1. The Concept of Value according to Jevons, Walras and the Austrian School

An account of the recent theory of value can suitably begin with a revision of Adam Smith’s rule already mentioned—the rule that the value in use and the exchange value are independent of one another. With de Quincey and Mill, we have seen that such a complete independence does not exist; on the contrary the value in use—understood as the benefit or enjoyment which a person thinks he has or expects to gain from an object—must necessarily be greater in the case of the object taken in exchange than in the case of the object given in exchange, and this for each of the exchanging persons. In the last-mentioned statement of fact an important state of affairs is already expressed; for it follows from this with mathematical necessity that the objects which are about to be exchanged for one another must stand, in respect of their value in use for one of the parties to the exchange, in a sequence opposite to that in which they stand for the other. In other words, the value in use of an object is no constant magnitude, but changes with different persons and under different circumstances; and this attribute of value in use is a necessary condition of exchange and consequently of exchange value. Not to have considered this, is a fundamental defect of Smith’s reasoning. The value in use is for him, as can easily be seen, the average utility, or perhaps even the greatest possible utility which an object or a certain quantity of goods of the same kind can possibly have. This utility does not, however, determine the exchange value; the latter is on the contrary regulated by what Jevons calls final utility and Wieser marginal utility: by the smallest utility which an object or the quantity of goods concerned really possesses or presumably will possess.¹

This matter becomes especially simple if one thinks of the very unequal degree of utility which any quantity of consumer goods can possess for us and of the unequal value which we are therefore accustomed to ascribe to them, according to whether we are already provided for a certain period of consumption with a greater or smaller supply of the article in question. Let us consider an example which Böhm-Bawerk gives of a colonist living alone in the virgin forest, whose entire wealth consists of a supply of corn which he has just harvested and which must suffice until the next harvest. One sack of corn will be absolutely necessary to him if he is to maintain life during the winter; another sack gives him enough nourishment to preserve his health and bodily strength; a third sack would be superfluous, but is nevertheless valuable because it enables him to keep poultry, and thus procures for him a desired change in an otherwise purely cereal diet; a fourth sack he converts into spirits. If, finally, he possesses in addition to that a fifth sack, he can procure for himself in exchange for it no greater increase of his well-being than, for example, the amusement of feeding parrots.

If we now suppose that our Robinson Crusoe is offered some other commodity in exchange for one of his sacks of corn, then it is clear that the value (according to his estimate) of the quantity of corn which he would dispose of, would be wholly determined by the least urgent of the above-mentioned modes of application, or by the need to which it corresponds. The sack he disposes of will not be one of the first four, but only the fifth; in other words, if he thinks the utility of the commodity offered him high enough to compensate him for the amusement of keeping parrots, he on his part will be prepared to make the exchange. If, however, he is asked afterwards to part with a further sack of corn and consequently to give up the enjoyment of spirits, which the possession of this sack had made possible for him, the object which is offered him now must be considerably more tempting than would be necessary in the previous case; and of course far more tempting still, if he is to be induced to exchange the third sack also, after which he would not be able to procure for himself animal food. Since the last two sacks are of fundamental importance for his life and health, he will not be able to make up his mind to exchange these even under the strongest temptation.¹

From this very nicely chosen example one learns at the same time, at least in its general features, the role which scarcity on the one hand and costs of production on the other—the two sources from which, according to the older theory, the natural value alternatively arises—really play in determining exchange value. Scarcity itself cannot, of course, increase the utility which the commodities in question are able to provide; but scarcity does, indirectly, ensure that, amongst the needs which can be satisfied at all by a certain kind of goods, only the most urgent ones will in fact be covered, so that even the least among them, which becomes the determining one for the exchange value, will still have a high significance. If our colonist had harvested instead of five sacks only three, the exchange of a single sack would already have deprived him of the possibility of procuring for himself animal food, etc.

As regards cost of production, one sees immediately that the colonist’s valuation of the different sacks by no means rises or falls with the expenditure of labour or with the effort which production of these has cost him. More probably, the opposite is the case. If he had been content with the production of only one or two sacks of corn, he could, perhaps, have achieved this by a working-time of merely one or two hours daily, and an effort so moderate would probably have given him more enjoyment than trouble. With each lengthening of working-time the laboriousness of labour increases, while the utility of the product, even if for every new amount of labour it is quantitatively the same, becomes smaller and smaller. When finally the toil becomes so great and the value of the probable product so small that, according to the estimate of the colonist, they approximately counterbalance each other, labour must logically cease.

We can, therefore, not speak positively of an intrinsic, value-creating power in labour. Labour, labour-time, or energy of labour is, on the contrary, to be understood as a commodity like every other, the subjective estimation of which, if it is still in the possession of the worker himself, depends on how much of it he has already disposed of or, according to the established order of labour, will dispose of, and how much he has consequently left for himself for sleeping, meals, family life, recreation purposes, etc. Every process of production, whether carried on with capital or without, can, resolved into its elements, always be understood as a kind of exchange, whose only fundamental condition is that, like every exchange, it must bring a gain of utility (Nutzgewinn) to both sides.

This, however, does not prevent the proportionality between exchange value and employed quantity of labour or other costs of production from holding good within certain limits, but it does so only as a secondary law (Böhm-Bawerk), since, in the case of free competition, capital, labour and natural resources are always attracted to the most remunerative branches of production until, through an increased supply (diminished scarcity) of the goods concerned, their exchange value decreases, and at the same time the conditions under which they are produced usually become more difficult, so that finally this branch of production becomes no more remunerative than the others.

All the facts mentioned here are, as will be admitted, of the simplest and most obvious kind, and it can scarcely be supposed that they could have been unknown to the great thinkers who have occupied themselves with economic problems. The novelty lies in the idea of establishing the variability of the value in use or of the subjective estimate of value—that small thing, so easily overlooked—as the sole principle of the whole theory of exchange value.

Once found, this principle is seen to be not only sufficiently general to include all the phenomena of exchange, but also so exact that full mathematical precision and sharpness can be given to it, and through it to the whole theory of exchange.

Let us first of all take the simplest case—from which the more complicated one can later be derived—that a certain commodity is not available (for the period concerned) by direct production, that it cannot be replaced by another kind of goods, and finally, that it can be divided in any way one pleases and consumed in any quantities. According to what we said before, it is clear that the utility of a new unit of quantity of this commodity can be regarded as a function in the mathematical sense—a decreasing function—of the quantity of the possessed supply as the (sole) variable. If, furthermore, one thinks of this supply as successively diminished, every unit of quantity to be omitted represents a new, different utility, and the sum of these utilities can be nothing else but the total utility of the supply in question. The marginal utility appears, therefore, as the differential coefficient of the total utility, as its first derivative with respect to the possessed quantity of goods as variable.

It is seldom a question of measuring this total utility itself. This can sometimes even be regarded as infinite or immeasurably great; usually only smaller changes of the supply or of the usual quantities of consumption of a commodity are concerned. However, the marginal utility is only measured in so far as it is compared with the marginal utility of other goods or of the same commodity under changed circumstances. But the possibility of doing this, in other words, the notion of values in use of different goods as commensurable, not incommensurable, is a postulate of the modern theory of value. As we shall see, the principle of thrift demands in the case of the simple exchange of goods which can be divided in any way, that exchange is carried out up to the point at which the small quantities of goods which are the last to be exchanged have the same utility—for each of the exchanging persons. If the commodities on both sides are measured according to conventional units of quantities, then this may also be expressed as follows : after having settled the exchange, the marginal utilities on both sides must stand in the same proportion as their respective prices. In the end, therefore, it may be possible to alter Smith’s rule already mentioned in such a way, perhaps, as to say that the exchange value of goods is really proportional to their value in use, namely to the value in use, or the utility, of the last unit of quantity of the commodity in question, given or taken in exchange.

Moreover, as we have already indicated above, ratios of exchange, real values of exchange, occur only under the influence of the market, and there also only approximately.

In the case of the individual exchange, both contracting parties can in general still find their profit in the exchange within rather wide limits; what the price will be within these bounds—in other words, in what proportions the goods in question will at last be exchanged against each other—depends on a great many circumstances : on the power of judgment, habits, and equanimity of each of the contracting parties, on the fair-mindedness of both, etc. Only in the open market, where most of these individual attributes and considerations are neutralized by universal competition, as we know from experience, there will be approximately only one price for every commodity, as is in fact assumed by the theory.

In this chapter as well as in the following one, I shall avail myself rather extensively of the method introduced by Jevons and Walras, which uses mathematical signs and symbols. Although this method is becoming increasingly common in economic literature, it will perhaps be appropriate to say a few words in justification thereof. The older attempts (by Canard amongst others) at a mathematical mode of treatment are said not to have been very happy. For the majority of economists it was, for a long time at any rate, a settled question that greater exactitude in the modes of reasoning and an extension of our knowledge cannot be gained in this way. Stuart Mill (in his Logic) also expresses the same thought. He reminds us of the fact that even in one of the highly mathematical sciences, astronomy, a problem so simple at first sight as that of the mutual attraction, and the movement caused thereby, of three celestial bodies (the famous three-body-problem), has so far defied all attempts at an exact mathematical treatment. All the more, he argues, must this be so in the case of the infinitely more complicated economic phenomena.

However, the example chosen would only have been convincing if Mill had shown that, whilst a mathematical treatment of the three-body-problem has never been attempted with success—this, by the way, is only true of the general aspect of this problem—some other mode of treatment of the problem might be attempted with more success. This would obviously be absurd. But the same is probably true of every science that deals with measurable quantities, whose mutual relations it tries to investigate. In so far as it does this, it is undoubtedly a mathematical subject. If the subject cannot be treated to some extent in a mathematical way, it cannot be treated at all: it contains at best a description of the phenomena in question, but it can never throw light upon their inner relationship.

It is another question, of course, whether we shall be able to pursue economic events and their laws so far that the use of mathematical formulae, equations, etc., will prove really useful—that is to say, really help to clarify and sharpen the reasoning. In this respect, I think, the works of Walras and Jevons can speak for themselves. In particular, I should like to draw attention to the equations which, in the problem of exchange of three (or several) commodities, express the quantities of goods exchanged and their prices. Without the help of mathematical symbols it would not be easy to express or derive these relationships with sufficient precision. It is also worth mentioning that the economists of the Austrian school, which avoids the use of mathematical symbols on principle, have not touched upon this problem at all, although it is fundamental for the whole theory of exchange (in so far as its discussion brings out clearly the significance of trade as well as of money).

I hope, too, that the mathematical dress in which, in the second chapter, I shall clothe Böhm-Bawerk’s theory of the relationship between capital interest and wages, will be found to give greater simplicity and clarity to this fine theory; just as the completion of this theory, which I myself first put forward,¹ and which also takes into consideration rent, could scarcely be given in any other form than a mathematical one.

One must, of course, beware of expecting from this method more than it can give. Out of the crucible of calculation² comes not an atom more truth than was put in. The assumptions being hypothetical, the results obviously cannot claim more than a very limited validity. The mathematical expression ought to facilitate the argument, clarify the results, and so guard against possible faults of reasoning—that is all.

It is, by the way, evident that the economic aspects must be the determining ones everywhere: economic truth must never be sacrificed to the desire for mathematical elegance. In my opinion, neither Jevons nor Walras has transgressed this rule, but their German follower Launhardt has done so several times.