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 Bohm-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."  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 [p. 124] of theories which utilize them. 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. [p. 125]
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 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 [p. 126] 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. 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."
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 [p. 127] 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.
 It is important to note that this chapter does not deal with prices or market values, but with subjective use-value. Prices are derivative of subjective use-value. Cf. below, Chapter XVI.
 Cf. Carl Menger, Grundsätze der Volkswirtschaftslehre (Vienna, 1871), pp. 88 ff.; Böhm-Bawerk, Kapital und Kapitalzins (3d ed. Innsbruck, 1909), Pt. II, pp. 237 ff.
 Classes are not in the world. It is our mind that classifies the phenomena in order to orgaize 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 logical permissible or not.
 Cf. Daniel Bernoulli, Versuch einer neuen Theorie zur Bestimmung von Glücksfällen, trans. by Pringsheim (Leipzib, 1896), pp. 27 ff.
 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.