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On the Measurement of Value

1 The Immeasurability of Subjective Use-Values

Although it is usual to speak of money as a measure of value and prices, the notion is entirely fallacious. So long as the subjective theory of value is accepted, this question of measurement cannot arise. In the older political economy, the search for a principle governing the measurement of value was to a certain extent justifiable. If, in accordance with an objective theory of value, the possibility of an objective concept of commodity values is accepted, and exchange is regarded as the reciprocal surrender of equivalent goods, then the conclusion necessarily follows that exchange transactions must be preceded by measurement of the quantity of value contained in each of the objects that are to be exchanged. And it is then an obvious step to regard money as the measure of value.

But modern value theory has a different starting point. It conceives of value as the significance attributed to individual commodity units by a human being who wishes to consume or otherwise dispose of various commodities to the best advantage. Every economic transaction presupposes a comparison of values. But the necessity for such a comparison, as well as the possibility of it, is due only to the circumstance that the person concerned has to choose between several commodities. It is quite irrelevant whether this choice is between a commodity in his own possession and one in somebody else's possession for which he might exchange it, or between the different uses to which he himself might put a given quantity of productive resources. In an isolated household, in which (as on Robinson Crusoe's desert island) there is neither buying nor selling, changes in the stocks of goods of higher and lower orders do nevertheless occur whenever anything is produced or consumed; and these changes must be based upon valuations if their returns are to exceed the outlay they involve. The process of valuation remains fundamentally the same whether the question is one of transforming labor and flour into bread in the domestic bakehouse, or of obtaining bread in exchange for clothes in the market. From the point of view of the person making the valuation, the calculation whether a certain act of production would justify a certain outlay of goods and labor is exactly the same as the comparison between the values of the commodities to be surrendered and the values of the commodities to be acquired that must precede an exchange transaction. For this reason it has been said that every economic act may be regarded as a kind of exchange. [1]

Acts of valuation are not susceptible of any kind of measurement. It is true that everybody is able to say whether a certain piece of bread seems more valuable to him than a certain piece of iron or less valuable than a certain piece of meat. And it is therefore true that everybody is in a position to draw up an immense list of comparative values; a list which will hold good only for a given point of time, since it must assume a given combination of wants and commodities. If the individual's circumstances change, then his scale of values changes also.

But subjective valuation, which is the pivot of all economic activity, only arranges commodities in order of their significance; it does not measure this significance. And economic activity has no other basis than the value scales thus constructed by individuals. An exchange will take place when two commodity units are placed in a different order on the value scales of two different persons. In a market, exchanges will continue until it is no longer possible for reciprocal surrender of commodities by any two individuals to result in their each acquiring commodities that stand higher on their value scales than those surrendered. If an individual wishes to make an exchange on an economic basis, he has merely to consider the comparative significance in his own judgment of the quantities of commodities in question. Such an estimate of relative values in no way involves the idea of measurement. An estimate is a direct psychological judgment that is not dependent on any kind of intermediate or auxiliary process.

(Such considerations also provide the answer to a series of objections to the subjective theory of value. It would be rash to conclude, because psychology has not succeeded and is not likely to succeed in measuring desires, that it is therefore impossible ultimately to attribute the quantitatively exact exchange ratios of the market to subjective factors. The exchange ratios of commodities are based upon the value scales of the individuals dealing in the market. Suppose that A possesses three pears and B two apples; and that A values the possession of two apples more than that of three pears, while B values the possession of three pears more than that of two apples. On the basis of these estimations an exchange may take place in which three pears are given for two apples. Yet it is clear that the determination of the numerically precise exchange ratio 2 : 3, taking a single fruit as a unit, in no way presupposes that A and B know exactly by how much the satisfaction promised by possession of the quantities to be acquired by exchange exceeds the satisfaction promised by possession of the quantities to be given up.)

General recognition of this fact, for which we are indebted to the authors of modern value theory, was hindered for a long time by a peculiar sort of obstacle. It is not altogether a rare thing that those very pioneers who have not hesitated to clear new paths for themselves and their followers by boldly rejecting outworn traditions and ways of thinking should yet shrink sometimes from all that is involved in the rigid application of their own principles. When this is so, it remains for those who come after to endeavor to put the matter right. The present is a case in point. On the subject of the measurement of value, as on a series of further subjects that are very closely bound up with it, the founders of the subjective theory of value refrained from the consistent development of their own doctrines. This is especially true of Böhm-Bawerk. At least it is especially striking in him; for the arguments of his which we are about to consider are embodied in a system that would have provided an alternative and, in the present writer's opinion, a better, solution of the problem, if their author had only drawn the decisive conclusion from them.

Böhm-Bawerk points out that when we have to choose in actual life between several satisfactions which cannot be had simultaneously because our means are limited, the situation is often such that the alternatives are on the one hand one big satisfaction and on the other hand a large number of homogeneous smaller satisfactions. Nobody will deny that it lies in our power to come to a rational decision in such cases. But it is equally clear that a judgment merely to the effect that a satisfaction of the one sort is greater than a satisfaction of the other sort is inadequate for such a decision; as would even be a judgment that a satisfaction of the first sort is considerably greater than one of the other sort. Böhm-Bawerk therefore concludes that the judgment must definitely affirm how many of the smaller satisfactions outweigh one of the first sort, or in other words how many times the one satisfaction exceeds one of the others in magnitude. [2]

The credit of having exposed the error contained in the identification of these two last propositions belongs to Cuhel. The judgment that so many small satisfactions are outweighed by a satisfaction of another kind is in fact not identical with the judgment that the one satisfaction is so many times greater than one of the others. The two would be identical only if the satisfaction afforded by a number of commodity units taken together were equal to the satisfaction afforded by a single unit on its own multiplied by the number of units. That this assumption cannot hold good follows from Gossen's law of the satisfaction of wants. The two judgments, "I would rather have eight plums than one apple" and "I would rather have one apple than seven plums," do not in the least justify the conclusion that Böhm-Bawerk draws from them when he states that therefore the satisfaction afforded by the consumption of an apple is more than seven times but less than eight times as great as the satisfaction afforded by the consumption of a plum. The only legitimate conclusion is that the satisfaction from one apple is greater than the total satisfaction from seven plums but less than the total satisfaction from eight plums. [3]

This is the only interpretation that can be harmonized with the fundamental conception expounded by the marginal-utility theorists, and especially by Böhm-Bawerk himself, that the utility (and consequently the subjective use-value also) of units of a commodity decreases as the supply of them increases. But to accept this is to reject the whole idea of measuring the subjective use-value of commodities. Subjective use-value is not susceptible of any kind of measurement.

The American economist Irving Fisher has attempted to approach the problem of value measurement by way of mathematics. [4] His success with this method has been no greater than that of his predecessors with other methods. Like them, he has not been able to surmount the difficulties arising from the fact that marginal utility diminishes as supply increases, and the only use of the mathematics in which he clothes his arguments, and which is widely regarded as a particularly becoming dress for investigations in economics, is to conceal a little the defects of their clever but artificial construction.

Fisher begins by assuming that the utility of a particular good or service, though dependent on the supply of that good or service, is independent of the supply of all others. He realizes that it will not be possible to achieve his aim of discovering a unit for the measurement of utility unless he can first show how to determine the proportion between two given marginal utilities. If, for example, an individual has a hundred loaves of bread at his disposal during one year, the marginal utility of a loaf to him will be greater than if he had one hundred and fifty loaves. The problem is, to determine the arithmetical proportion between the two marginal utilities. Fisher attempts to do this by comparing them with a third utility. He therefore supposes the individual to have B gallons of oil annually as well, and calls β that increment of B whose utility is equal to that of the 100th loaf of bread. In the second case, when not a hundred but a hundred and fifty loaves are available, it is assumed that the supply of B remains unchanged. Then the utility of the 150th loaf may be equal, say, to the utility of β/2. Up to this point it is unnecessary to quarrel with Fisher's argument; but now follows a jump that neatly avoids all the difficulties of the problem. That is to say, Fisher simply continues, as if he were stating something quite self-evident: "Then the utility of the 150th loaf is said to be half the utility of the 100th." Without any further explanation he then calmly proceeds with his problem, the solution of which (if the above proposition is accepted as correct) involves no further difficulties, and so succeeds eventually in deducing a unit which he calls a "util." It does not seem to have occurred to him that in the particular sentence just quoted he has argued in defiance of the whole of marginal-utility theory and set himself in opposition to all the fundamental doctrines of modern economics. For obviously this conclusion of his is legitimate only if the utility of β is equal to twice the utility of β/2. But if this were really so, the problem of determining the proportion between two marginal utilities could have been solved in a quicker way, and his long process of deduction would not have been necessary. Just as justifiably as he assumes that the utility of β is equal to twice the utility of β/2, he might have assumed straightaway that the utility of the 150th loaf is two-thirds of that of the 100th.

Fisher imagines a supply of B gallons that is divisible into n small quantities β, or 2n small quantities β/2. He assumes that an individual who has this supply B at his disposal regards the value of commodity unit x as equal to that of β and the value of commodity unit y as equal to that of β/2. And he makes the further assumption that in both valuations, that is, both in equating the value of x with that of β and in equating the value of y with that of β/2, the individual has the same supply of B gallons at his disposal.

He evidently thinks it possible to conclude from this that the utility of β is twice as great as that of β/2. The error here is obvious. The individual is in the one case faced with the choice between x (the value of the 100th loaf) and β = 2β/2. He finds it impossible to decide between the two, i.e., he values both equally. In the second case he has to choose between y (the value of the 150th loaf) and β/2. Here again he finds that both alternatives are of equal value. Now the question arises, what is the proportion between the marginal utility of β and that of β/2? We can determine this only by asking ourselves what the proportion is between the marginal utility of the nth part of a given supply and that of the 2nth part of the same supply, between that of β/n and that of β/2n. For this purpose let us imagine the supply B split up into 2n portions of β/2n. Then the marginal utility of the (2n-1)th portion is greater than that of the 2nth portion. If we now imagine the same supply B divided into n portions, then it clearly follows that the marginal utility of the nth portion is equal to that of the (2n-1)th portion plus that of the 2nth portion in the previous case. It is not twice as great as that of the 2nth portion, but more than twice as great. In fact, even with an unchanged supply, the marginal utility of several units taken together is not equal to the marginal utility of one unit multiplied by the number of units, but necessarily greater than this product. The value of two units is greater than, but not twice as great as, the value of one unit. [5]

Perhaps Fisher thinks that this consideration may be disposed of by supposing β and β/2 to be such small quantities that their utility may be reckoned infinitesimal. If this is really his opinion, then it must first of all be objected that the peculiarly mathematical conception of infinitesimal quantities is inapplicable to economic problems. The utility afforded by a given amount of commodities, is either great enough for valuation, or so small that it remains imperceptible to the valuer and cannot therefore affect his judgment. But even if the applicability of the conception of infinitesimal quantities were granted, the argument would still be invalid, for it is obviously impossible to find the proportion between two finite marginal utilities by equating them with two infinitesimal marginal utilities.

Finally, a few words must be devoted to Schumpeter's attempt to set up as a unit the satisfaction resulting from the consumption of a given quantity of commodities and to express other satisfactions as multiples of this unit. Value judgments on this principle would have to be expressed as follows: "The satisfaction that I could get from the consumption of a certain quantity of commodities is a thousand times as great as that which I get from the consumption of an apple a day," or "For this quantity of goods I would give at the most a thousand times this apple." [6] Is there really anybody on earth who is capable of adumbrating such mental images or pronouncing such judgments? Is there any sort of economic activity that is actually dependent on the making of such decisions? Obviously not. [7] Schumpeter makes the same mistake of starting with the assumption that we need a measure of value in order to be able to compare one "quantity of value" with another. But valuation in no way consists in a comparison of two "quantities of value." It consists solely in a comparison of the importance of different wants. The judgment "Commodity a is worth more to me than commodity b" no more presupposes a measure of economic value than the judgment "A is dearer to me—more highly esteemed—than B" presupposes a measure of friendship.

2 Total Value

If it is impossible to measure subjective use-value, it follows directly that it is impracticable to ascribe "quantity" to it. We may say, the value of this commodity is greater than the value of that; but it is not permissible for us to assert, this commodity is worth so much. Such a way of speaking necessarily implies a definite unit. It really amounts to stating how many times a given unit is contained in the quantity to be defined. But this kind of calculation is quite inapplicable to processes of valuation.

The consistent application of these principles implies a criticism also of Schumpeter's views on the total value of a stock of goods. According to Wieser, the total value of a stock of goods is given by multiplying the number of items or portions constituting the stock by their marginal utility at any given moment. The untenability of this argument is shown by the fact that it would prove that the total stock of a free good must always be worth nothing. Schumpeter therefore suggests a different formula in which each portion is multiplied by an index corresponding to its position on the value scale (which, by the way, is quite arbitrary) and these products are then added together or integrated. This attempt at a solution, like the preceding, has the defect of assuming that it is possible to measure marginal utility and "intensity" of value. The fact that such measurement is impossible renders both suggestions equally useless. Mastery of the problem must be sought in some other way.

Value is always the result of a process of valuation. The process of valuation compares the significance of two complexes of commodities from the point of view of the individual making the valuation. The individual making the valuation and the complexes of goods valued, that is, the subject and the objects of the valuation, must enter as indivisible elements into any given process of valuation. This does not mean that they are necessarily indivisible in other respects as well, whether physically or economically. The subject of an act of valuation may quite well be a group of persons, a state or society or family, so long as it acts in this particular case as a unit, through a representative. And the objects thus valued may be collections of distinct units of commodities so long as they have to be dealt with in this particular case as a whole. There is nothing to prevent either subject or object from being a single unit for the purposes of one valuation even though in another their component parts may be entirely independent of each other The same people who, acting together through a representative as a single agent, such as a state, make a judgment as to the relative values of a battleship and a hospital, are the independent subjects of valuations of other commodities, such as cigars and newspapers. It is just the same with commodities. Modern value theory is based on the fact that it is not the abstract importance of different kinds of need that determines the scales of values, but the intensity of specific desires. Starting from this, the law of marginal utility was developed in a form that referred primarily to the usual sort of case in which the collections of commodities are divisible. But there are also cases in which the total supply must be valued as it stands.

Suppose that an economically isolated individual possesses two cows and three horses and that the relevant part of his scale of values (that item valued highest being placed first) is as follows: 1, a cow; 2, a horse; 3, a horse; 4,a horse; 5, a cow. If this individual has to choose between one cow and one horse he will rather be inclined to sacrifice the cow than the horse. If wild animals attack one of his cows and one of his horses, and it is impossible for him to save both, then he will try to save the horse. But if the whole of his stock of either animal is in danger, his decision will be different. Supposing that his stable and cowshed catch fire and that he can only rescue the occupants of one and must leave the others to their fate, then if he values three horses less than two cows he will attempt to save not the three horses but the two cows. The result of that process of valuation which involves a choice between one cow and one horse is a higher estimation of the horse. The result of the process of valuation which involves a choice between the whole available stock of cows and the whole available stock of horses is a higher estimation of the stock of cows.

Value can rightly be spoken of only with regard to specific acts of appraisal. It exists in such connections only; there is no value outside the process of valuation. There is no such thing as abstract value. Total value can be spoken of only with reference to a particular instance of an individual or other valuing "subject" having to choose between the total available quantities of certain economic goods. Like every other act of valuation, this is complete in itself. The person making the choice does not have to make use of notions about the value of units of the commodity. His process of valuation, like every other, is an immediate inference from considerations of the utilities at stake. When a stock is valued as a whole, its marginal utility, that is to say, the utility of the last available unit of it, coincides with its total utility, since the total supply is one indivisible quantity. This is also true of the total value of free goods, whose separate units are always valueless, that is, are always relegated to a sort of limbo at the very end of the value scale, promiscuously intermingled with the units of all the other free goods. [8]

3 Money as a Price Index

What has been said should have made sufficiently plain the unscientific nature of the practice of attributing to money the function of acting as a measure of price or even of value. Subjective value is not measured, but graded. The problem of the measurement of objective use-value is not an economic problem at all. (It may incidentally be remarked that a measurement of efficiency is not possible for every species of commodity and is at the best only available within separate species, while every possibility, not only of measurement, but even of mere scaled comparison, vanishes as soon as we seek to establish a relation between two or more kinds of efficiency. It may be possible to measure and compare the calorific value of coal and of wood, but it is in no way possible to reduce to a common objective denominator the objective efficiency of a table and that of a book.)

Neither is objective exchange value measurable, for it too is the result of the comparisons derived from the valuations of individuals. The objective exchange value of a given commodity unit may be expressed in units of every other kind of commodity. Nowadays exchange is usually carried on by means of money, and since every commodity has therefore a price expressible in money, the exchange value of every commodity can be expressed in terms of money. This possibility enabled money to become a medium for expressing values when the growing elaboration of the scale of values which resulted from the development of exchange necessitated a revision of the technique of valuation.

That is to say, opportunities for exchanging induce the individual to rearrange his scales of values. A person in whose scale of values the commodity "a cask of wine" comes after the commodity "a sack of oats" will reverse their order if he can exchange a cask of wine in the market for a commodity that he values more highly than a sack of oats. The position of commodities in the value scales of individuals is no longer determined solely by their own subjective use-value, but also by the subjective use-value of the commodities that can be obtained in exchange for them, whenever the latter stand higher than the former in the estimation of the individual. Therefore, if he is to obtain the maximum utility from his resources, the individual must familiarize himself with all the prices in the market.

For this, however, he needs some help in finding his way among the confusing multiplicity of the exchange ratios. Money, the common medium of exchange, which can be exchanged for every commodity and with which every commodity can be procured, is preeminently suitable for this. It would be absolutely impossible for the individual, even if he were a complete expert in commercial matters, to follow every change of market conditions and make the corresponding alterations in his scale of use-values and exchange values, unless he chose some common denominator to which he could reduce each exchange ratio. Because the market enables any commodity to be turned into money and money into any commodity, objective exchange value is expressed in terms of money. Thus money becomes a price index, in Menger's phrase. The whole structure of the calculations of the entrepreneur and the consumer rests on the process of valuing commodities in money. Money has thus become an aid that the human mind is no longer able to dispense with in making economic calculations. [9] If in this sense we wish to attribute to money the function of being a measure of prices, there is no reason why we should not do so. Nevertheless, it is better to avoid the use of a term which might so easily be misunderstood as this. In any case the usage certainly cannot be called correct—we do not usually describe the determination of latitude and longitude as a "function" of the stars. [10]

[1] See Simmel, Philosophie des Geldes, 2d ed. (Leipzig, 1907), p. 35; Schumpeter, Wesen und Hauptinhalt der theoretischen Nationalökonomie (Leipzig, 1908), p. 50.

[2] Cf. Böhm-Bawerk, "Grundzüge der Theorie des wirtschaftlichen Güterwertes," Jahrbücher für Nationalökonomie und Statistik (1886), New Series, vol. 13, p. 48.

[3] See Cuhel, Zur Lehre von den Bedürfnissen (Innsbruck, 1906), pp. 186 ff.; Weiss, Die moderne Tendenz in der Lehre vom Geldwert, Zeitschrift für Volkswirtschaft, Sozialpolitik und Verwaltung, vol. 19, pp. 532 ff. In the last edition of his masterpiece Capital and Interest, revised by himself, Böhm-Bawerk endeavored to refute Cuhel's criticism, but did not succeed in putting forward any new considerations that could help toward a solution of the problem (see Kapital und Kapitalzins, 3d ed. [Innsbruck, 1909-12], pp. 331 ff. Exkurse, pp. 280 ff.).

[4] See Fisher, Mathematical Investigations in the Theory of Value and Prices, Transactions of the Connecticut Academy (New Haven, 1892), vol. 9, pp. 14 ff.

[5] See also Weiss, op. cit., p. 538.

[6] Cf. Schumpeter, op. cit., p. 290.

[7] Cf. further Weiss, op. cit., pp. 534 ff.

[8] See also Clark, Essentials of Economic Theory (New York, 1907), p. 41. In the first German edition of the present work, the above argument contained two further sentences that summarized in an inadequate fashion the results of investigation into the problem of total value. In deference to certain criticisms of C. A. Verrijn Stuart (Die Grundlagen der Volkswirtschaft [Jena, 1923], p. 115), they were omitted from the second edition.

[9] On the indispensability of money for economic calculation, see my book Die Gemeinwirtschaft: Untersuchungen über den Sozialismus(Jena, 1922), pp. 100 ff.

[10] [This chapter deals with technical matters which may present difficulty to readers unacquainted with general economic theory. It may be omitted on a first reading, but it is essential to complete understanding of certain issues, such as the index-number problem, which are dealt with later.—Editor.]

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