The Positive Theory of Capital

Eugen v. Böhm-Bawerk, from the Warren J. Samuels Portrait Collection
Böhm-Bawerk, Eugen v.
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William A. Smart, trans.
First Pub. Date
London: Macmillan and Co.
Pub. Date
39 of 55

Book V, Chapter V

Co-operation of the Three Factors


To put together the results at which we have arrived thus far. We have seen that there are three factors, each of which, independently of the other, is adequate to account for a difference in value between present and future goods in favour of the former. These three factors are: The difference in the circumstances of provision between present and future; the underestimate, due to perspective, of future advantages and future goods; and, finally, the greater fruitfulness of lengthy methods of production. The question now is:—how do these factors, working simultaneously, affect each other?


About the two first factors we know already: their effects are cumulative. In the case of a man badly provided for in the present, if the marginal utility of a present good were 100, and its true marginal utility in a future period only 80, the present good would be valued, relatively to the future, in the ratio of 100 to 80, if no other influence intervened. But if there is, besides, a perspective diminution of the true future marginal utility, say by one-eighth, the marginal utility would be put at 70 instead of 80, and the superiority of the present good to the future would be in the ratio of 100 to 70.


It is essentially different with the co-operation of the third factor. True, it also tends to strengthen the action of the other factors, but it does so alternatively, not cumulatively; that is to say, that factor which confers the greater advantage on present goods always stands out from the other as the active agent. Say, for example, that the first factor (the circumstances of provision), together with the second factor (that of perspective), taken cumulatively, would give present goods an advantage of 30%, while the factor of productivity would give an advantage of 25%, we should not get a total advantage of 55%, but of 30%, the advantage being based on the stronger factors.


The matter stands thus. The superiority of present goods, as making roundabout and more fruitful ways of production possible, cannot be increased by the perspective undervaluation of future goods, because the utility got from lengthy processes is itself a future utility, to which the perspective undervaluation applies as much as it applies to the future goods with which the present goods are compared. Say that, by employing a month's labour now, in 1888, in a one year's process, I can make, for 1889, a product of 200 units, and, by employing a month's labour of 1889, I can make for that same year—on account of the short and unproductive method—a product of 100 units only, it will be a reason for my valuing the present month of labour at double the next year's month. If, now, there comes in a ten per cent undervaluation of next year's utility, I shall, of course, value the next year's 100 units at 90 present units only; but, for exactly the same reason, I shall value the 200 units at 180 present units only; and the ratio of valuation, two to one, remains exactly as if the perspective undervaluation had never come into play at all.


As little can the third factor be strengthened by the first factor, namely, the consideration of a greater present want. For, evidently, employing a good to a great future productive utility, and employing it to satisfy an immediate pressing want, are mutually exclusive employments; and it is clear that a good, which can only be employed in the one way or the other, cannot obtain a cumulative advantage from the two together.


But these two factors do work into each other's hands in the following way. Present goods may be used to meet present wants, or they may be invested in production for the future. These are the two possible employments to which each individual may put his present goods. According to principles with which we are familiar, the stock of goods will be guided into these employments in such a way, that the most important chances of using the goods are utilised first, the next important second, and so on down the scale. Here, however, it is to be noted that the employments in producing for the future, as standing over against the employments in the satisfaction of immediate wants, must submit to the perspective diminution with which we are familiar. Say, for instance, that a man's particular circumstances are such that he estimates a utility, falling due in the following year, at 10% less than an equally great present utility; then a future utility of 110 becomes equal to a present utility of 100, and, on that account, when there comes to be a choice between employments, the future utility of 110 may be postponed to a present utility of 102. The last employment, then, which, on these principles, is still supplied from the stock of goods, indicates, as we know, the marginal utility, and, at the same time, the value of the unit of goods.


Now the following cases may occur. First, the individual may be badly off in the present. In that case the pressing wants of the moment will, by themselves, absorb the small stock of present goods, and, on the ground of this bad provision in the present, these goods will obtain a high value and a preference over future goods. The needy man prefers present goods because he must consume them in the present. The opportunities of employing the goods for productive purposes in the future remain in this case—since the poverty-stricken present, naturally, cannot afford any goods for purposes beyond itself—out of court as economically impossible, and, of course, without any influence on the value, or preferable value, of present goods.


Or, second, the individual may be equally well provided as regards both present and future, but may have less forethought. This case leads to a similar result. Before, it was urgent want that prevented portions of the stock of goods from being withdrawn from the service and enjoyment of the present, and invested in future production: now, it is want of thought for the future: and this want of thought confers, at the same time, on the present enjoyment, and on the present goods which minister to it, a preference over future. The spendthrift, greedy of pleasure, values present goods more highly than future, because he wishes to enjoy them in the present.—If bad provision goes along with small foresight, the two effects, as we have seen, are cumulative.


Or, third, the individual is well provided, and takes due thought for the future. In this case, of course, the two former sanctions of the preference do not come into play at all, or scarcely at all. In this case, beyond the satisfying of the immediate wants, the other course is economically open,—of investing a portion of his present goods in production for the future: thereby their economic centre of gravity, their marginal utility, and the formation of their value, are shifted to a sphere in which present goods enjoy a preference in value under the third sanction, that of their greater productiveness. A moderately rich and prudent man who has £10,000, must not, and will not consume his £10,000 in the present, but will, in any case, save for the service of the future. But if any one were to make him the proposal, to exchange his £10,000 of present money for £10,000 of future money, he would be fully justified in declining the transaction; as, with £10,000 (now) he can provide more effectually and richly for the future than with £10,000 at a future period.


But, finally, there is still a fourth case conceivable: an individual may be so badly off in the present, or have so little thought for the future, that, on those two accounts, he values present goods more highly than future. At the same time, however, he is tempted by business which promises him so good a return in the future that he stints himself still further in his present provision, and engages in the business. Here, after the analogy of the case worked out on p. 165, the available sums of goods are directed, successively, into the most important employments of the two spheres taken together, and the competition of these future employments has for result that the satisfaction of present wants is broken off at a higher point or level than it would otherwise be. This must, in the end, raise the value of present goods, and indirectly increase their superiority over future.*27


Thus the various sanctions come alternatively into play. Where the first two are active the third is suspended: but where the first two are not active, or not sufficiently active, there comes in the action of the third. One can easily understand how very directly this circumstance is calculated to give the phenomenon of the higher valuations of present goods an almost universal validity. The needy and the careless value present goods more highly because they urgently require them in the present, or only think about the present: the well-off and the saving value them because they can accomplish more with them in the future: and thus, in the long-run, every one, whatever his economical position, and whatever his economical temperament, has some ground for valuing present goods more highly than future. And, further, it is easy to understand how much the universal emergence of subjective differences in valuation must favour the extension of this phenomenon to the sphere of objective exchange value and price. If the third factor were to act cumulatively with the two first there would, indeed, be many who would value present goods at an extravagant rate, but it is not certain that there would not be as many, perhaps an overwhelming majority, who would have no preference for present goods, and it is doubtful how, in this case, the resultant of exchange value would turn out. But as the third factor is alternative in its action, it levels up, as it were, the depressions instead of exaggerating individual heights; thus it brings about a general raising of subjective valuations; and this is necessarily connected with a raising of the average line, the resultant exchange value.*28


Here we come to our last duty in this book: to show how the ratio that obtains between present and future goods in subjective valuations is transferred to their objective exchange value.


In the case of the single individual, extremely various subjective valuations will be formed, according as the one or the other of the above-mentioned factors is stronger or weaker. These encounter each other on the market where present goods are exchanged against future. There are many such markets and they take many different forms. In the next book we shall more exactly examine their constitution. In the meantime we must be content to examine the method in which prices are formed in its most general and typical outlines. Indeed the formation of price here takes the same course as it does elsewhere. The divergence of the subjective valuations which encounter each other on the market makes possible, economically, the exchange of property between the two parties.*29 Those who, on any subjective grounds, put a relatively high value on present goods, appear as buyers of present against future commodities; those who put a relatively low value,*30 as sellers: and the market price will be settled between the subjective valuations of the last competitors who actually exchange, and the first competitors who are shut out, or, as we have put it, between the valuations of the two marginal pairs. We may represent the position of the market by the following scheme:—

Intending Buyers. Present goods in units. Next year's goods in units. Intending Sellers. Present goods in units. Next year's goods in units.

A1 values 100 = 300 B1 values 100 = 99
A2 " 200 B2 " 100
A3 " 180 B3 " 101
A4 " 120 B4 " 102
A5 " 110 B5 " 103
A6 " 108 B6 " 105
A7 " 107 B7 " 106

A8 " 106 B8 " 107
A9 " 104 B9 " 108
A10 " 102 B10 " 110


In the circumstances of the market which this scheme represents, A7 and B7 form the upper marginal pair, A8 and B8 the lower. The market price for 100 present units of goods will be fixed between 106 and 107, say at 106½ next year's units, and this determines an agio of 6½% in favour of present goods.


Once a market price of this kind for present goods has been established, it exerts a reflex levelling influence on the subjective valuations which were originally so strongly divergent. Even those who, from personal circumstances, would value future goods only a little under, or perhaps at equal terms with, present goods, now value present goods according to the higher exchange value which the position of the market lends to them. This is the reason, and the only reason, why, in practical life, scarcely any one would be willing to exchange present goods against an exactly equal sum of future ones. There are plenty of people whose circumstances of want and provision for want are of such a kind, that the subjective use value of present and future goods to them stands almost equal. But the general position of the market is, almost invariably, so strongly in favour of present goods, that it assures them a preference in exchange value, of which, naturally, every one takes advantage.


Developed market exchange, however, brings with it a levelling effect from another side; that is to say, it brings the amount of agio in favour of present goods, as against future goods which fall due at variously remote points of time, into one normal ratio with the length of the elapsing time. It might easily be the case that the causes which tend to the undervaluation of future goods might chance to be quite disproportionately effective on goods belonging to different periods of time. Indeed, in the very nature of several of those causes (for instance, the consideration of the shortness of human life) they would scarcely obtain at all as against goods of the near future, while, as against goods of remote periods, they would obtain strongly and irregularly. In itself, therefore, it might be quite possible that, while 100 present units of goods, as against 100 units of next year's goods, obtained, in the market, an agio of 5 units only, as against goods of the next year they might obtain an agio of more than twice that, say 20, and, as against the third year's goods, perhaps an agio of 40. But such disproportionate prices for goods of different periods of remoteness could not long hold. By a kind of time arbitrage they would very soon be brought into an equal ratio. If, for instance, the various market prices mentioned above were found quoted at one given moment, speculators would immediately appear on the scene, who would sell present goods against two years' goods, cover the purchase by buying present against next year's goods, and arrange for paying the latter a year later by a second purchase of present against next year's goods. The business would work out thus. In 1888 the speculator buys 1000 present units for 1050 units of the year 1889, and sells them at the same time for 1200 of the year 1890. In 1889 be has to deliver 1050 units, and he gets them by buying, again with a agio of 5%, the then present (1889) goods for the then next year's (1890) goods. For the 1050 units he requires to deliver he must thus give 1102½ units of 1890. But, from the first transaction, he then receives 1200 of these very (1890) units. He has thus, on the whole business, a utility of about 100 units. Such arbitrage transactions must evidently bring the prices obtainable for goods of various future years to a level. The speculative demand for the much undervalued two years' goods must raise their price; the supply of next year's goods must depress their price; till such time as the agio is brought directly into proportion with the length of the time. When this happens—say, for example, that the agio has become equalised at 5% per year, it may hold on at that rate undisturbed. For then it is equally remunerative to exchange present goods against next year's goods for three years successively, or to exchange present goods directly against three years' goods, and the arbitrage we have just sketched has no further occasion to interfere in the formation of price.


Thus we may accept the following as positive result of the present book.


The relation between want and provision for want in present and future, the undervaluation of future pleasures and pains, and the technical advantage residing in present goods, have the effect that, to the overwhelming majority of men, the subjective use value of present goods is higher than that of similar future goods. From this relation of subjective valuations there follows, in the market generally, a higher objective exchange value and market price for present goods, and this, reflecting back on present goods, gives them a higher subjective (exchange) value even among those whose personal circumstances happen to be such that the goods would not naturally have any preference in subjective use value. Finally, the levelling tendencies of the market bring the reduced value of future goods into a regular proportion to their remoteness in time. In the economic community, then, we find universally that future goods have a less value, both subjective and objective, corresponding to the degree of their remoteness in time.

Notes for this chapter

Suppose, e.g., that a man has 6 units of goods, say 6 five-pound notes, at his disposal. There are present groups of wants, which these notes could supply, and their importance is indicated by the figures 10, 9, 8, 7, 6, 5. Now there appear opportunities of employing these in business transactions which will not yield any result for a year, but are so profitable that, even after deducting the necessary dis-agio on account of the year's delay, they are equal to a present utility of 7. The following will evidently be the disposition of the notes. Four of them will go to the present wants which bear the utility 10, 9, 8, 7, the remaining two to the future employments which, likewise, show the (reduced) figure 7. The marginal utility which attaches to the present five-pound note is, therefore, 7, while, without the competition of the profitable future employments, it would have been only 5.
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 observation; what did escape him was the way in which they work into one another. Consequently his work remains an eclectic piece of patchwork instead of being welded into an organic theory. He gathers together quite correctly all the primary phenomena required for the explanation. But he does not find the common channel through which they all work together to the one common end, and so he explains it differently from each different point of view, with a result that is eclectic and self-contradictory. After a most promising beginning he quite loses sight of the element of the different valuations put upon present and future wants, and for the rest gives a double explanation, full of contradictions, and scarcely rising much above the level of the old classical economy,—part of it taken from the Abstinence, part from the Productivity theory. (See my Capital and Interest, p. 400.) The not very independent treatment which the subject has received from Sax is in one respect better, while in another it is even more incomplete than that of Jevons. It shows an advance to find the element of the undervaluation of future wants generally interwoven into the explanation of interest. (See also on this point Launhardt, Mathematische Begründung der Volkswirthschaftslehre, Leipsic, 1885, § 2, and again my Capital and Interest, pp. 344, 427.) But, on the other hand, it is a sensible omission that the difference between the values of present and future goods is traced exclusively to this factor, and that the much more important factor that co-operates with it, that of the greater productiveness, does not get even the scanty consideration it gets from Jevons. (Sax, Grundlegung, p. 314.)
See above, p. 195.
For reasons with which we are now familiar almost all the competitors, whether buyers or sellers, will value present goods, absolutely, above future. But the valuation will be higher on the part of the buyers, as a class, than on the part of the sellers.

End of Notes

39 of 55

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