The Positive Theory of Capital

Eugen v. Böhm-Bawerk, from the Warren J. Samuels Portrait Collection
Böhm-Bawerk, Eugen v.
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William A. Smart, trans.
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London: Macmillan and Co.
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Book III, Chapter IV

The Marginal Utility


Turning now to the second question suggested in last chapter we ask, Of several or many wants which one is it that actually depends on a particular good?


This question would not be put at all if the circumstances of economic life were so simple that single wants always stood over against single goods. If a good were adapted to satisfy a single concrete want, and if it were at the same time the only one of its kind, or, at least, the only one of its kind available, it would be quite clear without further consideration that the satisfaction of the single want depended on our command over the single good. But in practical life the matter is scarcely ever so simple as this; on the contrary, it is usually complicated simultaneously from two sides. First, one and the same good is usually adapted to satisfy various concrete wants, which wants again possess various degrees of importance; and second, several goods of one and the same kind are frequently available, thus leaving it to caprice which good will be used for the satisfaction of an important, and which for an unimportant want. To give the simplest possible example. I have been shooting for a few days on the mountains, and by some accident I miss my companions. I am far from any house or village, and the only food I have for myself and my dog is two entirely similar baker's rolls. It is clear that the satisfaction of my hunger is of infinitely more importance to me than the satisfaction of the dog's hunger and it is just as clear that it lies with me which of the two rolls I shall consume and which I shall give to the dog. And now the question arises, Which of the two wants here is dependent on the bread?


One is tempted to answer, That want to which the bread was actually devoted. But it is evident at once that this is an erroneous conclusion. It would amount to saying that the two rolls, devoted as they are to the satisfaction of wants of different importance, must possess different values; while it does not admit of question that two similar goods, available under similar conditions, must be entirely equal in value.


Here, again, an easy casuistical consideration gives the proper solution. The problem is: Which, among several wants, is dependent on a commodity? This resolves itself very simply when it is known which want it is that would fail of its satisfaction if that commodity were not present: that want is evidently the dependent one. And now it is easy to show that the want which failed of its satisfaction would not be that want which the particular commodity was, accidentally and capriciously, selected to satisfy, but would always be the least important among all the wants in question; that is to say, among all those wants which would formerly have been provided for out of the total stock of this class of goods.


Consideration for one's own convenience, as obvious as it is imperative, induces every reasonable man who acts economically to maintain a certain fixed order in the satisfaction of his wants. No one would be so foolish as to exhaust the resources at his command in satisfying trifling wants, or wants that could be easily ignored, and thus to deprive himself of the means of satisfying necessary wants. On the contrary, every one would take care to use the resources at his command, in the first instance, to provide for his most important wants; then for wants that come after these in importance; then for those of the third rank, and so on;—always arranging in such a way that the lesser wants were only provided for when all the higher wants had been supplied, and there still remained some means of satisfaction to spare. We act according to the same obvious and reasonable principles when our stock undergoes a change by the loss of one member of that stock. Naturally this will alter the plan according to which we have been employing our resources. Not all the wants we had arranged to satisfy can now be provided for, and some abatement in the totality of satisfaction is unavoidable. But, of course, the wise man will try to lay the burden on the least sensitive spot; that is to say, if the loss chances to be in a commodity which was destined to a more important use, he will not give up the satisfaction of this more important want, and, by holding on obstinately to his old plan, provide satisfaction for the less important wants. We may be sure that he will satisfy the more important want, and will do so by withdrawing provision from that want, among all the wants hitherto marked out for provision, on the satisfaction of which least depends. To put it in terms of our former illustration: if our sportsman loses the roll which he has meant for himself, he will scarcely feed his dog with the one that remains, and expose himself to the danger of starving. He will suddenly change his plan, elevate the roll that remains into fulfilling its more important function only, and shift the loss to the least important function, the feeding of the dog.


The case, then, stands as follows. Wants which are more important than this "last" want will not be affected by the loss of the good, for their satisfaction is, as before, guaranteed in case of need by the replacement of substitutes. Nor will those wants be affected which are less important than this "marginal want," for they go unsatisfied whether the good is there or not. The only want affected is the last of those that otherwise would be satisfied: it will be satisfied if the good is there; it will not be satisfied if it is not there. It is thus the dependent want we were seeking.


Here then we have reached the goal of the present inquiry, and may formulate it thus: the value of a good is measured by the importance of that concrete want, or partial want, which is least urgent among the wants that are met from the available stock of similar goods. What determines the value of a good, then, is not its greatest utility, not its average utility, but the least utility which it, or one like it, might be reasonably employed in providing under the concrete economical conditions. To save ourselves the repetition of this circumstantial description—which, all the same, had to be somewhat circumstantial to be quite correct—we shall follow Wieser*9 in calling this least utility—the utility that stands on the margin of the economically permissible—the economic Marginal Utility of the good. The law which governs amount of value, then, may be put in the following very simple formula: The value of a good is determined by the amount of its Marginal Utility.


This proposition is the key-stone of our theory of value. But it is more. In my opinion it is the master-key to the action of practical economic men with regard to goods. In the simplest cases, as in all the tangle and complication which our present varied economic life has created, we find men valuing the goods with which they have to deal by the marginal utility of these goods, and dealing with them according to the result of this valuation. And to this extent the doctrine of marginal utility is not only the key-stone of the theory of value, but, as affording the explanation of all economical transactions, it is the key-stone of all economical theory.*10 Those who have observed practical life closely will, I think, be convinced that this claim is not exaggerated. Rightly to observe and rightly to interpret what has been observed, however, is an art not always easy; and in what follows accordingly we shall make use of the value theory to guide us in observing and interpreting what falls within its sphere. We begin, then, with an illustration of the greatest conceivable simplicity.


A colonial farmer, whose log but stands by itself in the primeval forest, far away from the busy haunts of men, has just harvested five sacks of corn. These must serve him till the next autumn. Being a thrifty soul he lays his plans for the employment of these sacks over the year. One sack he absolutely requires for the sustenance of his life till the next harvest. A second he requires to supplement this bare living to the extent of keeping himself hale and vigorous. More corn than this, in the shape of bread and farinaceous food generally, he has no desire for. On the other hand, it would be very desirable to have some animal food, and he sets aside, therefore, a third sack to feed poultry. A fourth sack he destines for the making of coarse spirits. Suppose, now, that his various personal wants have been fully provided for by this apportionment of the four sacks, and that he cannot think of anything better to do with the fifth sack than feed a number of parrots, whose antics amuse him. Naturally these various methods of employing the corn are not equal in importance. If, to express this shortly in figures, we make out a scale of ten degrees of importance, our farmer will, naturally, give the highest figure 10 to the sustenance of his life; to the maintenance of his health he will give, say, the figure 8; then, going down the scale, he might give the figure 6 to the improvement of his fare by the addition of meat, the figure 4 to the enjoyment he gets from the liquor, and, finally, to the keeping of parrots, as expressing the least degree of importance, he will give the lowest possible figure 1. And now, putting ourselves in imagination at the standpoint of the farmer, we ask, What in these circumstances will be the importance, as regards his wellbeing, of one sack of corn?


This, as we know, will be most simply tested by inquiring, How much utility will he lose if a sack of corn gets lost? Suppose we carry out this in detail. Evidently our farmer would not be very wise if he thought of deducting the lost sack from his own consumption, and imperilled his health and life while using the corn as before to make brandy and feed parrots. On consideration we must see that only one course is conceivable: with the four sacks that remain our farmer will provide for the four most urgent groups of wants, and give up only the satisfaction of the last and least important, the marginal utility—in this case, the keeping of parrots. The only difference, then, that his having or not having the fifth sack of corn makes to his wellbeing is that, in the one case, he may allow himself the pleasure of keeping parrots, in the other he may not; and he will rightly value a single sack of his stock according to this unimportant utility. And not only one sack, but every single sack; for, if the sacks are equal to one another, it will be all the same to our farmer whether he lose sack A or sack B, so long as, behind the one lost, there are still four other sacks for the satisfying of his more urgent wants.


To vary the illustration, assume that our farmer's wants remain the same, and that he has only three sacks of grain. What now is the value of one sack to him? The test again is quite easily applied. If he has three sacks he can and will provide for the three most important groups of wants. If he has only two sacks, he will be obliged to limit himself to the satisfying of the two most important groups and give up the satisfying of the third, that of animal food. The possession of the third sack—and the third sack, be it remembered, is not a definite sack but any of the three sacks, so long as there are other two behind it—directly carries with it, therefore, the satisfaction of his third most important want; that is, the last or least of those wants covered by the three sacks which constitute his total stock. Any estimate other than that according to the marginal utility would, in this case also, obviously run counter to facts, and would be quite incorrect.


Finally, suppose that our farmer's wants remain as before, and that he only possesses one single sack of corn. In this case it is perfectly clear that all less important methods of employing the corn are out of court, and that it will be devoted to and spent in sustaining the farmer's life—a function for which it just suffices. And it is as clear that if this single sack fails the farmer will no longer be able to support himself in life. His possession of the sack, therefore, means life; his loss of it means death; the single sack of corn has the greatest conceivable importance for the wellbeing of the farmer. And all this is still in conformity with our principle of marginal utility. The greatest utility—the preservation of life—is here the sole, as well as the last or marginal utility.


These estimates according to marginal utility are not merely "academic." No one will doubt that our farmer on due occasion—say, on an offer made him for the corn—would act practically according to the same estimates. Any one of us, placed in his position, would undoubtedly be inclined to let one of the five sacks go pretty cheap in consideration of and in correspondence with its small marginal utility. He would charge considerably more for one of the three sacks. And he would not let the irreplaceable single sack, with its enormous marginal utility, go for any price whatever.


Transfer, now, the field of illustration from the solitary in the primeval forest to the bustle of a highly organised economic community. Here we encounter, in an altogether dominating position, the empirical proposition that quantity of goods stands in inverse ratio to value of goods. The more goods of one kind there are in the market, the smaller, ceteris paribus, is the value of the single commodity, and vice versâ. Every one knows that economic theory has made use of this empirical proposition—the most elementary proposition in the doctrine of price—to establish the law of "Supply and Demand." But this proposition maintains its validity quite apart from exchange and price. For instance, how much more value does a collector put upon the single specimen, which represents a class in his collection, than upon one of a dozen of such specimens? It is easy to show that well-authenticated facts of experience like these follow, as a natural consequence, from our theory of marginal utility. The more individual goods there are available in any class, the more completely can the wants to which they relate be satisfied, and the less important are the wants which are last satisfied—those whose satisfaction is imperilled by the failure of one of the goods. In other words, the more individual goods there are available in any class, the smaller is the marginal utility which determines the value. If, again, there are available so many individual goods of one class that, after all the wants to which they are relative are completely satisfied, there still remains a number of goods for which no further useful employment can be found, then the marginal utility is equal to zero, and a commodity of that particular class is valueless.


Here, then, we have an entirely natural explanation of the phenomenon which originally struck us as so surprising, that comparatively "useless" things, such as pearls and diamonds, have so high a value, while infinitely more "useful" things, like bread and iron, have a far less value, and water and air no value at all. Pearls and diamonds are to be had in such small quantities that the relative want is only satisfied to a trifling extent, and the point of marginal utility which the satisfaction reaches stands relatively high.*11 Happily for us, on the other hand, bread and iron, water and light, are, as a rule, to be had in such quantities that the satisfaction of all the more important wants which depend on them is assured. Only very trifling concrete wants, or no wants at all, are dependent, for instance, on the command over a piece of bread or a glass of water. It is, of course, true that in abnormal circumstances—as, for instance, in besieged towns, or in desert journeys, where water and food are scarce, and small stores only suffice to meet the most urgent concrete wants of meat and drink—the marginal utility flies up. According to our principles the value of those goods, otherwise of so little account, must rise also, and the inference finds ample empirical confirmation in the enormous prices paid in such circumstances for the most wretched means of subsistence. Thus those very facts which, at first sight, seemed to contradict our theory that the amount of value is dependent on the amount of utility conditioned, on closer examination afford a striking confirmation of it.

Notes for this chapter

Ueber den Ursprung und die Hauptgesetze des wirtschaftlichen Werthes, p. 128. Jevons has the expressions "final degree of utility" and "terminal utility." With Menger, who first formulated the above law with entire clearness, but gets along without the convenience of a short technical expression, the law runs as follows (p. 98): "In every concrete case, accordingly, of the satisfactions of want guaranteed by the total quantity of goods, it is only those which have the smallest importance for the person that are dependent on his command over a definite part-quantity of the amount of goods at his disposal; and the value of a part-quantity of the available amount of goods is, accordingly, equal to the importance which the satisfactions of want that are least urgent among all the satisfactions guaranteed by the total quantity, and obtainable with a similar part-quantity, have for that person."
Even where men do not act egoistically but altruistically, they have occasion to consider the marginal utility, viz. that marginal utility which the goods given away have to the persons who get them. One gives donations, charities, and the like, when the importance of such, measured by their marginal utility, is very much higher as regards the wellbeing of the receiver than as regards that of the giver, and almost never when the converse is the case. I am glad to know that, in the idea expressed above, I am at one with so distinguished an economist as Walras. I can only express my entire concurrence with what he says, in the preface to his Théorie de la Monnaie, p. 11, as to the universal importance of the idea of marginal utility, both as regards theory and as regards the practice of economic life.
To guard against possible confusion it should be noted that the German writers on value generally speak of "satisfaction of want" under the metaphor of a descending scale: the increasing satisfaction creeps down the scale, and the point of saturation is zero, not 100.—W. S. Book III, Chapter V

End of Notes

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