8. The Law of Costs. Walras’s Theory of Production

So far we have only looked at the imaginary case where the valuation, on the part of each of the possessors, of the goods to be exchanged depends solely on the size of the possessed stock and the quantity of the commodity in question obtained by exchange, or, if two or several kinds of goods can partly replace each other, on all of these quantities of goods. This case includes, in reality, perhaps, the daily changes of market prices, and even these only in so far as it is a matter of goods which are intended for immediate consumption. In every other case buyers as well as sellers will keep watch over the future supply and demand and over the possibilities of production and sale in future, by which the present prices must also be influenced. And more especially, if the average level of prices during a longer period, e.g. during one or several years, is uncertain, then the factors of production must be taken into consideration before everything else. It is not simply commodities that are exchanged, but products, and in the last instance the productive services themselves: labour, natural resources and the employment of capital.

But has a new element really come into our problem of exchange? One would be inclined to think that the productive services could be treated in exactly the same way as the commodities, according to the rules of the equality or proportionality of their marginal utility for the owners, i.e. in this case the workers, the land-owners and the capitalists. Indeed, we shall see at once how such a manner of treatment of the problem was attempted by L. Walras.

Whoever desires a certain number of commodities, in fact desires by implication a certain amount of the productive services which are necessary for the production of just these commodities; and he himself has in the end, as means of payment for the goods successively demanded and consumed by him, nothing else to offer but the productive services of which he for his part can dispose, i.e. his labour in any case, then perhaps also the use of landed property or capital which he possesses. It could therefore seem as if the production and the exchange of goods were nothing else but an indirect exchange of the productive services concerned against each other, quite in accordance with the usual rules of the market; and this, moreover, was frequently asserted.

But the matter is certainly not as simple as this. Here the well-known dictum of J. S. Mill (to which he himself, to be sure, gave quite an undue extension) is confirmed, that ‘demand for commodities is not demand for labour’ (or for the other productive services). Production requires time, and the sellers of the productive services will generally not be able or willing to await the completion of the commodities in order to secure their remuneration from the amount realized by the sale: they obtain this remuneration from the proceeds of the production periods already completed. Production will therefore, in reality, never be like the simple market; it consists rather of a series of acts of exchange performed at different times which together span the whole period from the beginning of the production to the sale of the commodity in question. Only if one takes this fact into consideration can one adequately explain to oneself the role of capital in production, that mysterious ‘productivity’ of capital, and obtain at the same time the main key to the phenomenon of capital interest.¹ We shall discuss these questions in detail in the next chapter, where it will be our task to comment on the outstanding work done by Böhm-Bawerk. But first let us say something about the so-called law of costs in its older and newer forms.

Classical political economy had, as everybody knows, two ways of explaining exchange values: firstly, by pointing to the relationship between supply and demand—which, however, necessarily proved a little superficial without the inclusion of the concept of marginal utility; and secondly, by asserting that, at least on the home market, the exchange values of goods must finally always coincide with the cost of production. If the profits of the different entrepreneurs are included in the costs, this is certainly self-evident. But in order to be more than a mere triviality, and in order not to move in a hopeless circle, this mode of explanation had to seek for independent reasons for the different elements in costs. We have already seen how Ricardo’s sagacity was able to give this really impossible task at least a formal solution. The element of cost, labour, was determined by the means of subsistence of workers, which was assumed to be approximately constant; rent was eliminated in the known manner; interest, finally, though it could not be determined a priori, was at least represented as a magnitude which is proportional to the magnitude of the capital advanced, or, which was assumed to be the same, to the amount of labour employed.

The modern theory of value could, of course, not approve of this mode of explanation. It noticed at once that the value of the elements of costs is determined in the last resort by nothing else but the value of the goods produced; so that value and costs must always be regarded as magnitudes dependent on each other. To my knowledge, only Leon Walras attempted successfully to do justice to these reciprocal relations and thus actually to lay down ‘the equations of production.’

Walras sets out from the assumption that the real profit of enterprise is cancelled out by the reciprocal competition of entrepreneurs. Thus they are simply compensated for their work of managing the enterprise as other workers are, according to a measure fixed by competition. But then the assumption is made, or rather the fiction is introduced—and in this lies the weak point in Walras’s presentation—that the entrepreneurs would buy ‘on the market of the productive services’ the services needed for their production of goods, namely the use of land, the various uses of capital,¹ and finally labour—but not against cash or commodities but simply against the promise to repay the same quantities of these services later after the conclusion of the production. But instead of really doing this, they would sell ‘on the market of the products’ the finished goods to those who offer the productive services and who appear now as consumers and, consequently, as buyers. In this way the entrepreneurs would be absolved from their promise to return the productive services as such; because the exchange value of the products must be equal to the productive services necessary for their production, if equilibrium between production and consumption is to exist and if the entrepreneurs are to have neither loss .nor profit. The productive services themselves, therefore, are here exchanged against each other ‘en fin de compte,’ as Walras explicitly remarks, and this according to the principle of marginal utility; since the existing productive services possess a certain utility and marginal utility—directly for the owners themselves, as well as indirectly, in the form of finished products, for the consumers of these products (who on their part have also to dispose of productive services).

However ingenious this concept—developed by Walras in a strictly mathematical form—may appear, it nevertheless suffers from a fundamental mistake, which must necessarily render the result illusory. And this mistake is to have completely overlooked the significance of time in production. Although the productive services are measured by Walras according to units of time—so many years of lease, so many working days, etc.—in his presentation of the matter, the use, for instance, of one hectare of land for one year could be paid for in such a way that the owners of the land would be allowed at some future date to use a similar hectare of land for one year; and the same is true with regard to labour. This is obviously not the case. It is also untrue that the owners of land are remunerated by the proceeds from the products made with their assistance—still less the workers; rather, they get their payment in advance. If this were not so, one could ‘en fin de compte’ completely overlook the part of capital in production—for the different parts of capital, machines, buildings, etc., are in the last instance products of labour and forces of nature—so that the production would finally have to be regarded as being completely without capital.

This mistake of Walras is connected with the peculiar interpretation of the concept of capital, to which we shall come back in the next chapter. He wants only durable goods, as, for instance, buildings and machines, to be considered as capital; on the other hand, consumable goods, as ‘revenues,’ he wants to put on a par with capital expenditure. What Adam Smith called circulating capital, raw materials, half-finished goods, etc., as well as the means of subsistence of workers and of other persons employed in the production, are, according to Walras, revenues, and bear no interest themselves (though they can be used for the production of new interest-bearing parts of capital). This is, of course, not correct. However the scientific terminology is arranged, the actual facts cannot be altered. Consumable goods certainly bear interest, if they are used for production or otherwise as capital; and the fact that they do this is just the main problem of the theory of capital interest.

At this point, therefore, we are led directly towards a thorough investigation into the nature of capital interest, to which we shall now proceed.

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¹ The ratio of exchange of two objects will consequently depend, even in the case of the simple exchange, on at least four factors, namely on the marginal utility of each object for each of the exchanging persons.

¹ Strictly speaking, however, a decreasing utility will have to be distinguished also within the different modes of application of the supply of corn. The marginal utility of corn for the colonist will therefore finally be the same in all modes of application, however different their importance for his welfare may be. Compare the following section.

¹ An extract from this part of my work was published in Conrads Jahrbücher, December 1893.

² A true method of calculating will probably not be arrived at for a long time.

¹ It is, of course, assumed that for very small changes the marginal utility is approximately constant.

¹Mathematische Begründung der Volkswirtschaftslehre, Leipzig 1885.

² The use of the word ‘value’ in a mathematical sense, that is to say, simply as synonymous with ‘magnitude,’ which occurs here and quite often in what follows, will, I hope, give no occasion for misunderstanding.

³ Properly speaking, one therefore needs only to know the three ratios of these four values, as we shall see.

¹ That is to say, the area which is bounded by the curve, both the axes of co-ordinates, and the ordinate in question.

¹ That is, the commodity in terms of which price will be expressed. (Translator’s note.)

¹ This circumstance was put forward by Launhardt (p. 37) as a general rule, but it is evidently only valid under the above simplifying assumptions, which are, however, by no means general.

¹ To the possessor of the sheep, a single sheep would at the beginning appear to have no value at all. One, must therefore presume that the hundredth sheep can neither be fed nor consumed nor used by him in another way. The possibility of some other exchange we exclude on principle. For A, on the contrary, the value of one sheep is initially 10 Marks, etc.

¹ For A’s total utility increases by

and B’s by

This characteristic feature also was noticed by Launhardt. It is valid, however, only under the above-made assumptions, which, as he asserts, are by no means ‘to be regarded as approximately right,’ but at best permissible by way of example.

¹Cf. Marshall, Principles of Economics, Appendix, note XII.

¹ Since the x₁, x₂, ...; y₁, y₂, . . .generally become different from thex'₁, x'₂, . . .;y'₁, y'₂, . . . one must, of course, suppose that every possessor generally does business with several possessors of the commodities desired by him.

¹ For one has, as can easily be seen,

¹ Considered geometrically, it is represented by a curve which can nearly always be replaced by a broken line, but not by one and the same straight line.

¹ In Jevons’s book these signs are represented by ϕ₁( ), ϕ₂( ), ψ₁( ) and ψ₂( ).

² Jevons’s formula could be applied in one case only, namely when the marginal utility function concerned may be replaced by an approximating function of the first degree which is identical for all members of the market party in question. (It is a somewhat less special case than the one mentioned above, where this function must be identical for the members of both parties.) Then, as can easily be seen, the arithmetical mean of all the marginal utility values would only be dependent on the acquired or remaining total supply of the community concerned and on the number of the possessors in question. Jevons’s formula, which in that case would probably assume the form

would then indeed be sufficient to determine the proportion of exchange at which equilibrium rules on the market.

¹ Of other selling possibilities and of the production of the goods concerned, no account is taken here.

¹ Cf. the above treatment of this problem in respect of two exchanging persons.

² Launhardt reproached Walras with ‘great error’ in supposing that ‘what is generally best would most certainly be reached by the natural effect of the rule of free competition.’ As far as I know, however, Walras has never asserted this, although he expresses himself a little incautiously upon this subject.

However, it is precisely at this point that Launhardt himself goes seriously astray; for he believes that he has proved that ‘in the case of an exchange at equilibrium prices the greatest profit, economically speaking, is reached, if we assume that the exchange takes place in one single transaction’ (loc. cit., p. 38). This is completely wrong. What Launhardt has proved in the passage in question (p. 28) is something quite different: that for each of the exchanging persons, and consequently for all of them together, as was shown above, the highest satisfaction attainable at this price arises from exchange at equilibrium price. But he has not shown, and it is not generally true, that this total satisfaction would be greater than that which could arise from any other price. This is quite obvious if we suppose, for example, that the marginal utility in respect of both commodities for one of the exchanging persons (or parties) is so small that the gain of utility to this person (or party) cannot be taken into consideration at all. Then it is clear that the total gain also becomes greater in proportion as the other party is able to direct the price to its advantage.

¹ The problem of exchange of two commodities also could, of course, have been treated in this way. This would express the more general case, where each of the exchanging persons at first possess both commodities, and according to the level of prices acts as buyer of the one commodity and seller of the other, or vice versa.

¹ Obviously, any one of the commodities could itself be conceived as the standard of value, in which case the price of this commodity would = 1. For the sake of symmetry, however, we have adopted a different standard of value, as in fact, in most cases, agrees best with reality ; for even if two commodities are exchanged for each other in a simple way by reciprocal credit between two business-men, their value is initially almost always reckoned in money.

¹ In this case, the notation used above will have to be altered correspondingly.

² Theory of Political Economy, 2nd edition, p. 124 ff.

¹ We must here draw attention to tome discontinuities of our functions previously laid down, which we have not discussed so far. Our equations of value

no longer have any significance if they cannot be satisfied by a positive y and by an x which it at the same time positive and smaller than a. If p has already become to small that x, and consequently y alto, are zero, the above equations must, if p continues to decreases, be replaced by x = 0, y = 0; that is to say, the possessor in question no longer exchanges at all.

If, on the contrary, x becomes equal to a, ρ increasing, then the possessor will tell at this price his whole supply of (A). If the price is a little higher still, he will generally, even at this price, exchange hit whole supply, but not more, since he does not possess any more of (A). Our equations must then in the first instance give way to the more simple relationships x = a,y = pa.

If, moreover, we consider the discontinuities of the individual consumption and demand, x and y can by no means be regarded as continuous functions of p.

¹ Strictly speaking, however, this is generally only the case when the commodities (A) and (B) cannot replace each other, so that, as we have assumed above, the marginal utility of one of them depends simply on the quantity owned of this commodity or on the quantity acquired, and not at the same time on the quantity acquired or the quantity owned of the other commodity. But if both commodities can replace each other completely or partly, it is a different matter. Suppose, for instance, that (B) is wheat and (A) potatoes. If a possessor of wheat can cover with it the whole of his annual food requirements, but potatoes are cheaper in proportion to their nutritive value, then he will probably exchange every year a certain quantity of wheat for the cheaper potatoes. But if now the price of potatoes (expressed in terms of wheat) were to fall still lower, he could first of all procure for himself the same quantity of potatoes in exchange for a smaller outlay of wheat. But since he thus keeps more wheat, his annual requirements in the matter of food could be even more than covered in this way. Therefore, if it is for him only a question of satisfying these requirements, he will be able to keep without loss a still greater quantity of wheat and content himself with a smaller quantity of potatoes, so that his demand for potatoes would finally decrease with the falling price instead of increasing.

¹ Of the production of goods no account is taken here, of course.

² For, in accordance with his assumptions repeatedly mentioned, a simple marginal utility function (in respect of each of the commodities) was drawn, identical for both parties. Here, of course, the curves can only have one single (real) point of intersection in common.

¹ In this case, the curves of the commodity (B) also would, of course, intersect at three points, lying vertically under the points of intersection of the curves of commodity (A).

²Untersuchungen Uber die Theorie des Preises, Preface, p. XXIII.

¹ In the case of three commodities, these are identical with equations (9).

² In the case of three commodities the equations (7), with the help of the equations (8), may be considered solved in x, y, z, etc.; in which case the positive x’s and y’s are conceived as (individual) demands and the negative ones as supplies, etc. (the appropriate + or—sign must in this case, of course, be regarded as given by the nature of the task).

¹ Even the exchange of finished goods requires time. In so far as it does this, it can be added to the production and is itself a source of capital interest.

¹ We shall soon see what is meant by these according to Walras.