasoning used in the case of the or chard shows that not only will the value of the use of the machinery be doubled, but the cost of each new lllachine may be doubled, so as to leave the rate of interest at 5 per cent. As stated above, the doubling in productivity would naturally result in lowering the price of the services pro duced, so that the value of the doubled quantity of ser vices might be less than double the value of the original quantity of services. Consequently, the value of the new machines and the cost of replacing an old machine by a new one might not be double what they were before. But they certainly would not be unaffected.

The process of adjusting supply and price reconciles what has been said with the old cost-of-production theory of value. The reader lllay have felt that we have treated the value of the machines and the cost of replacement as though they had no relation whatever to the cost of pro ducing the machines. One cannot de:nY that the classical 1 For a mathematical formulation, see Appendix to Chap. II, § 1.

20 THE RATE OF INTEREST [CHAP.II economists were partly right in ascribing value to cost of production. But cost of production affects the value of a capital good only indirectly by affecting the scarcity of its products or uses. The value of its products or uses depends on its marginal utility. The marginal utility is dependent on the scarcity, and this scarcity depends, in turn, partly on cost of production, so far as this cost of production has any independent existence. 1 § 7 Extreme cases are always instructive, even when they are impossible of realization. As an extreme case, let us im agine a community in which the rate of interest is zero. In this case we can scarcely fail to observe the wide dif ference between physical-productivity and value-return; for we shall find that the disappearance of interest does not carry with it the disappearance of physical-produc tivity, though it does bring about the cessation of value return. Consider a plant of ten machines, of which the annual use is worth, as before, $100. The value of a new machine to last ten years will now be, not $772 as before, but $1000, this being the capital-value of ten annual in stalments of $100 each, reckoned at full value, Of, if we prefer to say so, each discounted at zero per cent. Simi larly, the value of a machine one year old, having nine more years of life, would be, not $711 as before, but $900; of one two years old, $800, and so on, making a total value, not of $4556, but $1000 + $900 + $800 + $700 + $600 + $500 + $400 + $300 + $200 + $100, or $5500. This is the capi tal-value of the plant. We next seek the net annual income from the ten machines. Strange as it may seem, this net income, if the plant is exactly kept up, would be zero; for the gross annual income from the ten machines is 10 X $100, or $1000, and the deduction for the cost of a new 1 See The Nature of Capital and Income, p. 173.

SEC. 7] PRODUCTIVITY THEORIES 21 machine is, as we have seen, also $1000. Consequently h ·· d hIt b· zerotenet Income IS zero, an t e va ue-re urn, elng 5500' is also zero. Yet the case supposed does not imply any reductio:Q.in physical-,productivity; the machines produce the same amount of work as when the rate of interest was supposed to be 5 per cent. It may be asked how it is possible that the plant, if it yields no income, could have any value. We have found it worth $5500 and yet it yields no net income. The answer is that the annihilation of net income which we have wit nessed takes place only so long as the up-keep of the plant is maintained. At any time that the owner of the plant sees fit to do so, he may draw income from the plant to any amount up to $5500,but no more. If, for instance, he decides at the end of ten years to withdraw from manu facturing, he may discontinue his annual renewals and ob tain in the first year thereafter his $100 income from each of the ten machines, or $1000 in all, without any deduc tion for up-keep. During the next year, as one machine will have been worn out andunreplaced, he will obtain the income from only nine machines, or $900, and likewise, in the years succeedingthis, he will obtain $700, $600, etc., until the last machine is worn out and no capital remains.

The total of this income is evidently $5500. In other words the owner of the machines, as long as he keeps up his capital, obtains no net income, but he has the possibility at any time of obtaining a total net income of $5500 simply by letting his plant run down. The possibility of obtaining this return keeps the value of the capital at $5500 as long as it is kept up. His capital is like a fixed treasure and remains $5500.1 The process of keeping up the capital is virtually to keep the $5500 in cold storage, so to speak. 1 For a mathematical treatment of this peculiar case, see Appendix to Chap. II, § 2.

22 THE RATE OF INTEREST [CHAP. II If it be asked what motive could ever prompt anyone to keep up his capital when, as long as he does so, all income is foregone, the answer is that, under our assump tion of zero interest, there would be no preference for the immediate over the remote income of $5500. The owner of the plant would just as willingly wait a hundred years for his $5500 as to receive it now. In actual fact, men are not thus willing to wait, and therein lies the unreality of our assumption that interest is zero. In our supposititious case the element of timepreference was abstracted with the element of interest. But this imaginary case shows that absenceof interest is quite compatible with the pres ence of physical-productivity, and that, therefore, whatever element is responsible for the existence of interest in the actual world, that element cannot be physical-productivity.

§ 8 It was with a view to meeting some of the difficulties which have just been pointed out in the productivity theo ries, that Alexander Del Mar and Henry George suggested tlleir theory of interest,! baSIng it on the productivity of those particular kinds of capital which reproduce them selves. They. state that, were all capital inanimate, the phenomena of interest would not exist'. because inanimate capital is incapable of increasing; but that the organic forms of capital are capable, without labor, of reproducing and increasing with time. Money, as Aristotle said, is barren, and coal and iron cannot breed. Were all capital of this non-increasing kind, it would, said Henry George, not yield interest. But a flock of sheep, herd of cattle, or group of Belgian hares will, from its own natural powers of breeding, increase and multiply; it will, as it were, ac1 Del Mar, Science ot Money, (Macmillan) 1896, p. 144. Henry George, Progress and Poverty. For a general criticism of this theory, see Dwight M. Lowry, "The Basis of Interest," American Academy oj Political and Social Science, March, 1892, pp. 53-76.

SEC. 9] PRODUCTIVITY THEORIES , 23 cumulate at compound interest. In like manner a 'forest will grow, and crops will spring up. These seem to show a rate of interest in Nature herself. Mr. George contends that a man who puts $1000 into a savings bank can de mand that it receive interest, for the reason that he might invest it in a flock of sheep and let it accumulate naturally. According to this theory, interest exists because plants and animals grow, because the seed becomes the crop, the sap ling becomes a tree, the egg a chick, and the chick a hen. The conclusionis drawn that, in the last analysis, the rate of interest consists in the "average rate of growth of ani mals and plants." We may remark at the outset that this theory, like the land-yielding theory of Turgot, is one-sided and partial; inasmuch as it makes the rate of interest from all capital depend on the rate of interest from one particular form of capital; and it does not seem likely, a priori, that any theory of interest can be true which does not apply alike to all forms of capital which yield interest. But, aside from this preliminary objection, a specific examination of his theory will show that Henry George has not escaped the fatal error of assuming a rate of interest in order to prove it. We propose to make a thorough reexamination of this .

theory, not because it has attracted any special attention or been accepted by others than its author or authors, but because it puts the productivity theory on its strongest grounds-stronger grounds than its opponents have usually acknowledged or understood - and more especially because, in a dormant state, it seems to exist in the minds of a great many persons. § 9 Let us imagine a forest growing at a certain rat~ such, for, instance,that an acreof sprucecontaining100 cordsof wood suitable for making wood pilip will, if let alone, in five 24 THE RATE OF INTEREST [CHAP.II years amount to 200 cords. Here is an increase of 100 per cent. in five years, which is at the rate of about 15 per cent. per annum. Does this 15 per cent .. represent a natural rate of interest? Would 100 cords of this year's timber exchange for 115 cords of next year's timber? If so, we certainly have a simple physical basis for the rate of interest quite independent of the psychological element.

But a little consideration will show that there is an error in the reasoning. If the supply of wood pulp is decreas ing as years go on, while the demand is steadily increasing (and these conditions correspond to the facts as they are to-day), it may well be that 100 cords of this year's timber would exchange for a relatively small amount of next year's timber, say 105 cords, in spite of the fact that it grows at 15 per cent. per annum instead of 5 per cent. That this rate of exchange of present wood for future wood is quite compatible with a much greater rate of growth will be come apparent as soon as we consider that growing timber is not the same thing as cut wood. It is clear that to cut young timber which is growing very fast is like killini __ the goose that lays the golden egg, and to reckon the value of the growing timber as only---equivalent to the wood contained in it is like reckoning a live goose equivalent to a dead one. TIle value, in cut wood, of 100 cords of rapidly growing timber will be considerably greater than 100 cords of cut wood. If, for instance, the possessor of the growing timber has the option, besides that of cutting it, of allowing it to stand for five years and then obtaining a stumpage of 200 cords, he will allow it to stand, for these 200 cords due five years hence are worth, in present esti mation, discounted at 5 percent., 157 cords. Thus his present 100 cords of standing timber is equivalent to 157 cords of present cut wood. The value of a tree at any time is therefore not necessarily the physical amount of wood then in it; it may be the discounted value of the future wood which the tree will produce if left to grow. It will actually be whichever of the two happens to be the greater. For, SEC. 9] PRODUCTIVITY THEORIES 25 of various optional employments of his :ccapital,the investor selects the one which offers the maximum present value.1 Wer~ it true that the value .of a tree in wood were always simply the physical amount of wood it contains, it would be a matter of indifference whether a tree were cut at the sapling stage or any other, whereas we know that part of the art of lumbering consists in selecting the right age for cutting.

The case may be illustrated by Figure 1. Let AB repreN B. 5 yrs. 5yrs. A A,' Xl FIG. 1. D sent the number of cords of wood on an acre of growing trees, A'B' the amount of wood which may be expected at the end of five years, A"B" what may be expected in ten years, and so on for successive years until the forest reaches its maximum growth, MN, at the end of AM 1 See The Nature 01 Capital and Income, pp. 221-222.

26 THE RATE OF INTEREST [CHAP. II years. The percentage-slope 1 of the curve BN at any point, therefore, represents the rate of growth of the forest. The value at present of the forest in terms of cords of wood will be represented, not by the height AB, but in a different manner, as follows: If from B' the discount curve 2 B'G' be drawn, the ordinates of which will represent the discounted values of A'B' at any times, AC' will repre sent the present value of A'B', the wood if cut in five years. Similarly, AC" will represent the present value of A"B", the wood if cut in ten years. Draw in like manner a num ber of discount curves until one is found, tT, which is tan gent to the curve BN. At will then be the correct value of the young forest, and D will represent the time at which it should be cut. Clearly, At is quite different from AB, the amount of wood at the present time, and also from DT, the amount of wood at the time of cutting. At is the maximum present value out of all possible choices. If the forest is for some reason to be cut at once, its value will be only AB; if it is to be cut at A', its present value will be AG'; if at A", its present value will be AC"; if at D, its value will be At. At is the maximum, for if the for est were cut at any other point on either side of T the dis count curve passing through that point would evidently pass below tT.

At the time A, then, the wood in the forest is only AB, but, assuming proper foresting, -the value of the forest in terms of wood is At; the rate of growth of the forest is the percentage-slope of BN at B, but the rate of interest is the percentage-slope (the same at all points) of tT. At the point of tangency alone, namely,T, are the rate of growth and rate of interest identical, and to that extent there is truth in the thesis that the rate of interest is the rate of growth. This element of truth in the organic 1 By percentage-slope is meant the ratio of the slope to the ordi nate. See The Nature 0/ Capital and Income, Appendix "to Chap. XII, § 2. 2 See The Nature 01 Capital ancllncome, Chap. XIII.

/ SEC. 9] PRODUCTIVITY THEORIES 27 productivity theory will be more fully discussed when we come to develop our own theory of the rate of in terest. But that this element of truth is insufficient to afford a determination of the rate} of interest is evident when we consider that the point at which the forest. iU.o be cut itself depends. among other causes, upon the rate of - \iit.erest. If the interest rate rises, the discount curves em ployed become steeper and the point of tangency T moves toward the left; that is, the forest will be cut earlier. This is undoubtedly one reason for the fact that forests in the United States have hitherto been cut early; the owners have not felt that they could afford to "lose the interest" in waiting. In Europe, on the other hand, where interest rates have been low, forestry culture, though often involv ing fifty years' waiting, has been profitable. It would not be correct, of course, to ascribe the difference in forest policy wholly to a difference in the rate of interest, for the European policy has also been more enlightened than the American.

Not only does the most favorable time for cutting depend upon the rate of interest, but the rate of interest itself depends upon the future distribution of the times of cut ting of many forests. If all the forests of a country are young, there will be a relative scarcity of present wood and a consequent enhancement of the rate of interest (in terms of wood) which will make for early cutting. 'In the United States at the present time the reverse is the case. There is a present abundant supply of spruce for wood pulp. But a single edition of a large metropolitan Sunday news paper will use up two acres of spruce. We have, therefore, to contemplate a growing scarcity of wood, and probably at the same time an increasing demand for it. The effect is to enhance the value relatively of future wood, that is, to lower the rate of interest in wood. This shifts the point of tangency T toward the right and introduces a ten dency to postpone cutting, as is manifested by speculation in spruce forests.

28 THE RATE OF INTEREST § 10 [CHAP. II From what has been said it is clear that although interest enters into the processesof nature, it is not because of their physical expansion, but because they require time. It is not because the seed grows into crops or the egg into a chick that there is interest, but because the crops or the chick are unavailable until a future time. The type. of interest is a "time-lock" like those used on the doors of some banks. Nature holds many treasures in her store house, but she will not unlock them all at once. The conclusion, therefore, from our study of the various forms of the productivity theory is that physical-pro ductivity, of itself, has no such direct relation to the rate of interest as is usually ascribed to it; and in the theories which we have examined, the rate of interest is always surreptitiously introduced. It is, however, ~~~ ~ ~4Ca:pit91 doe~ affeet the rat.e of interest; for it affects the relative valuation of present and f~e [,oods by aff.ecting the .relative endowment of ~ present and the fut~ It is quite true, in particular, that the rapidity of· growth of the organic world will affect the rate of interest by redistributing income between different points of time and by opening up a series of choices to the owner as to the time of cutting his forests or of reaping the rewards of other sorts of organic growth. It follows that the rate of growth will coincide at certain points with the rate of interest. These small grains of truth in the pro ductivity theories will be fully incorporated in our study at a later stage.

CHAPTER III COST THEORIES § 1 WE turn now from those theories of interest based mainly on the idea of productivityto those based mainly on that of cost. The first of the cost theories to be examined resembles closely the productivity theories, the only difference being that the "cQ~t Qf prod~ital" takes the place of the value of capit~: In the productIvity theories, the rate 'of interest was sought in the ratio between the income from capital and the value of that capital. In the cost theory now considered, on the other hand, the rate of in terest is sought in the J;atio between the income from calli: ~l and the cost of that capita"4 This theory is subject to many of the objections which apply to the productivity theories. In the first place, it is necessary, before the ratio of income to cost can be regarded as even commen surable with a rate of interest, that income and cost shall have been reduced to a common denomination of value, as, for instance, dollars. A loom renders its return, or ser vice, by the operation called weaving.. The cost of the 100m, on the other hand, consists of raw materials, the use of tools, dies, lathes, and other machine-shop appliances, together with human labor. Only when these miscella neous items are reduced to some common standard of value does the ratio of income to cost become a mere 'percentage like the rate of interest. But when this reduction to a common standard is effected, the suspicion immediately arises that, after all, the question of interest may have 29 30 THE RATE OF INTEREST [CHAP. III been begged in the process, - that the labor, materials, and use of tools all derive their value as costs, in part, at least, from discounting the prospective product to which they contribute. In other words, since the cost of capi tal must be obtained by a process of valuation, this valua tion may involve the very rate of interest to be determined.

Nevertheless, the theory which seeks the rate of interest in the ratio of return to cost of capital has certain advan tages over that which seeks it in the ratio of return to value of capital; for there are some costs which are not merely the discounted value of expected services. There are two kinds of costs, (1) It interactions" 1 and (2) labor and-trouble. The value of the former is always de termIned by discounting some future service; the value of the latter is determined (to the laborer) by the irksome ness or "undesirability" of labor compared with the de sirability of money. We are not called upon, however, to strengthen the cost theories by recourse to this distinc tion between costs which involve discounting and costs which do not; for the cost theories as actually held and advocated take no account of such a distinction, and the costs usually cited are mainly costs which do involve discounting, - in other words, interactions. Such costs certainly cannot be taken as a sufficient foundation for explaining the rate of interest. The tailor reckons among his costs the value of the cloth which he buys; the manu facturer of the cloth reckons among his costs the value of the yarn; the producer of the yarn reckons in his cost the value of the wool. But the value of the wool is found in part by discounting the value of the yarn to which it contributes; that of the yarn, by discounting the value of the cloth; that of the cloth, by discounting the value of the clothes.

I t is seldom possible in practice to find a case so pure as not to be obscured by a number of different ele ments; but let us, for the sake of illustration, consider 1 See The Nature of Oapital and Income, Chaps. VII-X.

SEC. 2] COST THEORIES 31 a dealer in trees, who buys saplings and sells them after they are full grown. In this case there are few other costs besides the cost of buying the saplings. We can here see clearly the fallacy involved in regarding the rate of in terest as determined by the ratio of the value of the full grown tree to the cost of the sapling; for the cost of buying the sapling is evi~ently itself obtained by discounting the value of the tree. In fact, in this case the cost theory becomes identical with the productivity theory; for the cost of buying the sapling is nothing more nor less than the value of the sapling. The only distinction between them is a formal one: the cost of buying the sapling is regarded as pertaining to the income and outgo account; the value of the sapling, to the capital account. Since, then, the cost of buying the sapling is the discounted value of the tree, this cost can be computed only by discounting, and discounting presupposes a rate of interest. In many cases, therefore, "c~." is merely the discounted value of "~." The cost, in these cas~s at least, depends on the rate of interest, not the rate of inter~st on the cost.

§ 2 It is true that an article sometimes costs less (or more) than the discounted value of the returns. The ratio of future return to present cost may then temporarily differ from the rate of interest on loans. Thus, a manufacturer calculates that a newly invented machine will earn him $10 a year for twenty years. If we suppose he is willing to invest on a 5 per cent. basis, namely, that subjectively he values this year's goods at a premium of 5 per cent. compared with next year's goods, then the price he is willing to pay for the machine is $125, this being the present ,worth,at 5 per cent., of $10 a year for twenty years. But it may be that the cost of obtaining the machine is not $125 but, say, $100, which corresponds to an 8 per 32 THE RATE OF INTEREST [CHAP. III cent. basis. Here seems to be a natural rate of interest of 8 per cent., in defiance of an interest rate of 5 per cent. em ployed by the manufacturer in discounting his returns.

The manufacturer, by investing .$100, makes 8 per cent. not, apparently, because he or anyone else discounts the future at that rate, but simply because of the productivity of the machine in relation to its cost. But such a disharmony between the 8 per cent. realized and the 5 per cent. employed in discounting will be only tem porary. It will work out its own correction, for the manu facturer who finds he can invest at 8 per cent. when he is willing to invest at 5 per cent. will increase his invest ment until the returns fall to 5 per cent. He will buy more machines; but the more he buys, the less will he make from each successive machine. The tenth machine will not increase his income rate by $10 over and above what it would be with only nine machines, but by, let us say, only $6.25. This reduction may be due to outrun ning his market and reducing the price he can get, or by increasing the cost of running, or in other ways. He will buy machines up to the point where the last increment earns 5 per cent., and by the "law of indifference" he will impute this same rate to all the machines. In other words, however much the ratio of return to, cost may temporarily deviate from the rate of preference for present over future goods, such deviation is done away with at the margin of final choice. Excessive rates of return could never serve as a permanent basis for market values, for the rush to secure these excessive returns would reduce them. If, on the other hand, the cost of the machine is $150, represent ing a basis of about 3 per cent., while the manufacturer continues willing to invest only on a 5 per cent. basis, there may seem to be a natural rate of 3 per cent. Here, too, the apparent disharmony will work out its own cor rection. The manufacturer will cease buying machines to replace the old ones which have worn out, until through such limitation the returns have increased to 5 per cent.

SEC. 3] COST ·THEORIES 33 In either case, when equilibrium is established the value of the machine is the discounted value of its future uses. For the individual purchaser, the cost of the machine appears as a fixed quantity, and he so adjusts the number of machines that the return of the marginal machine is 5 per cent. on this cost. For the market as a whole, how ever, the situation is reversed; the price of the machines is determined by their prospective return. § 3 So far as the cost theories of interest relate to labor cost, they are free from the objection of begging the ques tion, which has just been offered to the more general cost theory.; and yet, the ra~io of return on labor to the labor invested cannot, by itself, afford a sufficient basis for the rate of interest, for the reason that neither the return nor the labor are fixed quantities. With an increase in the amount of capital, the return will decrease, and the labor of obtaining it will ·increase. This, in fact, is the well known "law of diminishing returns."

To render our reasoning clear, we shall take a classical illustration of Roscher's. Let the labor sacrificedin produc ing a fishingnet be reckoned at 100 fish. This valuation of labor by the laborer is not quite like the valuation of the machine. Instead of being the value of future income dis counted, it is the value of present outgo in the form of effort. We cannot, therefore, maintain that in valuing the net the rate of interest is surreptitiously introduced. Our objections are now confined to the fact that both the labor of making the net and its return are not fixed elements to which the rate of interest is adjusted, but are themselves adjustable to that rate. With the net, the fisherman is enabled to catch 30 fish a day, whereas without it he could catch but 3. We may suppose that the net will last 90 days, getting in all 2700 fish. This is the return on the D 34 THE RATE OF INTEREST [CHAP. III labor invested, which has been reckoned at 100 fish. If the net requires care and attention, and this be reckoned t at 3 fish a day, there is still an excess of 30 - 3, or 27 fish \ a day to be credited to the net itself. For the 90 days this amounts to 2430 fish. Even if, for other reasons, we make further reductions, tIle return may still be a very large one compared with the 100 fish invested, - let us say 2000 fish.

The question now is, does the excess of this return over the labor invested explain interest? Certainly not. Granted that such an extraordinary return on one's labor invested were initially realized, it is evident that ~ I paying so handsomely would be made in lar.g~_Jl--E-~J;terS, I and that, ~ their numberswefe increased, tbe labor Ddffi~fioo cl m~~ :Creas~ or else the --product obtained from each a.dditional I ,..Det would decrease, or both. In this way the excess of return over cost wouldbectoubly reduced. Why should not this excess be reduced to zero? Evidently nothing in the physical nature of the net itself, or the condition of the fisheries, or the amount of labor involved in producing a net, will suffice to explain the point at which the process will cease and nets no longer be produced. On the con trary, it is evident that physically it would be possible to greatly overproduce the nets. It is also clear that the fisheries could not continue to yield fish indefinitely. The result might be that, as the nets were increased in num ber, the labor of obtaining materials and making nets would increase until, let us say, a net would cost labor reckoned equivalent to 1000 fish; at the same time the yield of each net might fall to, say, 10 fish a day for the 90 days, or 900 fish in all. Here would be an invest ment of 1000 for a return of only 900. The reason that this result would not, intentionally at least, be reached, is evidently not to be sought in any physical facts as to the net, the fish, and the labor of producing them, but in the fact that the net makers would of their own volition SEC. 4] COST THEORIES 35 cease producing nets before such a-superabundance was put upon the market. In fact, they would even refuse to invest 1000 for an equal return of 1000. In other words, the production of nets would proceed only up to the point where the excess of return over cost corresponded to the relative preference for present over future fish. The rea son, then, that the product keeps above the cost is simply that those who make nets decide to stop making them at a point earlier than that of equality between cost and re turn, and their decisions so to do are based not on a physical but on a psychical fact - their relative valua tions of·-present sacrifice and future return.

Leaving our special illustration, let us put the matter in general terms. It is often stated by economists that any capital will be constructed only so long as its mar ginalutility is equal to or greater than the marginal dis utility or marginal cost of its construction. The greater the desire for its services and the less the cost of produc. tion, the more of it will be produced before its marginal utility falls to the level of its marginal cost. But the proper statement would be, not that the marginal utility of the services of a capital instrument tends to equal the marginal cost of the instrument, but that it tends to reach a level slightly above that ·cost, such that the present or discounted estimate of the marginal utility of future ser vices will equal marginal cost. § 4 Sometimes the argument of the cost theorists takes a slightly different form. It is said that the net, for instance-, receives interest because it "saves labor." If by "saving labor" is meant that the net costs less than it produces, that the labor of constructing and tending the net, meas ured in fish, is less than the number of fish caught by the net, - the argument is merely a repetition, in different 36 THE RATE OF INTEREST [CHAP. III words, of the argument which has just been stated and criticised, that the net receives interest because it produces something over and above its cost. If, on the other hand, by "saving labor" is meant simply that the net catches more fish than its owner could catch without it (30 fish a day instead -of 3), the argument is superficial; it leaves entirely out of account the cost of constructing the net, which is evidently an essential factor in reckoning the rate of return. For aught which this statement of" labor saving" contains, the net might have cost or be worth 10,000 fish. Such a net, though "saving labor" for 90 days, would never earn its original cost, and there could be no interest, in spite of this" saving of labor."

The adherents of the labor-saving theory of interest may put their case in a third and stronger form. They may say (1) that the net first costs labor to produce, (2) that it afterward saves labor in operating, and (3) that the labor subsequently saved exceeds the labor originally ex pended. The excess of the labor saved over the labor expended, both being measured, say, in fish, is, according to their theory, the source of interest. There is an ele ment of trtlth in the theory as thus stated, and this element will be incorporated into the constructive argu ment in Chapter VIII. But the element of truth is in adeqtlate to form a conlplete theory of interest for the reason that the excess of labor saved over labor spent is not a fixed excess, but depends on the voluntary choice of the fishermen as to the number of nets they propose to make. Their choice depends on how much present labor they are willing to spend in order to save themselves a given amount of future labor; it depends, in other words, on their relative valuation of present and future labor.

§ 5 In the example of the net, labor-sacrifice and return were both measured in a common objective standard, - fish.

SEC. 5] COST THEORIES 37 A still more elementary case is that in which both cost and return are measured in a common subjective standard, utility. The desirability of the fish and the labor-cost of obtaining them are comparable magnitudes, the one being utility (or desirability) and the other disutility (or un desirability) . To change our illustration, let Robinson Crusoe be suddenly placed on a fertile island suitable for banana growing. He will be able at first, owing to the great fer tility, to get a high degree of satisfaction in consuming bananas by the expenditure of a low degree of labor in planting and cultivating the, trees. But the same objec tions apply' as before; for the excess of subjective satisfac tion over subjective effort is no more fixed than any other excess of return over cost, and Crusoe may, if inclined, be so industrious in his raising of bananas as to vastly increase the labor of raising them, or, by satiating himself with them, decrease the satisfaction which they yield" or both. This process will proceed far enough to reduce the excess of satis faction over effort to such dimensions as Crusoe's relative valuation of present effort and future satisfaction will allow. The stopping point is determined by him, not, by any natural yield of the soil. The mere fact that the island is naturally fertile, so that labor is especially pro ductive, cannot determine the degree of intensive culture which Crusoe may apply to it.

The same principles apply to every unusually lucrative employment. Man is continually hunting, as it were, for bargains with Nature; but he deals at Nature's bargain counter only up to a definite point, - a point decided upon by him and not by Nature.' We cannot obtain a true and complete explanation of interest without recourse to the psychological element of human choice. Those who have made the mos.t successful use of the Co.st theory of interest are John Rae 1 and Adolphe Landry,2 ( 1 TheSociological Theory of Capital, edited by ProfessorC. W. Mix- , ter, (Macmillan) 1905. '.L' Inter~t du Capital, Paris (Giard & Briere), 1904.

38 THE RATE OF INTEREST [CHAP. III and both of these expressly admit that the ratio of return to cost can influence the rate of interest only as the mar ginal excess of return over cost harmonizes with the degree of preference for present over future goods. No objection is here offered to the general reasoning of Rae and Landry. Their results and those shown in the present book are for the most part in agreement. The chief difference, in so far as the present topic is concerned, grows out of the fact that neither Rae nor Landry made use of any definite theory of income, the relation of cost to income, and the distinc tion between labor-costs and" interactions." § 6 Some economists, whom Professor Bohm-Bawerk clas sifies as the" labor theorists of the English school," have attempted to explain the rate of interest as a sort of wage for the labor of producing capital. This theory is very crude and does not need extended discussion; for it is evi dent that the labor which produces the capital very seldom receives the interest. Suppose that a tree twenty-five years old is worth $3, and was planted at a cost of $1 ,vorth of labor. The laborer was paid $1 when the tree was planted; evidently not he, but the capitalist who pays him, receives the $3 twenty-five years later and therebyen joys an increase of value of $2. If this $2, which is inter est, is produced by the laborer who planted the tree, why does he not get it? It is quite true that the laborer pro duces this "surplus value," and yet he is forced to let another receive it.

This paradox has been made use of by the socialists, who maintain that interest ought to go to the laborers who produce the capital, but that they are robbed of it by the capitalist. This" exploitation theory of interes~ con sists virtually of two propositions: first, that the value of any product usually exceeds its cost of production; and, secondly, that the value of any product ought to be exa.ctly SEC. 6] COST THEORIES 39 equal to its cost of production. The first of these proposi tions is true, but the second is false. Economists have usually pursued a wrong method in answering the social ists, for they have attacked the first proposition instead of the second. The socialist is quite right in his contention that the value of the product exceeds the cost. In fact, this proposition is fundamental in the whole theory of cap ital and interest. Ricardo here, as in many other places in economics, has been partly right and partly wrong. He was one of the first to fall into the fallacy that the value of the product was normally equal to its cost, but he also noted certain apparent" exceptions," as for instance, that wine increased in value with years. As a matlter of fact, as Bohm-Bawerk has fully shown, this increase of value, instead of being exceptional, is universal in the whole realm of production. It is just because the value .2L.a £roduct does exceed its cost that there exists the' possi bility of any perpetual net income.1 Not only, therefore, is there no necessity that cost should equal return, but on the contrary, it never can normally do so. By making cost of production a corner-stone of the theory of value, the classical economists weakened their system greatly.2 In attemptingto provethat the laborershouldreceivethe whole product,the socialistthus stands on stronger ground than has sometimes been admitted. He cannot be an1 See Chap. II and its Appendix, where it is shown that if each ma chine costs exactly what it returns, and if the up-keep of a group of machines is maintained, the net annual income from the group is zero.

2 Besides the error that the cost of production theory omits the interest element, there was the error that most costs of production all "interactions," in fact - are themselves not the cause but the result of value, being future values discounted. See The Nature 0/ Capi tal and Income, Chaps. X, XIV, XVII. This objection to the cost theory of value does not apply to labor-cost; but even labor-cost is not a necessary or universal accompaniment of value. A mineral spring may produce a valuable water without labor-cost. Land also is largely costless except for the cost of transferring it, which is an "interaction." Other classical examples of articles which have no cost of production are autographs of Milton and similar memora bilia.

40 THE RATE OF INTEREST [CHAP. III swered offhand by saying that capital aids labor, and that the owner of a plow deserves an interest payment for its use quite as truly as the laborer who operates the plow deserves wages for his labor. The socialist contends that the payment for the use of the plow should belong, not to the man who holds it, but to the man who made it. He is quite correct in believing that the value of the uses of the plow is entirely due to the laborers who made it, but that, nevertheless, the capitalist, not the laborer, enjoys the value of these uses. The capitalist is, as a matter of fact, always living on the product of past labor. A millionaire who gets his income from railroads, ships, and houses, all products of labor, is reaping what labor sowed. The capi talists of to-day are receiving compound interest on the labor of yesterday. § 7 But it does not follow that in this any injustice l1as been done to the laborer. Let us revert to the case of the tree which was planted with $1 worth of labor, and 25 years later was worth $3. The socialist virtually asks, "'fly should not the laborer receive $3 instead of $1 for his work?

The answer is that he may receive it, provided he will wait 25 years for the $3! As B6hm-Bawerk says: 1 "The perfectly just proposition that tbe laborer should receive the entire value of his product may be understood to mean either that the laborer should now receive the entire present value of his product, or should receive the entire future value of his product in the future. But Rodbertus and the socialists expound it as if it meant that the laborer should now receive the entire future value of his product." To take another example: if a number of laborers work upon a railroad which requires 5 years before it can be completed, and which, when completed, is worth $7,000,000, there is no reason, if the laborers are willing to wait until the road is completed, that they should not own and 1 Capital and Interest, p. 342.

SEC. 7] COST THEORIES 41 operate it. They would then be receiving, in the future, the future value of their product. If, however, they are paid at the time their work is being done, they may be paid in one of two ways. One is by having assigned to them such parts of the road as they have created so that they may retain the same until it is a finished product to return income to them in future years. The other method, 'and the one which they much prefer,' is to be paid in cash, convertible immediately into food, .clothes, and other en joyable income. Under these circumstances the road, which is to be worth $7,000,000, will be paid for in wages, not by $7,000,000, but by, say, $5,000,000, distributed at the rate of $1,000,000 a year for the 5 years required to build the road. Socialists would cease to think that this is extortion if they would try the experiment ·of sendin.g a colony of laborers into the unreclaimed lands of the West, letting them develop and irrigate those lands and build railways on them, unaided by borrowed capital. The colonists would find that interest had not disappeared by any means, but that by waiting they had themselves reaped the benefit of it. They would need to wait, ·let us saY,5 years before their railway was completed. At the end of that time they WOllld own every cent of its earnings, and no "capi talist" could be accused of robbing them of it. But they would find that, in spite of themselves, they had now become capitalists, and they had become so by stinting for those 5 years, instead of receiving in advance, in the shape of food, clothing, and other real income, the discounted value of the railroad. This example was almost literally realized in the case of the Mormon settlement in Utah.

Those who went there originally possessed little capital, and did not pay interest for the use of other persons' cap ital. They created their capital, and passed from the category of "laborers" to that of "capitalists." It will be seen that capitalists are not robbers of labor, but labor bro~ers who buy work at one time and sell its products at 42 THE RATE OF INTEREST [CHAP. III another. Their profit on the transaction (or rather, that part of it which is interest) is due to the time elapsing between the labor and its return to the capitalist. § 8 Among those who have attempted to justify interest taking on a labor basis is a peculiar group of theorists who maintain that interest does actually go to the laborer - not the laborer who produces the capital, but the laborer who manages it. In other words, the " entrepreneur;' II under taker," or-"enterpriser" is the one who creates interest and therefore deserves it. This is another of the many at tempts to maintain that every economic product must be a mere equivalent for some corresponding labor-outgo.

The only evidence the adherents of this school can offer for the truth of their theory is, however, that capital can produce nothing without proper management. If, they say, no one lifts a finger to make capital productive, it will not be productive, and the man who plans, organizes, and controls the use of capital is the one who creates interest and ought to receive it. This theory, however, is evidently fallacious, if not self-destructive. For the person who receives interest, par excellence,is not the active" entrepre neur," but his" sleeping partner." If the active capitalist produces the interest on the capital he borrows from his sleeping partner, who" does not lift a finger," why does he surrender any of it to that partner? Is the sleeping part ner tl exploiting" his active associate? Of course it is true that the mere investor could get no interest were it not for some intelligent, active management of capital.

But this management is paid for in the shape of entre preneur's profits. The mere fact that the entrepreneur's work is usually indispensable to the production of income would not justify his receiving all of that income. In fact, we may conversely state that the capital intrusted to the SEC. 9] COST THEORIES 43 entrepreneur is quite as indispensable to him as is his work to the inactive capitalist. S dt · dh b §h 9 0 of· /V~-~~o e ermIne ave een t e attempts to JUstl y Interest v· ),/? . on the ground of some cost of production that, in the ab- ...~.//,./ sence of any other item which can be called cost, a special ,--"".. constructive cost called "abstinence" or "waiting" has been invoked to meet ·the--emergency. C~rench economists have even gone so far as to call this the "labor of saving." The abstinence theory in its various forms holds that the capitalist, by abstaining from the consumption of his capital, obtains a reward in the shape of interest.

The abstinence theory bears a close resemblance to the " agio" theory of interest, which is believed by the writer to be essentially correct. In fact, it has been claimed by some writers that the a~nce th.eory diffexs from the, agio merel in words. This claim is perhaps true of certain versions of the theory, and against these no criti cism need here be offered, unless it be a verbal one. If by saying that interest is the reward of waiting or abstinence it is only meant that men prefer not to wait for the future, but to enjoy the present, the only objection which need be offered is that the mode of statement is somewhat unhappy; it implies, apparently, that future rewards are caused by making present sacrifices, rather than that present sacri fices are caused by the prospect of future rewards. But in the sense in which the abstinence theory is usually held, it differs from the agio theory not only in words but in essence. As Bohm-Bawerk has shown, it assumes that it abstinence" is an independent item in cost of productio1b to be added to the other costs and~ treated in all ways like them. With this proposition issue is here joined.' 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 con44 THE RATE OF INTEREST [CHAP. III sidered as costs. An illustration will make clear the dif ference between true costs and the purely constructive cost of waiting. According to the theory that waiting is a cost, if planting a sapling costs $1 wortll of labor, and in 25 years, without further expenditure of labor, 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 ~ WT is claimed, II worth of labor and $2 worth of "waiting."

J-I According to the theory of the present book, however, -the \ cost of producing the tree is the $1 worth of labor, ~~d V\J~ 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. At first it would seem a mere matter of words whether we call the $2 a surplus above cost, or an item constituting another cost, known as "waiting.'-' But examination will show that the two so-called U costs" are radically different. If waiting is a cost like other costs, it should be subject i to the law of discount, according to which the capitalJ value of any article of wealth is equal to the discounted I value of its expected income less the discounted value of its " ~ expected outgo. The value of the tree which has just 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 iIlcome which the tree will yield at the end of eleven more years. According to our own theory, this $3 is the only future item of income or outgo. But according to the theory here criticised, 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 10cents for the first year and gradually increasing to 15 cents. for the last year. Now if these costs really exist, they ought to be discounted and their discounted value deducted from the discounted value of the $3 of expected income. But we should then have to assign a value to the tree not of $2, as it actually is, but of about $1, which is SEC. 10] COST THEORIES 45 erroneous. 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. The fact that it cannot be applied to the so-called "cost of waiting" without leading to an erroneous result is a proof that the "cost of waiting" differs radically from true costs.

Thus, the theory that waiting i§=&~~! or outgo is a ~ ~ e~.the ~pf if,t;fullacy t1.mtsay· .. explained in The atUre of Capital and M n·come. oth have to deal with the increase of capital-value; the one theory regards this increase as income, the other as outgo. As a matter of fact, it is neither income nor outgo, but increase of capital only. § 10 As an answer to the objection just urged against treating waiting as a cost, namely, that it cannot be discounted, it might be pointed out by the abstinence theorists that while waiting-cost is certainly not a discountable cost, its inclu s~!!!:ihe list of costs obviates me nece~sity of disc~ th~ other items of cost or of income. If all income and all cost items, including waiting;"are counted at full value, capital may be valued simply by taking their net sum, without subjecting any item to the discounting process. To count "waiting", as a cost, then, appears as an alterna tive method of keeping accounts. Accepting this answer for the sake of argument, we observe that while it obviates the objection to the abstinence theory of cost so far as its application to capital value is concerned, it leaves objec tions equally great to its application to income. If wait ing is· a cost like other items, it must be included on the outgo side of the income account. To show how this 1 Chap. XIV. Cf. as to the fallacy here considered, Bohm-Bawerk, Recent Literatureon Intere8t (Macmillan), 1903, p. 35 n.

46 THE RATE OF INTEREST [CHAP. III would apply to the cost of the tree, the following table is presented: CAPITAL INCOME OUTGO NET VALUE AT INCOME END OF' YEAR -1st year. 00.00 Labor 1.00 "Waiting" .05 1.05 2d year 00.00 " Waiting" .05 1.10 3d year 00.00 "Waiting" .05 1.15 * * * * * * * * * * * * * * * *14th year 00.00 "Waiting" .10 2.00 * * * * * * * * * * * * * * * *25th year, from sale of tree 3.00 " Waiting" .15 3.00 Total 3.00 3.00 00.00 According to this method of accounting, we see that during the year in which the sapling is planted its cost con sists 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 the 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 bookkeeping, as the fol lowing additional examples will show.

Suppose a person owns an annuity amounting to $100 a year for 10 years. According to any ordinary method SEC. 10] COST THEORIES 47 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 an nuity during that year, due to his waiting for the future instalments of income of which his annuity consists.1 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 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 result in the following table:CAPITAL INCOME OUTGO NET VALUE AT INCOME BEGINNING OF YEAR 1st year money, $100 "Waiting" $ 39 $ 61 $772 2d year money, 100 "Waiting" 35 65 711 3d year money, 100 " Waiting" 32 68 646 4th year money, 100 "Waiting" 29 71 578 5th year money, 100 "Waiting" 25 75 507 6th year money, 100 " Waiting" 22 78 432 7th year money, 100 "Waiting" 18 82 354 8th year money, 100 " Waiting" 14 86 272 9th year money 100 " Waiting" 9 91 186 10th year money, 100 " Waiting " 5 95 95 $1000 $228 $772 Is it ~d bOQkkeep~ to introduce a new and strange element of cost which results in making the net income of the annuitant not the $100 which he actually receives, 1 This is evident, since the value of his annuity, capitalized at 5 per c,ent.,reckoned at the beginning, is $772, whereas, reckoned at the end of the first year, before his $100 is paid, it is $811.

48 THE RATE OF INTEREST [CHAP. III but the sums given in the table; namely, $61, $65, $68, and so forth? 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 $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 cost of waiting is to be re garded as a deduction from income, like other costs, 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 money-income the $100 of waiting, the remainder each year is zero! It may be said that we have not always a mere annuity to deal with but a definite capital such as a house or a factory. which has involved cost in its construction and the "sacrifice" of waiting for an income, whereas the capital might have been consumed at once. In all such cases, ho"rever, we are dealing with the very same prin ciple. The possession of the house or factory, like the title to the annuity, is valuable only because of the service or the income which it is expected to yield. If there is for the house or factory an initial labor-cost or expense, this is also true of the annuity. On the other hand, the one as well as the other may come by inheritance and so involves no cost to its owner. What it is desired to em phasize is that in any case the present value is the dis counted value of the expected future services or income and that it is not any sacrifice or cost of waiting which produces this value but that, on the contrary, it is the existence of this future value which prompts the waiting.

§ 11 It is obvious that the theory which calls "waiting" a, cost has worked out its own absurdity. The most that can SEC. 11] COST THEORIES 49 be said in its favor is that it makes the capital-value of any article equal to its cost of production. ,The idea that the value of an article should equal its cost seems to pos sess a certain fascination for many, if not most, students of economics. That it is false' has been sufficiently shown by B6hm-Bawerl{ through reasoning somewhat similar to the foregoing. That it is absurd when carried to its logical conclusion is evident when 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 c-allital value ~!!Y.. article is normallynot, l~, but equal to, the expected inco~, Thus, to revert to thecaseortlietree, lerus 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 cost 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 consid ered has, at the beginning, property worth $772. This, according to any proper bookkeeping, is the discounted value of the future income of $100 a year for 10 years, the total amount of which is $1000. But, according to the abstinence theorists, the income which he 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. 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 reck oning, the total income' froin such an annuity is infinity, although its present capital value is only $2000. But E t :::t: ~ pi .0/",........~f,t1.""~ ..~, ~~'_.f,' ..A "-,',,::,.' ~" I 50 THE RATE OF INTEREST [CHAP. III according to the abstinence theorists the income itself is not infinite, but only $2000.1 Those who are enamored of the 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.

§ 12 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 tangible costs. Waiting means nothing unless there is something waited for, and the cost of waiting can only be estimated in pro portion to the magnitude of what is waited for. It will doubtless take a long time for many to accept the doctrine that the value of capital is not only less than its future expected income, but normally greater than its past cost. 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, in terest, however explained, is regarded as one of the costs of production. It is true that for a debtor who pays in terest, the interest is, to him, a real cost, and is debited on 1 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 in come 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 II remainder term" which will, in · the supposed accounting, make the total income distributed through all eternity simply equal to the capital value, $2000.

SEC. 13] COST THEORIES 51 his books. But we need only to be reminded of the debit and credit bookkeeping which was considered at length in The Nature of Capital and Income to see that this item is counterbalanced on the books of the creditor, to whom this interest is by no means a cost, but 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 consti tutes 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 inde pendent 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. 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" enterpriser." Since he usually pays interest, he comes to think of it purely as a cost.

We have devoted cOfIlsiderablespace to the refutation of the abstinence theory, because its errors are so subtle and insidious as to beguile many of the best and most wary of economists. § 13 The results of the present chapter may be summed up by grouping the cost theories under two heads: those which regard· interest as in some sense a cost; and those which regard interest as a surplus above cost. As we have seen, the contention of the first group is erroneous, whether the concept of cost employed is the "cost of producing capi tal," the "cost of managing," organizing, or investing it, or the purely constructive cost of "waiting," "abstinence," or t'labor of saving." The contention of the second group, which considers interest as a surplus above cost, is correct; but the explanations which are given of this surplus are in correct, or at any rate, incomplete, whether those explana ..

52 THE RATE OF INTEREST [CHAP. III tions take the fanciful form of the socialists that interest is extortion, or the mere statement of fact of the cost produc tivity theories, that nature yields a surplus above cost. In this last statement, however, lies the only grain of truth which can be ascribed to the cost theories. Although . nature does not of herself yield a fixed surplus above cost, which may be called interest, she offers a series of such opportunities of getting a surplus, of which opportunities man takes advantage, and with respect to which he adjusts his efforts to his returns until the surplus yielded corre sponds to his subjective preference for present over future goods. In other words, just as in the case of the theories based on productivity, we find that the theories based on cost have an element of truth only as far as the oppor tunities presented by nature are reviewed in the mind of man and decided upon according to his time preference.

CHAPTER IV ' BOHM-BAWERK'S THEORY § 1 IN the preceding three chapters the most common of the existingtheoriesof interesthave been stated and criti cised. There remains one, however, which has received a large degree of currency among economists. Hitherto, in order to condense our review, we have employed the impersonal method and have rarely discussed the special interpretations which individual writers have made of the several theories. In the present chapter, however, we shall depart from this practice. The reason for criti cising Bohm-Bawerk's specific theory is that, unlike the theory of any other individual writer, it has become widely accepted. Capital and Interest and The Positive Theory of Capital have become economic classics. There can be no question that they deserve the high esteem in which they are held, for they contain the material, both in their destructive criticism and in their constructive argument, for a correct theory of interest. For the most part, Bohm. Bawerk's work will doubtless always stand. At only one vit~IEO!;nt-99.....lY!LI.ega'Id it asdQie8ti"Je. \ Bohm-Bawerk's theory is called by him the It agio theory"

of interest, since it finds,,.the.J~,ssen.Get~h~t in t~~,~.~i? ?~,Il:eI~~:!Ym,>~,cmc¥~,~~ww~i41xchanged fo~~,;J§IYIe::gaoas:c-"..·,,>rThis theory is in the main accepted by the present writer as the natural and proper starting point for any rational discussion of the subject. Bohm... Bawerk has presented the agio theory clearly and forcibly, and has disentangled it from the crude and incorrect 53 54 THE RATE OF INTEREST [CHAP. IV \) notions with which it had previously been associated. It is only when he attempts to add to it hi~ special feature 4 of a "technical superiority of present over future go~ds " t~has impaired rather than im~ed it. The agio theory may be said to have been foreshadowed by med~ters, some of whom stated that interest could be justified by !!t..E!!J-Qr "delay"; and the theory appears in a ~de form in the abs~inence_~~~~,ri~~ of Senior and others, which wereCliScus-sed-rrrttH~--precearng~ In a more definite form it was advanced by John Rae in 1834, in a work"WlllCh-hashitherto received far lessatten tion than it deserved; 1 and in a less complete form, and quite independently of Rae, by Jevons,2 Sax,3 and Laun hardt. 4 But excepting Rae, none of these writers can compare with Bohm-Bawerk for the thoroughness with which the theory is worked out.

Bohm-Bawerk distinguishes two problems: (1) ~_. do~~~exist ? and (2) Wha~_g~t~rmi_~~~ .,~~r.~.~~E: ticular rate of interest? In answer to the first problem, be states virtually tliat this 'Yorld__!§~!L9QI.!~~I~~,ted that most of us.prefer··present··goodsto future goods of like'·kinu" anti number. This preference is due, according to Boh:m Bawerk~ to three circumstances: (1) the '~ersPE1ctive \ 1 Bohm-Bawerk reintroduced independently the main argument of Rae. Several years later Rae's book was unearthed and brought into prominence by Professor C. W. Mixter. The original being out of print, Professor Mixter has edited a reprint, rearranged for modern readers, under the new title, The Sociological Theory 01 Capital (Mac millan),1905. Rae's work labored under the disadvantage, compared with Bohm-Bawerk's, of being written before the modern theory of value had been expounded. Its shortcomings are chiefly due to this fact. On the other hand, it surpasses Bohm-Bawerk's treatise in some respects, notably in its treatment of invention. See Bohm-Bawerk's comments on Rae in Recent Literature on Interest (Macmillan), 1903, and the reply by Mixter, "Bohm-Bawerk on Rae," Quarterly Journal 01 Economic8, May, 1902, pp. 385-412.

2 Theory 01 Political Economy, London, 3rd ed. (Macmillan), 1888. B Grundlegung der theoretischen Staatswirthsckalt, Vienna, 1887. 4 M athematische Begrundung der Volkswirtschaltslehre, Leipsic, 1885.

SEC. 2] BOHM-BAWERK'S THEORY 55 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 of the "provision," for present wants as compared with the provision f~e wants, or in other words, the relative scarcity of present goods compared with future goods; (3) the "~chnical suueriority" of present over future goods, or the fact, as Bohm-B"iwerk conceives it, that the "roundabout" or " capitalistic" processes of production are more remu nerative than those which yield immediate returns. The first two of these three circumstances are undoubtedly pertinent, and will be incorporated, under a somewhat different form, in the theory of the present book. It is the third circumstance -the so-called technical superiority of present over future goods - which we believe to contain essential errors.

§ 2 According to Bohm-Bawerk, labor invested in long processes of production will yield larger returns than labor invested in short processes, and will therefore confer a H toohnical advantage" upon those who have the command of that labor. In the reasoning by which Bohm-Bawerk attempts to prove this" technical superiority," there are t.bree principal .steps. ThEl-Jirst<. cQn~lstL~f ... E~s~~ting ~~~~~!t,<£~,:!.Y~[~~,_l1mdu~Jj2!l~~~riod " representing the length of the productive processes of the community; .. ~. seQQRQ cQJlSists",.>DL*,t~~positio.D-Ji!t~!i",,~h~~~J2,!!g~r~~~ih!,,~~,".,!Y~rf&&e..·~, ,~prQdl1ctWIL,.~peclod",;".~the\~)~~eatm:'0·~~!Jl <.~~ .. " ~~~'" .. EEQ(tH~Q~~!and the third consists in the conclusion' that in'''cons~quence' ~':t!~::gfEi:fi::Ii~~~!··.IJI~~f··~'gpods possessa l' techrllc~r~f ru~ure..!20ds. ~~eiiaeavor to 's!ioWttiat"'Qie thir<:ronTieSe"'steps contains a fatal error. The first step also is not wholly satisfactory.

56 THE RATE OF INTEREST [CHAP. IV A serious defect in Bohm-Bawerk's concept of an aver age production period is that it lacks sufficient definiteness to form a basis for the reasoning that he attempts to base upon it. He begins by stating that every article is the result of the cooperation of land and labor, and (abstract ing the element of land) he proceeds to consider the period of production for the element of labor. If, he says, an arti cle costs 100 days'labor, of which 20 days must be spent 10 years before the completion of the article, 20 days 9 years before completion, and thereafter 5 days in each succeeding year until completion, whereupon 20 days' labor are spent in finishing touches, the production period for this article is the average age of these several brief terms of labor; namely, 20 x 10 + 20 x 9+5 x 8 + 5 x 7 + 5 x 6 + 5 x 5 + 5 x 4+ 5 x 3 + 5 x 2 + 5x 1 + 20 x 0 ~ 100 100 or 5.6 years.1 In other words, all the labor expended in the prodllction of the article is regarded as concentrated at one point of time 5.6 years prior to its completion.

This point is what mathematicians call the "c~nter of gravity" of the various portions of labor expended~ First, in regard to the location of this point, we may ask why the particular method of averaging which B6hm Bawerk employs is assumed by him to be the correct one. His average is a "weighted arithmetical mean." There are many other possible methods of averaging any series of numbers. The particular kind of average chosen in any special problem is a matter of prime importance in cases, like the present, in which the numbers are widely divergent. In cases in which the numbers do not vary widely, there is little practical need of distinguishing be tween the different methods of averaging. Experience with index numbers shows, for instance, that the arith metical, geometrical, and harmonical "means" and an 1 The Positive Theory 0/Capital, English translation, London (Mac milla.n), 1891, p. 89.

SEC. 2] BOHM-BAWERK'S. THEORY 57 infinite number of other Cl means," 1 will agree very closely. But where, as in the present case, some of the elements averaged are very small and others very large, their means will differ widely according to the different methods of averaging. Thus, in the example used by Bohm-Bawerk, if we apply, instead of the weighted arithmetical, the weighted geometrical mean, we shall obtain 0 years,2 instead of 5.6 years as the average. The weighted harmoni cal mean will also be o. But suppose the question of the correct formulation of the average production period for an individual article to have been satisfactorily settled, in what manner is it proposed to combine the production periods of different articles? Here are involved, considerably magnified, all the well-known difficulties of constructing a suitable index number. Supposing the average production period of cloth is 2 years and iron 5 years, how are we to obtain the average production period for cloth and iron? No one would maintain that in such averaging between dif ferent commodities, they should all be assumed as equally important. They must be weighted. To obtain the aver age of 2 and 5 for the cloth and iron, are we to weight these two commodities according to the value of the amounts annually consumed? If so, ,viII not the rate of interest be involved in the value of the cloth and the iron?

Again, Bohm-Bawerk's theory of the production period requires us to combine a number of seemingly discon nected time-elements. Thus, the "period of production" , . 1 For a mathematical statement of this topic, see Appendix to Chap. IV, § 1. 2 To be exact, not quite 0 years; for it is physically impossible to have the last instalment of labor, namely, 20 days, all put in at an instant. Bohm-Bawerk speaks of this 20 days of labor as immedi lately preceding the finishing of the productive process. I t, like the other elements of labor, is located in the past, though its remoteness from the present is very small, let us say one day, or 'Ito-years. Then the geometrical mean would be, not zero, but 1°V'102J x 9~O X 86 X 76 X ij6 X {)6 X 46 X 36 X 26 X 16 X (1"t'5)20 or 1.3 years.

58 THE RATE OF INTEREST (CHAP. IV of obtaining water from a well is not, by Bohm-Bawerk's method of estimation, the time consumed in merely send ing down and drawing up the bucket. His theory requires us to add to this interval of time some fraction of the time of digging the well, and to this, some fraction of the time of making the spade by which the well was dug, and then, some fraction of the time of making the machinery by which the spade was manufactured, and again, some frac tion of the time of constructing the tools by which the machinery was made, and so on, thus carrying our calcula tions indefinitely into the past. Waiving other objections, what is to insure that the items representing the distant past will be, as Bohm-Bawerk alleges,! negligible quantities? Such an assertion as to the convergence of the mathe matical series in question should receive substantiation. Professor Fetter 2 and others S have criticised Bohm Bawerk's concept of a production period so fully that we need not mention additional perplexities.4 § 3 Passing over the second step,5 to which no objection is offered, we come to the third and crucial step in Bohm Bawerk'stheoryof the technical superiority of present goods; namely, that the productiveness of long processes confers a special" technical advantage" to the possessor of present goods or labor. This advantage produces, so Bohm-Bawerk believes, a preference for present over future goods which is entirely apart from and in addition to the preference due to the perspective underestimate of the future or 1 The Positive Theory of Capital, p. 88.

:I See liThe Roundabout Process in th,e Interest Theory," by F. A. Fetter, Quarterly Journal 01 Economics, Vol. XVII (November, 1902), p. 13 passim. Cf. Taussig, Wages and Capital, p. 12. 'See Lexis, Jahrbuch fur Gesetzgebung, Verwaltung und Volk8 wirt8chaft, 1895, pp. 332-337; Bortkiewicz, ibid., 1906, p. 69. • See, however, Appendix to Chap. IV, § 2. I See Appendix to Chap. IV, § 3.

SEC. 3] BOHM-BAWERK'S THEORY 59 that due to the underendowment of the present. Grant ing for the moment the validity of the concept of a pro duction period, and that the longer the period, the greater its product, it may still be shown that no such "technical superiority" follows. Since Bohm-Bawerk' regards this part of his theory as the most essential of all, and repeat edly states that the theory must stand or fall by the truth or falsity of that J)art, it becomes necessary to examine his claim in considerable detail. Bohm-Bawerk supports his assertion of the existence of a "technical superiority" 1 by elaborate illustrative tables, reproduced below :A MONTH'S LABOR AVAILABLE IN 1888 YIELDS For the Units of True Marginal" Marginal Amount of Utility Reduced Value of EntireEconomic Period Product Utility of Unit in Perspective Product 1888 100 5 5 500 1889 200 4 3.8 760 1890 280 3.3 3 840 1891 350 , 2.5 2.2 7701892 400 2.2 2 800 1893 440 2.1 1.8 7921894 470 2 1.5 7051895 500 1.5 1 500 A MONTH'S LABOR AVAILABLE IN 1889 YIELDS For True Marginal Reduced EconomicPeriod Units Utility Marginal Value Utility 1888 - 5 5 1889 100 4 3.8 380 1890 200 3.3 3 600 1891 280 2.5 2.2 616 1892 350 2.2 2 700 1893 400 2.1 1.8 720 1894 440 2 1.5 6601895 470 1.5 1 470 1 The P08iti1JeTheory 0/ Capital, p. 266.

60 THE RATE OF INTEREST [CHAP. IV A MONTH'S LABOR AVAILABLE IN 1890 YIELDS For True Marginal Reduced Units Marginal ValueEconomic Period Utility Utility 1888 - 5 5 -1889 -- 4 3.8 1890 100 3.3 3 300 1891 200 2.5 2.2 440 1892 280 2.2 2 560 1893 350 2.1 1.8 630 1894 400 2 1.5 6001895 440 1..5 1 440 A MONTH'S LABOR AVAILABLE IN 1891 YIELDS For True Marginal Reduced Units Marginal ValueEconomic Period Utility Utility 1888 - 5 5 -1889 - 4 3.8 1890 - 3.3 3 1891 100 2.5 2.2 220 1892 200 2.2 2 400 1893 280 2.1 1.8 504 1894 350 2 1.5 525 1895 400 1.5 1 400 Beginning with the first table we see that it represents, in the second column, the units of product obtainable in various years through the investment of a month's labor in 1888. Thus, a month's labor in 1888 may be in vested so as to produce 280 units in the year 1890, or 470 units in the year 1894. The third column gives the marginal utility of the prod uct to the investor in the various years. This column is formed on the assumption that the individual is in "grad ually improving circumstances," so that in 1895 a unit of product will be estimated in his mind at 1.5 units of utility, whereas in 1888 the same unit would have been estimated at 5.

S~c. 4] BOHM-BA WERK'S THEORY 61 The fourth column shows the present valuation of the \ aforesaid marginal utilities. Thus, the unit of product in 1895, while worth 1.5 units of utility at that date, is, when foreseen in perspective, worth only 1. The fifth column shows the (subjective) value of the product. This is obtained by multiplying the number of units of product by the reduced marginal utility; that is, multiplying the items in the second column by the cor responding items in the fourth column. Beginning with the first table, Bohm-Bawerk selects the maximum figure (underscored) in the last column. This maximum signifies that a month's labor available in 1888 would best be.invested so as to mature in 1890, because the present value of the product attainable in 1890, but reck oned in 1888, is the maximum, 840, of all the present values. In the same way it is seen from the second table that a month's labor available in 1889 will be so invested as to mature in 1893; fOf, when thus invested, it has its maximum present value (reckoned in 1888). But this maximum present value is only 720, which is less than the previous maximum present value of the product (840) if the labor were invested in 1888. There is, therefore, says Bohm-Bawerk, a "technical advantage" in having the labor available in 1888 over having it available only in 1889. In the same way, it is still less advantageous to have a month's labor available in 1890, as the product is in that case worth only 630 in the present (1888). Like wise, a month's labor available in 1891 is still less valuable, having a value (in 1888) of only 525. Thus we see that the longer the labor is deferred the less the value of its best product, as reckoned in the present (1888).

§ 4 The result is correct; but Bohm-Bawerk is mistaken in ascribing any part of the result to the fact that the l?nger 62 THE RATE OF INTEREST [CHAP. IV processes are the more productive. In his tables he assumes the existence of one or both of the other two factors, - the relative overprovision for the future as compared with the present, and the perspective under valuation of the future, due to lack of intellectual imagi nation and of selfcontrol. Examination will show that it is these elements, and these alone, which produce the advantage of present over future goods which the tables display. Bohm-Bawerk has curiously deluded himself, as well as many of his followers, on this point. He says: 1 "I repeat emphatically that this result is not an accidental one, such as might have made its appearance in consequence of the par ticular figures used in our hypothesis. On the single assumption that longer methods of production lead generally to a greater out put, 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."

As a matter of fact, however, the result does not at all follow from H the single assumption that longer methods of production lead generally to a greater output." It has nothing whatever to do with that assumption. In other words, it has nothing to do with the fact tllat the series of numbers in the second column of the tables in creases, but with the fact that the series of numbers in the fourth column decreases. If we should make the opposite assumption from that of Bohm-Baw~~me a e roductiy~ ~ocess t e smaller will be the retur r same res\!lt would follow. The labor would still be invested at the earliest posSible moment. Let the figures in the second column 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 immediate returns instead 1 The Positive Theory 01 Capital, p. 268.

SEC. 4] BOHM-BAWERK'STHEORY of being invested in a two years' process as Qefore. The present value, in 1888, of the investment of the month's labor of that year in an immediately returning process would be, as before, the product of 100 by the marginal utility, 5, or 500, whereas if the labor were invested for a year the present value would be less; for its amount is found, as before, by multiplying the -number of units of product (now assumed less than 100) by the marginal utility (which is less than 5). Likewise, the month's labor available in 1889 would also be invested so as to yield an immediate return and would possess a value of 100 x 3.8, or 380. If similar calculations are performed for each year and the results are compared, it will appear that the invest ment in 1888yields the highest return, just as it. did on the previous hypothesis. Again, the s~me result would follow if the productivity increased and then decreased in all the tables, as follows: 100,200, 230, 200, 100,etc.F()r examination will showthat the labor available in 1888wouldhave a maximum value of 200 x 3.8, or 760; that available in 1889,a value of 200 x 3, or 600; that in 1890,a value of 230 X 2, or 460; that of 1891, 230 x 1.8, or 414,etc. These results, 760, 600, 460, 414,etc., constitute a descending series, and show again the greater desirability of labor which is avail~ble early as compared with labor which is available late. It is just as easy to show that if the productivity first decreases and then in creases, the same advantage of present over future labor will result.

Such illustrative figures could be reproduced indefi nitely. The reader can readily convince him~elf by trial that as long as the column of "reduced marginal utility" decreases, the column of "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.1 1 For a mathematical proof, see Appendix to Chap. IV, § 4.

64 THE RATE OF INTEREST § 5 [CHAP. IV On the other hand, if the conditions are reversed and the fourth column of "reduced marginal utility" does not decrease, the earlier available labor will not have a higher value, whatever may be the character of the second column of "units of product." Bohm-Bawerk, however, specifically denies this: 1_ "The superiority in value of present means of production, which is based on their technical \superiority, is not one borrowed frOln 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, and we get the follow ing figures:A MONTH'S LABOR OF THE YEAR 1888 1889 1890 1891 1888 500 - - ~ Q 1889 800 400 - ril ~ S D E-t ~ 924 660 a30 ~ 1890 - < ~~ > ~ 0 1891 875 700 500 250 r:.

rn ~ 1892 880 770 616 440 0 ~ 0 '(fl ~ ~ 1893 924 840 735 588 8 Z ~o 1894 940 880 800 700 ~~ 1895 750 705 660 600 It is, as Bohm-Bawerk remarks, still true that the month's labor available in 1888 is more highly valued than the same month's labor available at a later date. But he has care fully retained in his illustration one of the "two circum stances " which he stated could be discarded; namely, the 1 The Positive Theory of Capital, p. 268.

SEC. 5] BOHM-BAWERK'S THEORY 65 relative overprovisionfor the future. To leave one of these two circumstances effective instead of both is merely to change slightly the series in the fourth column of the pre vious tables; namely, to cllange it from the descending series, 5, 3.8, 3, 2.2, 2, 1.8, 1.5, 1, to another descending series, 5, 4, 3.3, 2.5, 2.2, 2.1, 2, 1.5. The change in the par ticular numbers is quite immaterial as long as the series is still descending. It does not m~tter whether the descent is due to perspective, or to the relative overprovision for the future, or to both. The essential fact is that the numbers in the fourth column still constitute a descending series. The only fair test of the independence of B6hm-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 mar ginal utilities; in other words, to make the numbers in the fourth column all equal. Bohm-Bawerk, for some reason, hesitates to do this. He says: 1_ "But if we were also to abstract the difference in the circum stances of provision in different periods of time, the situation would receive the stamp of extreme improbability, even of self..contra diction."

This is very true indeed; for to abstract both the under estimate of the future and underprovision for the present .'is to abstract the whole basis for interest and not a part merely. Yet this is no t~ason for refusing to push the inquiry to its limit. The! consideration of this extreme case will in fact show clearly the error of Bohm-Bawerk; for although we shall have abstracted all true foundation for interest, there will be left what B6hm-Bawerk wrongly imagines to be a' basis of interest. Let us, therefore, make all the factors in the \"reduced utility" column alike, say 5. The tables for 1888 and 1889, condensed, would then read as follows:1 Ibid., p. 269. F ')l 66 THE RATE OF INTEREST A MONTH'S LABOR AVAILABLE [CHAP. IV IN 1888 YIELDS IN 1889 YIELDS FOR ECONOMIC UNITS OF REDUCED VALUE UNITS OF REDUCED VALUEPERIOD PRODUCT UTILITY PRODUCT UTILITY 1888 100 5 500 - 5 -1889 200 5 1000 100 5 500 1890 280 5 1400 200 5 1000 1891 350 5 1750 280 5 1400 1892 400 5 2000 350 5 1750 1893 440 5 2200 400 5 2000 1894 470 5 2350 440 5 2200 1895 500 5 2500 470 5 2350 2500 The figures in the value columns for 1888 and 1889 are here absolutely alike; hence the maximum of the former, if there be a maximum, must be identical with the maxi mum of the latter.

Though Bohm-Bawerlc 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: 1_ I H 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 round about 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 experi ence." Bohm-Bawerk's confusion here is probably to be ascribed to his insistence on the indefinite incre~§e of product with ~-....=...-.----- ~, -~ 1 Ibid~, p. 269.

SEC. 5] BOHM-BAWERK'S THEORY 67 a Ien~ of the production period. Had he admitted into his possibilities the particular possibility that the prod uct would ultimately decrease with a lengthening of that period, the error which he had committed would have made itself too evident to escape his notice. As it was, he found himself dealing with an infinite.series; and as ·the history of mathematics shows, it is not easy in such inquiries to keep clear of pitfalls. Yet even in the hypothesis of a law of indefinite increase in returns with increased length of productive period, the error, though concealed, exists and may be shown. In order not to tamper prematurely with any of Bohm Bawerk'shypotheses,let us then still assume this lawof in definite increase of value proportionately with the length of the productive process. The result of such a fact would be simply that productive processes indefinitely long would be chosen by investors. The possessor of a month's labor"

whether available in 1888 or 1889, would invest it in an 1 infinite production process, - a result extremely fantastic, Jj but involved in the hypothesis. We need not assume that I the product of an infinite production period is itself infinite. The increasing product may approach a definite limit. This ought, in fact, to be assumed; for we could not imag ine that a finite earth would have an infinite product. To fix our ideas, let us suppose that with each year after 1895, with which Bohm-Bawerkbreaks off his table, the product leaps up halfway toward 1000 units. Thus, in 1896 the product rises to 750, a rise of half the interval between 500 units (the product of 1895) and 1000 units. In 1897 it becomes, in like manner, 875, in 1898, 937.5, etc. The limit of such a series is 1000 units. A month's labor, whether available in 1888 or 1889, will now have the same maximum value, exactly 1000, and there will be no "technical superiority" in present over future goods whatever.

It is noteworthy that in treating this case Bohm-Bawerk shifts his ground. For the case of undiminished marginal 68 THE RATE OF INTEREST [CHAP. IV utilities, the only comparison which he makes between the two series (that for 1888 and that for 1889) is not a com parison between their maxima, such as he made in his previous cases, but a comparison between individual terms. He states in a footnote: 1_ ". . . The month's labour of 1888 remains superior to that of 1889. For, as regards anyone remote period, say, the year 1988, the former, as employed in a process longer by one year, could pro duce a somewhat greater product than the latter." Such an individual comparison is, of course, beside the point; but granted that it should be made at all, why is it made between two items relating to the same calendar yearf Why not make it between two items relating to the same production period? Why conclude that a month's labor of 1888 is superior to that of 1889 becau~e, say in 1892, the first yields 400, whereas the second yields only 350, rather than conclude that they are equal, since, in a four years' process, the labor of 1888 yields 400, and that of 1889 yields also 400? That the fruition is deferred one year in the latter case is no disadvantage under the present hypothesis, for we have expressly eliminated from consideration any Qverprovision or underestimation of the future; it becomes a matter of entire indifference whether the 400 is obtained in 1892 or 1893.2 § 6 Thus far we have not altered any of Bohm-Bawerk's hypotheses; but if we allow ourselves to assume, as prac1 Ibid., p. 269.

3 Cf. Bortkiewicz, "Der KardinalfehIer der Bohm-Bawerkschen Zinstheorie," Jahrbuch fur Gesetzgebung,Verwaltung und Volkswirt 8chalt, 1906, pp. 71-73.

SEC. 6] BOHM-BAWERK'S THEORY 69 tically we ought to assume, that sometime the product decreases, no matter for how long" a production period, we shall have a more practical illustration of the fact that the labor available in 1888 and that available in 1889 stand on a perfect equality. Let us assume that Bohm-Bawerk's table of products holds true as far as he carries it, 1895, but that thereafter the numbers decrease, as in the next table. In this table are also given the products of a month's labor available in 1889 and other years:PRODUCT OF A MONTH'S LABOR AVAILABLE IN FOR THE ECONOMIC 1888 1889 1890 1891 1892 PERIOD 1888 100 - - ..- 1889 200 100 - - 1890 280 200 100 - 1891 350 280 200 100 1892 400 350 280 200 100 1893 440 400 350 280 200 1894 470 440 400 350 280 UNITS OF r PRODUCT 1895 500 470 440 400 350 1896 490 500 470 440 400 1897 480 490 500 470 440 1898 460 480 . 490 500 470 1899 430 460 480 490 500 1900 410 430 460 480 490 If, as before, we suspend the operation of the two "circumstances "(overprovision and underestimation of future) and employ for the ·"reduced utility" the constant number, 5, we have the following table for the" value"

columns:~ 70 THE RATE OF INTEREST A MONTH'S LABOR AVAILABLE IN [CHAP. IV YIELDS IN VALUE FOR 1888 1889 1890 1891 1892THE ECONOMIC PERIOD 1888 500 -- -- -- -1889 1000 500 -- -- 1890 1400 1000 500 -- 1891 1750 1400 1000 500 -1892 2000 1750 1400 1000 500 1893 2200 2000 1750 1400 1000 1894 2350 2200 2000 1750 1400 VALUE 1895 2500 2350 2200 2000 1750 1896 2450 2500 2350 2200 2000 1897 2400 2450 2500 2350 2200 1898 2300 2400 2450 2500 2350 1899 2150 2300 2400 2450 2500 1900 2050 2150 2300 2400 2450 This table of values is simply the previous table of prod ucts magnified fivefold, and is only given separately lest there be any possible room for doubt that the reasoning applies to "value" as well as to "product." We see clearly that the labor of 1888 will be invested in a seven-year productive process maturing in 1895, and having a present value, reckoned in 1888, of 2500 units of value; that the labor of 1889 will likewise be put into a seven-year pro ductive process, maturing in 1896, and having a present value in 1888of 2500. Similarly, the labor of each succeed ing year matures seven years later, but is worth to-day (1888) its full value of 2500.

Our conclusion is that if we eliminate the "other two circumstances" (relative underestimate of, and over provision for, the future), we eliminate entirely the supe riority of present over future goods, and the supposed third circumstance of "technical superiority" therefore turns out to be non-existent. The fact is that the only reason anyone can prefer SEC. 7] BOBM-BAWERK'S THEORY 71 the product of a month's labor invested to-day to the product of a month's labor invested next year is that to-day's investment will mature earlier than next year's in vestment. If a fruit tree is planted to-day which will bear fruit in four years, the labor available to-day for plant ing it is preferred rather than the same amount of labor available next year; because, if the planting is deferred until next 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 possi bility of a number of different investments. A month's labor to-day 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 productiv~ process that the so-called "technical superiority of present over future goods" derives all its force. The imagined "third circumstance" producing a superiority in present goods is only the first two circumstances in disguise. § 7 But our distinguished author 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: 1_ ". • • 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 wouldilnmediately 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 1 Ibid., pp. 269, 270.

\ 72 THE RATE OF INTEREST [CHAP. IV its service, and those instruments employed in more fruitful meth ods 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 circum stances 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 independ ent of any of the two already mentioned." The argument here is that if "the other two circum stances" which produce interest, namely, underestimate of the future and underendowment of the present, are tem porarily 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 these" other two circum( stances" and is not" independent." The essential fact is that its presence does not produce interest when the other two are absent. In short, the" technical superiority" of ~present goods is a delusion,! and the only way in which tIle ;existence of long processes of production acts on interest lis by overendowing the future and underendowing the ..~ present, thus creating a "scarcity value" of present goods. Since the foregoing criticism on B6hm-Bawerk's theory of the technical superiority of present over future goodswasfirst written, very similar criticism has been made by Adolphe .Landry 2 and by Ladislas von Bortkiewicz.3 So far as the writer knows, Landry is the first to have set forth clearly and definitely the fallacy contained in Bohm1 Of. Bortkiewicz, "Der Kardinalfehler der Bohm-Bawerkschen Zinstheorie," Jahrbuch tur Gesetzgebung, Verwaltung und Volkswirt 8chajt, 1906, pp. 61-90.

2 L'Interet du Capital. s Loc. cit., pp. 61-00.

SEC. 7] BOHM-BAWERK'S THEORY 73 Bawerk's theory of it technical superiority." Every reader of Bohm-Bawerk, however, must have felt dissatisfied with his explanations; and sundry expressions of Bohm Bawerk's suggest that he was dissatisfied himself. His theory of technical superiority stands out as incongruous with the rest of his work, and is more in keeping with the productivity theories which he has done so much to demolish. It would seem as though, like a successful warrior, he had been haunted by the ghosts of his slain enemies. As Professor Fetter has said: 1 "It has been a surprise to many students of Bohm-Bawerk to find that he has presented a theory, the most prominent feature of which is the technical productiveness of roundabout processes. His criticism of the productivity theories of interest has been of such a nature as to lead to the belief that he utterly rejected them. But evidently such is not the case. Critics have pretty generally agreed that the theory of the roundabout process is a productivity theory of interest."

It is, therefore, somewhat strange to find Bohm-Bawerk strenuously insisting on the importance of his. (( technical" theory. He writes: 2_ "The statement of how the productivity of capital works into and together with the other two grounds of the higher valuation of present goods, I consider one of the most difficult points in the theory of interest, and, at the same time, the one which must decide the fate of that theory. It is just at this point that we discover the chief weakness in Jevons's otherwise suggestive work. None of the groups of phenomena concerned escaped his keen observa tion; what did escape him was the way in which they work into one another." ' And, referring to Launhardt, he says: 3 "But, on the other hand, it is a sensible omission that the differ ence between the values of present and future goods is traced 1 "The 'Roundabout Process' in the Interest Theory," by Frank A. Fetter, Quarterly Journal of Economics, Vol. XVII, November, 1902.

2 The Positive Theory of Capital, p. 277, footnote. S Ibid., p. 278.

'74 THE RATE OF INTEREST [CHAP. IV exclusively to this factor, and that the much more important factor that cooperates with it, that of the greater productiveness, does not get even the scanty consideration it gets from Jevons." Before leaving the subject, justice requires that we should dissent from Bohm-Bawerk's opinion that he has made no substantial contribution to the theory of interest aside from his particular U technical" feature. His work in historical criticism is a model both for the historian and for the critical analyst, and his enunciation of the agio theory, while partially anticipated by Jevons, Sax, and Launhardt, was so much more clearly and perfectly worked out that it gains an almost independent form in his hands. The only writer who has equaled B6hm-Bawerk was one with whom the latter was not acquainted, namely, John Rae. His valuable contribution to the subject was, through a curious chain of circumstances, lost to two generations of readers, and has only recently been revived and made accessible through Professor Mixter.

If we cast out from the agio theory Bohm-Bawerk's special feature, his alleged" technical superiority of present goods," the theory which remains is believed to be correct. It is, however, still incomplete, for there remains the gap which B6hm-Bawerk sought to fill, - the formulation of the exact manner in which the "technique" or actual con ditions of production enter into the determination of interest. In Part III we shall attempt to supply this deficiency.