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
52 of 55

Book VII, Chapter III

The Rate in Market Transactions—(continued)


But our task is not yet finished. Following the same lines as we took in developing the general law of the price of goods,*21 we must attempt to lay down the concrete determinants which decide the degree of productiveness of the last extension, and from our knowledge of these we must, in particular, try to get an explanation of the variations to which the interest rate is subject in practical life,—sometimes rising, sometimes falling, but with a constant tendency in the latter direction, over the whole field of economical development in historical times. This analysis too will give us a welcome opportunity of verifying our abstract theory by experience. If we find that our theory, starting with certain assumed conditions of fact, leads us, of internal necessity, to expect just that movement of interest which, in the experience of practical life and history, we see actually and always taking place when these conditions are realised, we shall be justified in taking it is a strong guarantee that our theory, although it uses such abstract machinery in the stating, is no vain imagining, but a theory obtained from the study of practical life. Moreover in what follows I shall be in much less marked opposition to old doctrines than I have been in the foregoing chapters. For certain connections between the rate of interest on the one side, and definite facts on the other, are so distinctly and unquestionably given by experience, that it was impossible for the adherents of any interest theory, however erroneous, to overlook them; and, however different the theoretical points from which they may have started, they find themselves at one in recognising these.*22 All the same I venture to hope that what follows will give more accuracy and definiteness, as well as a new and more adequate explanation, to many a proposition long accredited by experience.


Following the line of inquiry already pursued, I shall try to investigate the concrete determinants of the rate of interest, and the manner of their working, in such a way that we can successively vary the individual assumptions in our illustrative scheme, and then see what result the variation gives us as regards the formation of the interest rate. Let us look first, then, at the influence of the amount of the national subsistence fund.


Assume that, other circumstances remaining unchanged, the available subsistence fund amounts, not to £1500,000,000 but to £2400,000,000. The repetition of the same calculation as made above leads us to the conclusion that the equilibrium of the market cannot now be attained otherwise than by an eight years' production period, a £60 rate of wages, and a corresponding interest rate of 3.54%. We may check this result from Table II. on p. 389, which is calculated on the £60 rate of wage. It shows that, where the rate of wages is £60—the rate of productivity being given—the undertaker finds an eight years' production period the most profitable; that 4.16 labourers may be employed by £1000 of capital, and, therefore, 10,000,000 of labourers by £2400,000,000; and, finally, that this (relatively) most profitable method of production yields 3.54% interest on the undertaker's capital.


As compared with the earlier ones this rate shows a considerable decline, the reason of which is very easily explained. When the subsistence fund is increased men can only keep it fully employed by entering on further extensions of the production period, which extensions are accompanied by steadily decreasing surplus returns. Indeed the surplus return of the last extension of production economically possible (from seven to eight years) is only 30s., and the surplus return of the first non-permissible extension (from eight to nine years) is only 20s. And since the rise of the year's wage from £50 to £60 requires, for the one year's extension, not a capital of £25, but a capital of £30 per man, the marginal limits for the interest rate are 30s. or £30 (i.e. 5%) as upper limit, and 20s. on £30 (i.e. 3 1/3%) as lower limit. As a fact the agio of 3.54%, which we found empirically, falls between these determining marginal limits.*23

WAGE £42.
Production Period in years. Annual Product. Annual profit per labourer. Number of employed. Total annual profit on the £1000.
1 £35 0 — £7 0 47.62 Loss
2 45 0 3 0 23.81 £71.43
3 53 0 11 0 15.87 174.57
4 58 0 16 0 11.905 190.48
5 62 0 20 0 9.524 190.48
6 65 0 23 0 7.93 182.39
7 67 0 25 0 6.8 170
8 68 10 26 10 5.95 157.675
9 69 10 27 10 5.29 145.475
10 70 0 28 0 4.76 133.28


Assume, conversely, that the available subsistence fund amounts only to £1000,000,000, the equilibrium, as will be seen from Table IV., is attained at a rate of wage of £42, and an agio of 19.048%. This is accompanied by some interesting circumstances which will repay a moment's attention, as they may be often enough realised in practical life, although not seen there in their full abstract purity. At a prevailing wage of £42, as it happens, two different production periods of four and five years respectively are equally profitable, and pay 19.048% interest on the capital invested in them. The result of this is that neither of them economically shuts out the other; both may be adopted simultaneously; indeed, not only may, but must, to keep the equilibrium. If the four years' period alone were adopted, only £840,000,000 of capital would find employment at a wage of £42.*24 If, again, the five years' period were exclusively adopted, the existing capital would employ only 9,524,000 labourers;*25 and in either case the unemployed elements would, as we know, disturb the equilibrium by overbidding and underbidding. The equilibrium can only be found if the two equally profitable methods of production are engaged in simultaneously, when 7,619,000 labourers will be employed by a capital of £800,000,000 in five years' production and 2,381,000 labourers by a capital of £200,000,000 in four years' production.


And, in virtue of this peculiarity, the latitude allowed in fixing the agio by the valuations of the marginal pair will be much more sharply limited in this than in the former examples. The last economically permissible extension of production is from four to five years, which brings in a surplus return of £4, that being a surplus on £21, half the year's wage. But, as it happens, the first excluded extension of production is also that from four to five years, inasmuch as—as shown above—the existing capital allows only a portion of the producers to take the five years' production period. Consequently the surplus return of the first excluded process—that which forms the lower limit of the interest—is also fixed at £4. The upper and lower limit, therefore, coincide, and the interest must be determined strictly at the rate of £4 on £21; that is, at 19.048%, just as actually shown in our former scheme.*26


Now the agio here is considerably higher than in the former cases. And our theory again explains it quite simply. The reason is that the diminished subsistence fund allows only of comparatively short processes on the average, and consequently the "last extension of production"—that which decides the interest rate—falls in a sphere where any extension of the production periods is attended by very considerable surplus returns.


So much for the effect of an alteration in the amount of the subsistence fund: we have still to follow the effect of an alteration in number of workers. Any detailed calculation here, however, should not be necessary. It does not require much consideration to see that a change in the number of labourers must exert its influence on the rate of interest in exactly the opposite direction. Whether, for example, the number of labourers remains steady at 10,000,000, and the subsistence fund contracts from £1500,000,000 to £1000,000,000; or whether the subsistence fund remains at £1500,000,000 and the labourers increase from 10,000,000 to 1500,000,000;—in either case the subsistence fund is just sufficient to employ the existing labourers partly in four, partly in five years periods, while the "last" and decisive surplus return is £4 on £21, and the resulting rate 19.048%. And it is as clear that, if subsistence and labourers vary simultaneously in the same direction—say that both increase—the variations will weaken the efficiency of both, and the final movement of the rate will follow that direction taken by the stronger of the varying factors; and that, on the other hand, if both factors vary not only in the same direction but also in the same ratio, the rate will remain unchanged. Suppose, for instance, that the number of workers and the amount of the subsistence fund both double, it is evident that the doubled fund will be sufficient to provide for the doubled numbers over the same production periods as before, and that the "last" and decisive surplus, and with it the interest rate, will remain unchanged. If, again, the fund were to double while the numbers increased only by a half, it is obvious that, on the average, a longer production period could be adopted than formerly; in which case the decisive "last" surplus return would be reduced to a lower point on the descending scale of surpluses, and the interest rate would also fall.


Finally, we might inquire, on the same lines, what will be the effect of an alteration in a third factor, the state of productivity, assuming that subsistence fund and number of labourers remain constant. Here also we may spare ourselves any detailed tabular statement. It does not require any exact calculation to prove that if, other circumstances remaining unchanged, the scale of surplus returns constantly shows higher figures, the surplus return yielded by the last extension of production that is economically permissible—that which decides the interest rate—must be higher, and vice versâ. Say that subsistence fund and number of labourers stand in such a relation as to permit of an average five years' production period, the interest will be higher if the extension of the production period from four to five years is attended by a surplus return of £6 as against £4, or of £4 against £l.


We have, then, over the sphere of our investigations so far, to record three elements or factors which act as decisive determinants of the rate of interest: the Amount of the rational subsistence fund, the Number of workers provided for by it, and the Degree of productivity in extending production periods. And the way in which these three factors affect the rate may be put as follows:—


In a community interest will be high in proportion as the national subsistence fund is low, as the number of labourers employed by the same is great, and as the surplus returns connected with any further extension of the production period continue high. Conversely, interest will be low the greater the subsistence fund, the fewer the labourers, and the quicker the fall of the surplus returns.


This is the way in which the interest rate should be formed, and the way in which it should alter, if our theory is correct. How is it in actual life?—Exactly as our formula predicts, and thus experience gives that formula the most complete verification. For, first, it is one of the best accredited and recognised facts of economic history that the increase of the subsistence fund, or, to use an expression not quite so accurate but yet roughly significant, the increase of the community's capital, has a tendency to depress the rate of interest. Second, it is no less familiar and self-evident that here we do not speak of the absolute amount of the national capital, but of the relation between that capital and the numbers of the population: in other words, we mean that an increase of population, without a simultaneous increase of capital, has a tendency to raise the interest rate. And, thirdly, it is also an acknowledged empirical fact that the discovery of new and more productive methods of production, outlets, business opportunities, etc., which conduce to check the fall of surplus returns, tend to raise the rate of interest, while the closing of former opportunities of production or sale, or other occurrences which end in a reduction of the previous degree of productiveness, tend to lower the interest rate. We find, therefore, that all those factors to which, on the lines of our former inquiry, we were forced to ascribe a decisive influence on the interest rate, do, as a fact, possess and exert that influence.


And now it is time to give, one by one, the features and forms of actual life to our abstract scheme.

Notes for this chapter

See above, p. 218.
As, e.g., in the familiar proposition that an increase of the national capital tends to reduce the interest rate. In the points here raised, I am in very thorough agreement with Walras, who, like Thünen, starts from a theory of interest which, in my opinion, is essentially wrong, and yet is able to arrive at many details correctly and with fine scientific feeling. The coming second edition of his Élements,d'Économie Politique Pure, the proof sheets of which, by the kindness of the author, I was permitted to see, contains many forcible and noteworthy passages on this subject. I can only regret that they are expressed in the troublesome and difficult language of mathematics. The conception of political economy as pre-eminently a mathematical science is one on which, notwithstanding what the distinguished economist has recently said (p. 191 in new edition), I fear we shall never be able to agree.
In this case it falls considerably nearer the under limit on account of the relative abundance of the capital, which would be almost sufficient for general adoption of a nine years' production period.
That is to say, with £1000 capital, as the table shows, 11.905 labourers could be employed in four years' production. To employ all the existing ten million labourers, therefore, a capital is required which follows this proportion

1000 : x = 11.905 : 10,000,000.

The solution of this proportion gives

x = 10,000,000,000 : 11.905 = 840,000,000.

With £1000 capital 9.524 labourers are employed in five years' production; with 1000 millions of capital, therefore, 9.524 millions of labourers.
I may call attention to the fact that now we arrive at the figure 19.048 by a quite different way, by quite different lines of thought, and by quite different calculations, than in the above table. There we sought and found empirically the figures of wage and interest at which, under the given assumptions, the equilibrium of Supply and Demand may be established. Now, applying the law of the marginal pair to the concrete case, we have deduced that the interest must lie between the surplus returns of the last extension of production still permissible, and the first excluded, and arrived thereby exactly at the same figure 19.048. In the former case we get our figures immediately by multiplication of the number employed by the gain made per labourer (11.905 × 16 and 9.524 × 20). Here we get the same figure by dividing the dependent last surplus product by half the wage (4 : 21). I may, therefore, take this agreement as a proof that our deductive reasoning correctly expressed the results empirically established.—Here also it may be the most suitable place to point out the error into which Jevons fell as regards this question. Jevons recognises perfectly correctly that the "last surplus return" decides the interest rate; but, owing to an oversight in principle, he makes the mistake of fixing on that other amount to which this surplus return must be put in relation, and deduces the rate of interest, not from the relation of the last surplus return to the sum of subsistence which allows the last extension of production, but from the quite different relation in which that surplus return stands to the value of the whole product which might have been obtained without the last extension of production. "The interest of capital is the rate of increase of the produce divided by the whole produce" (Pol. Econ. second edition, p. 267). The seriousness of this oversight will be best seen from a concrete example, which, for the sake of easier comprehension, I shall take from the case of isolated exchange spoken of above (p. 378). Remembering what was then said, let us suppose the case of an undertaker whose means would allow him to carry through an eight years' production period with a yearly return of £68:10s., and who, by a loan of £30, which would guarantee him subsistence for a ninth year, is put in a position to go on to a nine years' production period with a return of £69:10s., or a surplus return of 20s. According to Jevons this should allow an interest rate of £1 on £68:10s., or 1.46%. But evidently there is no ground whatever why the suitor for the loan should be ready to offer £1 per year and no more as interest for a sum of £68:10s. It is not the amount of £68:10s., but that of £30, whose acquisition makes the extension of production possible, calls forth the surplus return of £1, and, consequently, maybe paid, in the most extreme case, by £l, but, on the assumption noted on p. 378, note 1, by as much as £2 per year. As a fact, then, in the case of this illustration, it is not, as Jevons assumed, an interest of £1 on £68:10s., or 1.46%, that is economically possible, but an interest of £1 on £30, or 3 1/3%, indeed, on the above assumption, a rate of £1 on £15, or 6 2/3%. A certain very modest kernel of truth may be found, all the same, in Jevons's t error; but to point it out I should require to go still further afield into discussions in which I could not assume that the majority of many readers would find sufficient interest.

End of Notes

52 of 55

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