Front Page Titles (by Subject) 1: The Law of Marginal Utility - Human Action: A Treatise on Economics, vol. 1 (LF ed.)
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The Law of Marginal Utility
Action sorts and grades; originally it knows only ordinal numbers, not cardinal numbers. But the external world to which acting man must adjust his conduct is a world of quantitative determinateness. In this world there exist quantitative relations between cause and effect. If it were otherwise, if definite things could render unlimited services, such things would never be scarce and could not be dealt with as means.
Acting man values things as means for the removal of his uneasiness. From the point of view of the natural sciences the various events which result in satisfying human needs appear as very different. Acting man sees in these events only a more or a less of the same kind. In valuing very different states of satisfaction and the means for their attainment, man arranges all things in one scale and sees in them only their relevance for an increase in his own satisfaction. The satisfaction derived from food and that derived from the enjoyment of a work of art are, in acting man’s judgment, a more urgent or a less urgent need; valuation and action place them in one scale of what is more intensively desired and what is less. For acting man there exists primarily nothing but various degrees of relevance and urgency with regard to his own well-being.
Quantity and quality are categories of the external world. Only indirectly do they acquire importance and meaning for action. Because every thing can only produce a limited effect, some things are considered scarce and treated as means. Because the effects which things are able to produce are different, acting man distinguishes various classes of things. Because means of the same quantity and quality are apt always to produce the same quantity of an effect of the same quality, action does not differentiate between concrete definite quantities of homogeneous means. But this does not imply that it attaches the same value to the various portions of a supply of homogeneous means. Each portion is valued separately. To each portion its own rank in the scale of value is assigned. But these orders of rank can be ad libitum [(Latin) freely] interchanged among the various portions of the same magnitude.
If acting man has to decide between two or more means of different classes, he grades the individual portions of each of them. He assigns to each portion its special rank. In doing so he need not assign to the various portions of the same means orders of rank which immediately succeed one another.
The assignment of orders of rank through valuation is done only in acting and through acting. How great the portions are to which a single order of rank is assigned depends on the individual and unique conditions under which man acts in every case. Action does not deal with physical or metaphysical units which it values in an abstract academic way; it is always faced with alternatives between which it chooses. The choice must always be made between definite quantities of means. It is permissible to call the smallest quantity which can be the object of such a decision a unit. But one must guard oneself against the error of assuming that the valuation of the sum of such units is derived from the valuation of the units, or that it represents the sum of the valuations attached to these units.
A man owns five units of commodity a and three units of commodity b. He attaches to the units of a the rank-orders 1, 2, 4, 7, and 8, to the units of b the rank-orders 3, 5, and 6. This means: If he must choose between two units of a and two units of b, he will prefer to lose two units of a rather than two units of b. But if he must choose between three units of a and two units of b, he will prefer to lose two units of b rather than three units of a. What counts always and alone in valuing a compound of several units is the utility of this compound as a whole—i.e., the increment in well-being dependent upon it or, what is the same, the impairment of well-being which its loss must bring about. There are no arithmetical processes involved, neither adding nor multiplying; there is a valuation of the utility dependent upon the having of the portion, compound, or supply in question.
Utility means in this context simply: causal relevance for the removal of felt uneasiness. Acting man believes that the services a thing can render are apt to improve his own well-being, and calls this the utility of the thing concerned. For praxeology the term utility is tantamount to importance attached to a thing on account of the belief that it can remove uneasiness. The praxeological notion of utility (subjective use-value in the terminology of the earlier Austrian economists) must be sharply distinguished from the technological notion of utility (objective use-value in the terminology of the same economists). Use-value in the objective sense is the relation between a thing and the effect it has the capacity to bring about. It is to objective use-value that people refer in employing such terms as the “heating value” or “heating power” of coal. Subjective use-value is not always based on true objective use-value. There are things to which subjective use-value is attached because people erroneously believe that they have the power to bring about a desired effect. On the other hand there are things able to produce a desired effect to which no use-value is attached because people are ignorant of this fact.
Let us look at the state of economic thought which prevailed on the eve of the elaboration of the modern theory of value by Carl Menger, William Stanley Jevons, and Léon Walras. Whoever wants to construct an elementary theory of value and prices must first think of utility. Nothing indeed is more plausible than to assume that things are valued according to their utility. But then a difficulty appears which presented to the older economists a problem they failed to solve. They observed that things whose “utility” is greater are valued less than other things of smaller utility. Iron is less appreciated than gold. This fact seems to be incompatible with a theory of value and prices based on the concepts of utility and use-value. The economists believed that they had to abandon such a theory and tried to explain the phenomena of value and market exchange by other theories.
Only late did the economists discover that the apparent paradox was the outcome of a vicious formulation of the problem involved. The valuations and choices that result in the exchange ratios of the market do not decide between gold and iron. Acting man is not in a position in which he must choose between all the gold and all the iron. He chooses at a definite time and place under definite conditions between a strictly limited quantity of gold and a strictly limited quantity of iron. His decision in choosing between 100 ounces of gold and 100 tons of iron does not depend at all on the decision he would make if he were in the highly improbable situation of choosing between all the gold and all the iron. What counts alone for his actual choice is whether under existing conditions he considers the direct or indirect satisfaction which 100 ounces of gold could give him as greater or smaller than the direct or indirect satisfaction he could derive from 100 tons of iron. He does not express an academic or philosophical judgment concerning the “absolute” value of gold and of iron; he does not determine whether gold or iron is more important for mankind; he does not perorate as an author of books on the philosophy of history or on ethical principles. He simply chooses between two satisfactions both of which he cannot have together.
To prefer and to set aside and the choices and decisions in which they result are not acts of measurement. Action does not measure utility or value; it chooses between alternatives. There is no abstract problem of total utility or total value.1 There is no ratiocinative operation which could lead from the valuation of a definite quantity or number of things to the determination of the value of a greater or smaller quantity or number. There is no means of calculating the total value of a supply if only the values of its parts are known. There is no means of establishing the value of a part of a supply if only the value of the total supply is known. There are in the sphere of values and valuations no arithmetical operations; there is no such thing as a calculation of values. The valuation of the total stock of two things can differ from the valuation of parts of these stocks. An isolated man owning seven cows and seven horses may value one horse higher than one cow and may, when faced with the alternative, prefer to give up one cow rather than one horse. But at the same time the same man, when faced with the alternative of choosing between his whole supply of horses and his whole supply of cows, may prefer to keep the cows and to give up the horses. The concepts of total utility and total value are meaningless if not applied to a situation in which people must choose between total supplies. The question whether gold as such and iron as such is more useful and valuable is reasonable only with regard to a situation in which mankind or an isolated part of mankind must choose between all the gold and all the iron available.
The judgment of value refers only to the supply with which the concrete act of choice is concerned. A supply is ex definitione [(Latin) by definition] always composed of homogeneous parts each of which is capable of rendering the same services as, and of being substituted for, any other part. It is therefore immaterial for the act of choosing which particular part forms its object. All parts—units—of the available stock are considered as equally useful and valuable if the problem of giving up one of them is raised. If the supply decreased by the loss of one unit, acting man must decide anew how to use the various units of the remaining stock. It is obvious that the smaller stock cannot render all the services the greater stock could. That employment of the various units which under this new disposition is no longer provided for, was in the eyes of acting man the least urgent employment among all those for which he had previously assigned the various units of the greater stock. The satisfaction which he derived from the use of one unit for this employment was the smallest among the satisfactions which the units of the greater stock had rendered to him. It is only the value of this marginal satisfaction on which he must decide if the question of renouncing one unit of the total stock comes up. When faced with the problem of the value to be attached to one unit of a homogeneous supply, man decides on the basis of the value of the least important use he makes of the units of the whole supply; he decides on the basis of marginal utility.
If a man is faced with the alternative of giving up either one unit of his supply of a or one unit of his supply of b, he does not compare the total value of his total stock of a with the total value of his stock of b. He compares the marginal values both of a and of b. Although he may value the total supply of a higher than the total supply of b, the marginal value of b may be higher than the marginal value of a.
The same reasoning holds good for the question of increasing the available supply of any commodity by the acquisition of an additional definite number of units.
For the description of these facts economics does not need to employ the terminology of psychology. Neither does it need to resort to psychological reasoning and arguments for proving them. If we say that the acts of choice do not depend on the value attached to a whole class of wants, but on that attached to the concrete wants in question irrespective of the class in which they may be reckoned, we do not add anything to our knowledge and do not trace it back to some better-known or more general knowledge. This mode of speaking in terms of classes of wants becomes intelligible only if we remember the role played in the history of economic thought by the alleged paradox of value. Carl Menger and Böhm-Bawerk had to make use of the term “class of wants” in order to refute the objections raised by those who considered bread as such more valuable than silk because the class “want of nourishment” is more important than the class “want of luxurious clothing.” 2 Today the concept “class of wants” is entirely superfluous. It has no meaning for action and therefore none for the theory of value; it is, moreover, liable to bring about error and confusion. Construction of concepts and classification are mental tools; they acquire meaning and sense only in the context of theories which utilize them.3 It is nonsensical to arrange various wants into “classes of wants” in order to establish that such a classification is of no avail whatever for the theory of value.
The law of marginal utility and decreasing marginal value is independent of Gossen’s law of the saturation of wants (first law of Gossen). In treating marginal utility we deal neither with sensuous enjoyment nor with saturation and satiety. We do not transcend the sphere of praxeological reasoning in establishing the following definition: We call that employment of a unit of a homogeneous supply which a man makes if his supply is n units, but would not make if, other things being equal, his supply were only n − 1 units, the least urgent employment or the marginal employment, and the utility derived from it marginal utility. In order to attain this knowledge we do not need any physiological or psychological experience, knowledge, or reasoning. It follows necessarily from our assumptions that people act (choose) and that in the first case acting man has n units of a homogeneous supply and in the second case n − 1 units. Under these conditions no other result is thinkable. Our statement is formal and aprioristic and does not depend on any experience.
There are only two alternatives. Either there are or there are not intermediate stages between the felt uneasiness which impels a man to act and the state in which there can no longer be any action (be it because the state of perfect satisfaction is reached or because man is incapable of any further improvement in his conditions). In the second case there could be only one action; as soon as this action is consummated, a state would be reached in which no further action is possible. This is manifestly incompatible with our assumption that there is action; this case no longer implies the general conditions presupposed in the category of action. Only the first case remains. But then there are various degrees in the asymptotic approach to the state in which there can no longer be any action. Thus the law of marginal utility is already implied in the category of action. It is nothing else than the reverse of the statement that what satisfies more is preferred to what gives smaller satisfaction. If the supply available increases from n − 1 units to n units, the increment can be employed only for the removal of a want which is less urgent or less painful than the least urgent or least painful among all those wants which could be removed by means of the supply n − 1.
The law of marginal utility does not refer to objective use-value, but to subjective use-value. It does not deal with the physical or chemical capacity of things to bring about a definite effect in general, but with their relevance for the well-being of a man as he himself sees it under the prevailing momentary state of his affairs. It does not deal primarily with the value of things, but with the value of the services a man expects to get from them.
If we were to believe that marginal utility is about things and their objective use-value, we would be forced to assume that marginal utility can as well increase as decrease with an increase in the quantity of units available. It can happen that the employment of a certain minimum quantity—n units—of a good a can provide a satisfaction which is deemed more valuable than the services expected from one unit of a good b. But if the supply of a available is smaller than n, a can only be employed for another service which is considered less valuable than that of b. Then an increase in the quantity of a from n − 1 units to n units results in an increase of the value attached to one unit of a. The owner of 100 logs may build a cabin which protects him against rain better than a raincoat. But if fewer than 100 logs are available, he can only use them for a berth that protects him against the dampness of the soil. As the owner of 95 logs he would be prepared to forsake the raincoat in order to get 5 logs more. As the owner of 10 logs he would not abandon the raincoat even for 10 logs. A man whose savings amount to $100 may not be willing to carry out some work for a remuneration of $200. But if his savings were $2,000 and he were extremely anxious to acquire an indivisible good which cannot be bought for less than $2,100, he would be ready to perform this work for $100. All this is in perfect agreement with the rightly formulated law of marginal utility according to which value depends on the utility of the services expected. There is no question of any such thing as a law of increasing marginal utility.
The law of marginal utility must be confused neither with Bernoulli’s doctrine de mensura sortis [(Latin) of measurement] nor with the Weber-Fechner law. At the bottom of Bernoulli’s contribution were the generally known and never disputed facts that people are eager to satisfy the more urgent wants before they satisfy the less urgent, and that a rich man is in a position to provide better for his wants than a poor man. But the inferences Bernoulli drew from these truisms are all wrong. He developed a mathematical theory that the increment in gratification diminishes with the increase in a man’s total wealth. His statement that as a rule it is highly probable that for a man whose income is 5,000 ducats one ducat means not more than half a ducat for a man with an income of 2,500 ducats is merely fanciful. Let us set aside the objection that there is no means of drawing comparisons other than entirely arbitrary ones between the valuations of various people. Bernoulli’s method is no less inadequate for the valuations of the same individual with various amounts of income. He did not see that all that can be said about the case in question is that with increasing income every new increment is used for the satisfaction of a want less urgently felt than the least urgently felt want already satisfied before this increment took place. He did not see that in valuing, choosing, and acting there is no measurement and no establishment of equivalence, but grading, i.e., preferring and putting aside.4 Thus neither Bernoulli nor the mathematicians and economists who adopted his mode of reasoning could succeed in solving the paradox of value.
The mistakes inherent in the confusion of the Weber-Fechner law of psychophysics and the subjective theory of value have already been attacked by Max Weber. Max Weber, it is true, was not sufficiently familiar with economics and was too much under the sway of historicism to get a correct insight into the fundamentals of economic thought. But ingenious intuition provided him with a suggestion of a way toward the correct solution. The theory of marginal utility, he asserts, is “not psychologically substantiated, but rather—if an epistemological term is to be applied—pragmatically, i.e., on the employment of the categories: ends and means.”5
If a man wants to remove a pathological condition by taking a definite quantity of a remedy, the intake of a multiple will not bring about a better effect. The surplus will have either no effect other than the appropriate dose, the optimum, or it will have detrimental effects. The same is true of all kinds of satisfactions, although the optimum is often reached only by the application of a large dose, and the point at which further increments produce detrimental effects is often far away. This is so because our world is a world of causality and of quantitative relations between cause and effect. He who wants to remove the uneasiness caused by living in a room with a temperature of 35 degrees will aim at heating the room to a temperature of 65 or 70 degrees. It has nothing to do with the Weber-Fechner law that he does not aim at a temperature of 180 or 300 degrees. Neither has it anything to do with psychology. All that psychology can do for the explanation of this fact is to establish as an ultimate given that man as a rule prefers the preservation of life and health to death and sickness. What counts for praxeology is only the fact that acting man chooses between alternatives. That man is placed at crossroads, that he must and does choose, is—apart from other conditions—due to the fact that he lives in a quantitative world and not in a world without quantity, which is even unimaginable for the human mind.
The confusion of marginal utility and the Weber-Fechner law originated from the mistake of looking only at the means for the attainment of satisfaction and not at the satisfaction itself. If the satisfaction had been thought of, the absurd idea would not have been adopted of explaining the configuration of the desire for warmth by referring to the decreasing intensity of the sensation of successive increments in the intensity of the stimuli. That the average man does not want to raise the temperature of his bedroom to 120 degrees has no reference whatever to the intensity of the sensation for warmth. That a man does not heat his room to the same degree as other normal people do and as he himself would probably do, if he were not more intent upon buying a new suit or attending the performance of a Beethoven symphony, cannot be explained by the methods of the natural sciences. Objective and open to a treatment by the methods of the natural sciences are only the problems of objective use-value; the valuation of objective use-value on the part of acting man is another thing.
[1. ]It is important to note that this chapter does not deal with prices or market values, but with subjective use-value. Prices are a derivative of subjective use-value. Cf. below, Chapter 16.
[2. ]Cf. Carl Menger, Grundsätze der Volkswirtschaftslehre (Vienna, 1871), pp. 88 ff. [It should be noted that it was translated into English by James Dingwall and Bert F. Hoselitz as Principles of Economics, Free Press of Glencoe, Ill., 1950; later merged with Crowell-Collier, then Macmillan; reprinted by the Institute of Humane Studies and New York University Press, 1981; and by Libertarian Press (Grove City, Pa.), 1994. The pages cited in the German 1871 edition (pp. 88 ff.) are pp. 123 ff. in the English.]; Böhm-Bawerk, Kapital und Kapitalzins (3d ed. Innsbruck, 1909), Pt. II, pp. 237 ff. [It should be noted that Kapital und Kapitalzins was translated into English by Hans F. Sennholz as Capital and Interest (South Holland, Ill.: Libertarian Press, 1959). The pages cited in the German (Pt. II, pp. 237 ff.) are pp. 137 ff. in Volume II of the English translation.]
[3. ]Classes are not in the world. It is our mind that classifies the phenomena in order to organize our knowledge. The question of whether a certain mode of classifying phenomena is conducive to this end or not is different from the question of whether it is logically permissible or not.
[4. ]Cf. Daniel Bernoulli, Versuch einer neuen Theorie zur Bestimmung von Glücksfällen, trans. by Pringsheim (Leipzig, 1896), pp. 27 ff.
[5. ]Cf. Max Weber, Gesammelte Aufsätze zur Wissenschaftslehre (Tübingen, 1922), p. 372; also p. 149. The term “pragmatical” as used by Weber is of course liable to bring about confusion. It is inexpedient to employ it for anything other than the philosophy of Pragmatism. If Weber had known the term “praxeology,” he probably would have preferred it.