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.
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Book VII, Chapter II

The Rate in Market Transactions


The character of the market in which present goods are exchanged against future goods has already been described.*6 We now know the people who appear in that market as buyers and sellers. We know that the supply of present goods is represented by the community's current stock of wealth—with certain unimportant exceptions—and that the demand for them comes (1) from the suitors for productive credit who wish to equip themselves for their own work in production, (2) from the suitors for wage-paid labour, and (3) from the suitors for consumption credit. To these three categories we may add, under certain reservations, the maintenance of the landowners. Finally, it will be remembered that the resultant market price must, as a rule, be in favour of present goods, and must lead to an agio on the same. What we have now to do is to group together the causes which determine the height of this agio in one adequate and typical picture.


If we were to attempt all at once to draw a picture like this, covering, as it does, the whole area of the varied influences that cross and intersect each other on the market, we should meet with great, indeed insuperable difficulties, in the way of statement. I shall, therefore, act on the principle, divide et impera, and first consider how the price is determined under the assumption that, confronting the supply of present goods, there is one single branch of demand, though, in present circumstances, by far the most important branch, viz. the demand of the Wage-Earners. Once we have drawn in broad clear lines the most important and difficult part of the whole picture, it will be relatively easy to define the kind and measure of the share which all the remaining market factors have in forming the resultant, and so gradually to make the picture true to the full complexity of practical life. For good reasons I also retain provisionally the former assumption, that the whole supply and the whole demand for present goods meet in one single market embracing the entire community. And, finally, we shall suppose meanwhile that all branches of production show the same productiveness, and also the same increment of productiveness on each extension of the production period: that is to say, we shall assume an identical scale of surplus returns.


Suppose, then, that in our community the stock of wealth in the market, as supply, amounts to £1500,000,000, and that there are 10,000,000 of wage-earners. Following the scheme on p. 378, the annual product of each worker increases in all branches of production, in proportion to the length of the production period, from £35 (in a one year's process*7) to £70 (in a ten years' process). The question is; in these circumstances of the market how high will rise the agio on present goods?


It is quite certain, as we have already explained, that the agio will settle at that level where supply and demand exactly balance each other, and this lies between the subjective valuations of the last pair who actually exchange. But the fixing of these valuations here encounters a quite exceptional difficulty, and one which does not occur in any other exchange transaction, but has its basis in a special peculiarity of the commodity "labour." Every other commodity, that is to say, has a predetermined subjective value to the one who wishes to buy it. Labour has not, and for this reason. It is valued according to its prospective product, while the prospective product varies according as that labour is invested in a short or in a long production process. We said above that, in the subjective circumstances of the capitalist, a sum of present goods was, as a rule, worth as much as the same sum of future goods. The capitalist will, therefore, count the value of labour equal to just as many present shillings as it will bring him in in the future. But, according as this labour is invested in a short or a roundabout process, it may bring him in £35 or £58 or £70. At which of these figures is the capitalist to value it?


It may be answered: According to the product aimed at in entering upon the method of production which is, economically, the most reasonable. He will, therefore, value the year's labour at £35 if, on reasonable grounds, he meditates adopting a one year's process; at £70 if he considers a ten years' period the most suitable. This would be very well if only it was certain beforehand what period was the most suitable for the undertaker. But this is not certain: on the contrary, the length of the process is itself dependent on the rate of wage fixed as resultant price on the labour market. If the wage, for instance, stands at £25, a one year's process is the most favourable for the undertaker. At £25 he gains £10 in the year—or, to put it exactly, in the six months, since, on the average, the advance extends over only six months;*8 that is, 80% per annum. In a ten years' process for the £25 in wages he gets £70, and the surplus return of £45 is, absolutely, much greater, but, when divided as profit over an average of five years,*9 gives only £9 for one year, or a profit of 36%. On the other hand, if the year's wage is £50, it is quite clear that it would be as absurd to choose a one year's process, with its product of £35, as it was most reasonable in the previous circumstances, and only those longer production periods which show an annual product over £50 could be thought of.


The matter, therefore, stands as follows. Elsewhere, in the case of other commodities, the employment for which the buyers wish to acquire them is already determined. It is the fixed point,—the thing which first of all helps to determine the price offered by the buyers, and then through that the resultant market price. Here, in the case of the commodity Labour on the contrary, the employment is an undetermined amount, an x, which is first determined by the resultant price. In these circumstances it is clear that the fixed point of the price transactions must be got somewhat differently from the ordinary way; not, of course, according to different principles or laws, but with a certain casuistical modification in detail which we have now to examine.*10


In place of the fixed point, which is not available because the employment of the labour itself is not fixed, we find a substitute in the fact that another amount, usually indetermined, is here fixed, viz. the quantities sold. It may be taken as certain that all the labour offered, like the whole sum of present goods offered, finds a market. The certainty of this is based on a peculiar circumstance. Exactly as, in the science of money, it is a familiar dogma that, in the long-run, any sum of money, be it great or small, is sufficient to do the work of circulation in a community, so is it true that any sum of present goods, be it great or small, is sufficient to buy up the whole supply of wage labour that exists in the community, and to pay its wages. All that requires to be done is to contract or extend the production period. If there are ten million wage workers, and fifteen hundred millions of capital, this stock is just sufficient to pay the ten million workers £30 a year each over a ten years' production process.*11 If there are only five hundred millions of capital no labourers need go idle on that account: only, of course, they cannot have their maintenance advanced them for a ten years' process, but (at the same wage of £30) only for a three and a third years' process, and the average duration of the production period must be curtailed accordingly. Suppose there are only fifty millions of capital, all the labour could still be bought, but now only for a four months' process, and it must be secured, by a further shortening of the production period, that the scanty amount of present goods is renewed after every short period by the accession of fresh returns.


It is, therefore, always possible for the existing stock of wealth to buy all the labour, and there are certain reasons in this case that work very strongly towards always making the possible into the actual. Between capitalists and labourers the economic conditions are—with very few exceptions—extremely favourable to the effecting of exchange. The labourers urgently need present goods, and cannot, or can scarcely turn their own labour to any account; they will, therefore, to a man rather sell their labour cheaply than not sell it at all. But very much the same is true of the capitalists. In their peculiar circumstances of want and provision for want, their present goods—which they, in any case, would lay up against the future—are not worth more to them than a similar sum of future goods. They will, therefore, prefer any purchase of labour where there is an agio, however little it may be, rather than let their capital lie dead; and the consequence is that all capital, like all labour, actually comes to a sale. As a fact we see that, in all economic communities, although the quantitative relations between wealth and number of wage-earners are extremely various, these two amounts exactly buy up each other. There are everywhere a few labourers who have no work, and a few capitals which are not employed, but this is, of course, not in contradiction to what has been said. I need scarcely point out that the presence of such unemployed is never traceable to the purchasing power of capital being insufficient to the whole number of the labourers—in a poorer country, indeed, a capital of half the amount would have to pay the same number of labourers, and actually does pay them—but always to certain frictional and temporary disturbances of organisation, such as are inevitable in a mechanism so complicated as the industrial division of labour in a great country.


We may, therefore, assume it as certain that the whole supply of labour, and the whole supply of present goods, come to mutual exchange. In this fact the length of the production period, and thus the amount of product which the undertaker may obtain through the labour he buys, obtains a certain definiteness. That is to say, we must, in any case, assume such a period of production that, during its continuance, the entire disposable fund of subsistence is required for, and is sufficient to pay for, the entire quantity of labour offering itself. If the period were to be shorter than this, some capital would remain unemployed; if longer, all the workers could not be provided for over the whole period; the result would always be a supply of unemployed economic elements urgently offering their services, and this could not fail to upset the offending arrangements.*12


But we are not yet finished with the subject. It is not one single definite production period that harmonises with the above assumption, but a great many different periods. Obviously, given the capital and the number of workers, a very varying number of years can be provided for according as the wage of labour is high or low. With a capital of fifteen hundred millions for instance, our ten million workers can be kept in work and wage for ten years at a wage of £30, or for five years at a wage of £60, or for six years at a wage of £50. Now which of these possible cases will be the one actually adopted?—This will be determined, by the play of the same egoistic motives as regulate the formation of price in competition generally, in the following way.


Assume for a moment that the usual wage is £30. A capitalist then with £1000—for convenience sake we shall take this amount as the unit throughout the following discussion—may employ either 66.6 labourers in a one year's process, or 33.3 labourers in a two years' process, or 22.2 in a three years' process.*13 Naturally he will choose the process which he finds most advantageous. Which process that is will be seen from the following table, based on the former scheme of productivity on p. 378, showing how many workers can be employed by £1000 in each production period, and how much annual profit may be got from that sum.

WAGE £30.
Production Period in years. Annual Product. Annual profit per labourer. Number of employed. Total annual profit on the £1000.
1 £35 0 £5 0 66.66 £333.30
2 45 0 15 0 33.33 500
3 53 0 23 0 22.22 511.11
4 58 0 28 0 16.66 466.66
5 62 0 32 0 13.33 426.66
6 65 0 35 0 11.11 388.85
7 67 0 37 0 9.52 352.84
8 68 10 38 10 8.33 320.82
9 69 10 39 10 7.4 292.5
10 70 0 40 0 6.66 266.66


The table shows that, in the given circumstances of all the factors, it is most profitable for the undertakers to devote themselves to a three years' production period. They obtain thereby the very considerable rate of 51.1%, while both in the longer and in the shorter processes the profit is lower. In these circumstances naturally all undertakers will seek to adopt this length of process. But to what does this lead? In a three years' process £1000 can employ 22.2 workers, and therefore to employ all the available capital in the community (viz. £1500,000,000) 33 1/3 million workers would be needed—while there are only ten millions. These ten million workers could be employed by a sum of four and a half million pounds, leaving capital to the amount of ten and a half millions lying idle. Of course these ten and a half millions of capital could not and would not remain so: they would compete for employment; attract labourers by offering higher wages; and the necessary result would be a rise of the rate of wages. The £30 rate, then, assuming the above position of the factors, cannot possibly be a permanent one.


Suppose now that the rate of wages is £60, we get the following table.

WAGE £60.
Production Period in years. Annual Product. Annual profit per labourer. Number of employed. Total annual profit on the £1000.
1 £35 0 —£25 0 33.33 Loss
2 45 0 —15 0 16.66 "
3 53 0 — 7 0 11.11 "
4 58 0 — 2 0 8.33 "
5 62 0 2 0 6.66 £13.33
6 65 0 5 0 5.55 27.77
7 67 0 7 0 4.76 33.33
8 68 10 8 10 4.16 35.41
9 69 10 9 10 3.70 35.15
10 70 0 10 0 3.33 33.33


This table proves that, if we assume £60 as the rate of wages, production in anything less than a five years' period shows a positive loss, while, of the longer periods, the eight years' process is the most profitable. It yields the modest interest of 3.54%, but, relatively speaking, it is the most favourable rate that can be got. It is easy to see, however, that it is as impossible for a wage of £60, as it was for £30, to be the definite resultant price of labour. Under the assumed circumstances of productivity the eight years' period is the most profitable length of process at a £60 rate of wage. By adopting it a capital of £1000 can employ only 4.16 labourers; consequently the entire capital of £1500,000,000 can employ only six and a quarter million workers; and the remaining three and three-quarter millions must starve. This again is impossible; the unemployed will offer their services in competition with each other; and wages will be pressed below the rate of £60.


At what point, then, will this overbidding and underbidding, which come from unemployed capital when wage is too low and from unemployed labour when wage is too high, come to an end? Obviously it will be when the most reasonable production period exactly absorbs the wage fund on the one side, and the labour offered on the other. This will be the case, as the following table shows, at a wage of £50.

WAGE £50.
Production Period in years. Annual Product. Annual profit per labourer. Number of employed. Total annual profit on the £1000.
1 £35 0 — £15 0 40 Loss
2 45 0 — 5 0 20 "
3 53 0 3 0 13.33 £40
4 58 0 8 0 10 80
5 62 0 12 0 8 96
6 65 0 15 0 6.66 100
7 67 0 17 0 5.71 97.07
8 68 10 18 10 5 92.5
9 69 10 19 10 4.44 86.66
10 70 0 20 0 4 80


At a wage of £50 the six years' production period proves the most profitable. It gives an interest of 10% on the invested capital, while a five years' process would return only 9.6%, and a seven years', 9.7%. Moreover, as at that wage the £1000 employs 6 2/3 labourers, the entire ten million workers and the entire fifteen hundred millions of capital find employment; and the point is reached where the formation of price may come to rest. All who have it in their power to disturb the settlement by further over or under bidding have no inducement to do so, and all who might have an inducement have not the power, as, on economic grounds, they are already excluded from competition. There is no idle capital which might be tempted to seek employment by overbidding, and there are no idle labourers who might be tempted to seek employment by underbidding. And, finally, the undertakers who have placed their production on the footing which makes this favourable position of things possible are rewarded by this arrangement being at the same time the most profitable for them, and they too have no inducement to make any change. Those undertakers, on the other hand, who might have wished to engage in longer or shorter processes, and would thus have made either capital or labour insufficient, are excluded from any such disturbing competition by the fact that such methods of production show either a loss or a smaller profit.


The price of labour, then, will and must*15 settle at a wage of £50, and this involves, at the same time, an agio of 10% on present goods. I say, it must do so, for, so long as this point is not reached, there are certain tendencies always at work to force the price towards it. If, for example, the wage were only a little higher, say £51, the six years' process would still be the most profitable, but only 9,800,000 labourers could be employed by the available capital of £1500,000,000; the unemployed, by the urgency of their circumstances, would exert a pressure on the price of labour, till such time as they also could be taken in, which would be the case when wage came down to £50. If, on the contrary, the wage were a little lower; say £49, the employment of the ten million workers would take up only £1470,000,000 of capital; the unemployed remainder would attract employment through overbidding; and the result again would be a rise of wage till such time as the point was reached at which equilibrium all round could take place.


In the assumed state of all the factors an agio of 10% is therefore the economically necessary result. Why exactly 10%?—The considerations hitherto presented can only answer negatively that the necessary equilibrium could have been reached at no other rate of interest. But we may now inquire whether our figures do not bring out some other circumstances which may positively indicate a rate of 10%, and give us matter for a precise positive law of the interest rate.


To arrive at a position of equilibrium, the capital of the community had to be taken out of shorter processes where full employment could not be found for the existing stock of labour, and employed in gradually extending methods till all the labourers were fully occupied. This was arrived at in the six years' process. On the other hand, the adoption of still longer processes, for which again the capital is not sufficient, had, economically, to be prevented. In these circumstances the six years' producers are the last buyers, the "marginal buyers"; the would-be seven years' producers are the most capable excluded suitors for means of subsistence; and, according to our well-known law, the price that results must fall between the subjective valuations of these two. How does it stand with these valuations?


What we have to look to simply is: What is the utility which, for those two sets of buyers, depends on the disposal over a definite sum of means of subsistence? Here, first of all, it may be put down generally that, on the disposal over each half year's wage,—in the present case, £25,—depends one year's extension of the production period per worker.*16 Accordingly, with respect to the six years' producers, it specially depends on their possession or non-possession of the £25 whether, as regards one labourer, they can embark on or continue in the six years' process instead of the shorter five years' process. But according to our scheme of productivity the year's return of one worker in a five years' process amounts to only £62, while in a six years' process it amounts to £65. What, therefore, as regards the marginal buyer, depends on his having the disposal over £25, is the obtaining of a yearly surplus product of £3. On the other hand, those would-be producers who are trying to take means of subsistence out of the market in order to extend the production period to a seventh year, could gain by their extension only a surplus return of £2 (£67 - £65). For them, therefore, all that depends on their disposal over the £25 is a surplus of £2, and they are excluded from competition inasmuch as the resultant price has established an agio which exceeds the rate of 2 on 25 (8%).


If therefore—and this is indispensable to equilibrium being reached—the extension of the production period is to halt at the limit of six years, the agio established by the fixing of the price must lie between the rate that represents the valuation of the last buyers (£3 on £25, or 12%) as upper limit, and the rate representing the valuation of the competitors first excluded (8%) as lower limit. And thus our former empirical and circumstantial demonstration of the rate of wage and the rate of interest at which equilibrium may be reached on the market, must point provisionally to the rate of 10%. It must at least point to the zone between 8% and 12%. The fact that, within this zone, the rate of 10% is exactly brought out, is due, of course, not to the limitations indicated by the valuations of the marginal pair, but, as described on p. 215 simply to the quantitative effect of supply and demand. We shall see immediately, however, that the wide latitude (8% to 12%) which our abstract scheme leaves for the narrowing action of supply and demand, looks considerable only on account of the figures accidentally chosen; in practical life the latitude given is almost always vanishingly small.


Meanwhile we may put the results at which we have arrived in general form as follows:—


The rate of interest—on the assumptions already made—is limited and determined by the productiveness of the last extension of process economically permissible, and of the further extension economically not permissible; in this way that the unit of capital, which makes this extension of process possible, must always bear an amount of interest less than the surplus return of the first-named, and more than the surplus return of the last-named extension.*17 Within these marginal limits the price may be more exactly determined by the quantitative relation between wage fund and number of workers, according to the law of supply and demand.


In practical life, however, the latter method of determining price is seldom taken. It is true that in our abstract scheme there was an unusually wide latitude to come and go on, because we had assumed a sudden decrease of the surplus return from £3 to £2; that is, a fall of fully one-half. But in practical life sudden differences like this scarcely ever occur. The figures which represent the productiveness of the last permissible, and the first non-permissible extension come usually very close to each other, and, consequently, they are sufficient to limit the variations of the interest rate so strictly and sharply that the theoretically more exact determination by means of the relation of supply and demand is practically unimportant.*18 Indeed, assuming that these two marginal limits are very near each other, one of them may even be left out of account without any serious inaccuracy,*19 and the law be simply formulated thus:—The rate is determined by the surplus return of the last permissible extension of production. This coincides almost to a word with Thünen's celebrated law which makes the rate of interest depend on the productiveness of the "last applied dose of capital."*20

Notes for this chapter

See above, p. 319, and particularly p. 330.
The case of production carried on entirely without capital, which, according to the scheme, would return only £15, we may leave out of account as practically of no importance.
Only the wages of the first month are outstanding nearly a whole year; those of the second month are outstanding only eleven months, and so on; all wages of the first six months outstanding more than half a year. Against this the wages of the second six months are outstanding for as much less than the half-year.
The calculation is exactly similar to the foregoing.
Perhaps one or other of my readers will take exception to my looking upon the production period, in which the work of undertaking is carried on, as not a fixed immovable amount. It will be said that each undertaker has made the arrangements for his production on a quite definite footing, and works in any case in the production period corresponding to and determined by these given arrangements. This is not the case. Even where the visible outlines of the arrangements, such as workshops, number and kind of employés, and so on, may be pretty permanent, yet, within these fixed lines, a number of little noticed alterations are possible, by which the length of the production period might be changed not inconsiderably. In the simplest shoemaking shop, e.g., the buying of a new machine-made tool, the wholesale purchase of finished uppers, or, above all, the acquiring of labour-saving instruments such as sewing-machines and the like, involves no unimportant extension of the production period. True, in the shoemaking shop itself one does not notice that the production of shoes has now become a more lengthy process. But all the more noticeable will it be in those preparatory stages of production where, on account of the shoemaker's demand—not, of course, the demand of the one shoemaker, but of many,—people must now stretch away back in time, as it were, and invest original productive powers in machine-making, founding of factories, and so on. The shoemaker, therefore, according as he covers his demand for the instruments of his business in one way or the other, may as a fact cause a lengthening or shortening of the total production period, and naturally he makes the choice which, in the circumstances, is economically the more advantageous. If, e.g., the level of wages is very high, he will prefer to buy machine-made uppers, put up a sewing-machine in his own shop, etc.; that is to say, in entire correspondence with the statement given in the text, he will prolong the production period: while, if the level of wages is low, he will prefer directly to employ the cheap hand labour—that is to say, so far as in him lies, to keep the production period short.
On the assumption of a production arranged in the form of stages, whereby (as shown on p. 328, and in Appendix I.) the initial fund need only contain subsistence for half the production period.
If, e.g., the existing stock of subsistence is so great as to defray four million years pay—in which case, as we know, where production is by stages, an initial capital amounting to two millions of wages only would be required—and if there are one million labourers in the country, then it is shown that an average four years' production period must be taken. For if, say, a three years' period were taken, the three years' payment of one million of workers would take up only a capital of one and a half millions of wage, and the rest of the capital would have to go idle. In a five years' production, again, an initial fund of two millions of wages would only defray the subsistence of 800,000 labourers for five years, and the remaining 200,000 would go starving—a position which evidently is as untenable.
I here assume a well-organised production by stages, where no portion of the capital remains idle, and where, consequently, the initial fund need only contain something like half the amount of subsistence required during the course of the whole production period. I may note, however, that the correctness of the conclusions drawn in the text is quite independent of the pure question of fact whether the initial capital must be exactly half, or something more than half, or, perhaps, just so much as the amount of subsistence successively consumed by the workers during the production period. According as this is determined the figures puat down in the following tables will, of course, vary—they have no value, indeed, but as illustrative—but not the laws that underlie these figures. With other figures representing the productiveness and the capital, the calculation would lead to different concrete rates of interest, but to the same laws as regards height of the interest rate, as will be shown more clearly further on.
To be exact the figures of profit from the larger periods of production should be set down at somewhat less. They fall due, of course, all at once at the end of the total production period, and are thus less in value by the amount of the intermediate interest. In a ten years' production period, e.g., the capital of £1000 realises a total profit of £2666.6, which is less favourable than £266.66 for each single year, because in the latter case the interests falling due earlier might increase by compound interest. I consider it, however, less of a mistake to give up mathematical exactness than to include involved calculations of compound interest, and make the illustration so difficult and circumstantial that, in the end, it might be perhaps more difficult to understand than the rule which I mean it to illustrate. It is not committing any blunder in principle: the neglect of compound interest leads only to the same result as if I had made the progression of the annual returns—which in any case is arbitrary and only given for purposes of illustration—a little more rapid, and then had calculated exactly.
Leaving out of account special disturbing causes, the influence of which I cannot pursue here: my business just now is to develop the fundamental law of the interest rate, just as I have already developed the fundamental law of the formation of price. See Conrad's Jahrbücher, vol. xiii. p. 480.
Always assuming a complete arrangement of production by stages. I may add the mathematical proof of this somewhat paradoxical thesis. To employ 30 labourers in a 5 years' period arranged by yearly stages, the 6 labourers of the first stage need an advance of wage over full 5 years, that is, in all, 30 annual wages: the 6 labourers of the second stage require an advance over 4 years, that is, 24 wages: similarly, the labourers of the third stage require 18, those of the fourth 12, those of the fifth 6: a total of 90 wages. To support the same 30 labourers in a 6 years' production, the first stage, now embracing only 5 labourers, requires the advance for 6 years, that is, 30 wages; the second stage, 25; the third, 20; the others, respectively, 15, 10, and 5 wages: in all, 105 wages. The extension of the production period for 30 labourers by a whole year requires therefore, as a fact, the augmenting of the wage fund by the amount of only 15 wages, which gives the case maintained in the text.
From this formulation it will be seen why the law now deduced does not depend, and has no need to depend, for its correctness on the concrete numerical ratio between the amount of the wage fund and the length of the production period. (See above, p. 387, note 1.) Suppose, e.g., that not a half but a whole year's wage were necessary to extend the production period by a year, all the same a capital sufficient to defray the wages of a whole year would require to bear something like the return of the last extension of the production period as interest. The figures may change as they will, but the typical relation holds, that the interest of that unit of capital required for a definite extension of the production period lies between the surplus return of the last permissible and the first non-permissible extension.
See above, p. 217.
See above, p. 221.
Der isolirte Staat, second edition, part ii. div. i. p. 100. It is very notable that Thünen, without knowing the law of marginal utility, without any general price theory based on that law, and, finally, even without any clear insight into the origin of interest, was able to solve the special problem of the rate of interest with almost entire correctness, and in the sense of those general theories of which he had perhaps a dim

End of Notes

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