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An Introduction to the Theory of Value

on the Lines of Menger, Wieser, and Böhm-Bawerk

First Edition – 1891


by William Smart (1853-1915)


Chapter V
The Marginal Utility


ITV-E1-5.1 Thus far we have seen that, utility being the general relation in which all goods, by their very definition, stand to human wellbeing, value is that higher, more intimate, more limited relation in which some particular importance to human wellbeing is conditioned by the having or losing of some particular good, and a relation of actual dependence is established between the want and the good. We pass now to the positive consideration of the measurement of value.
ITV-E1-5.2 If one good stands over against one want; that is to say, if the satisfaction of a single want is dependent on the possession of or power over a single good, there is no difficulty: the value is the entire utility which the good affords in the given case.
ITV-E1-5.3 But the estimates of value which practically concern us are not so simple. We must face the fact that most goods which we have to value are present in stocks, and that, at the same time, most goods are capable of satisfying several wants. Water, for instance, may be used for drinking, for washing, for cooling, for ornamental fountains, etc., as books may be used for reading, for lending, for ornament, for packing, for waste paper and so on. But these are wants of very varying importance, and the question is: Which of these wants is it that determines the value? This important point cannot be too plainly put, and I follow the Austrian writers generally in risking being tedious rather than obscure.
ITV-E1-5.4 A sailor and his dog, the sole survivors from a wreck, have been tossing on a raft for many days. Land is in sight, but still far away, and the provision is reduced to a couple of biscuits. Both dog and man are equally famished, and it is evident that, unless each gets a biscuit, one of them will not live to reach the shore. Here we are confronted with the opposing claims of two wants, that of the sailor and that of his dog; and, as the sailor is, presumably, the valuer, the two wants are of very different importance to him. The question is, what measures the value of the biscuits? According to our formula the answer will be found by ascertaining which is the dependent want – which is the satisfaction that the biscuits condition.
ITV-E1-5.5 At first sight one would say that the actual destination of the biscuits determined this, but that would be to say that two exactly similar biscuits, both available to the one man, and available under exactly similar conditions, were of different value. In this dilemma one little consideration easily determines the point. If one of the biscuits were lost, which want would go unsatisfied? For the want which is satisfied if the good is present, and unsatisfied if it is not, is evidently the dependent want.1
ITV-E1-5.6 The dependent want, in this case, is that of the dog; that is, it is the less important of the two wants.
ITV-E1-5.7 To put it now in more general terms. As we saw, the (necessarily) limited resources at each man’s disposal he, consciously or unconsciously, apportions out among his various wants according to his particular scale, taking care that the more urgent ones are provided for before the less urgent. It is obvious that, in these circumstances, there is a least want that is satisfied, although ordinarily we are not conscious what it is. But it immediately comes to the front when, from any cause, our resources are diminished. If a working man’s wage is reduced from twenty shillings to nineteen shillings a week, he becomes painfully conscious that some want, hitherto satisfied, must go bare, and the particular want on which he economises immediately points out which was his least, or least urgent, or final want. Here all the wants previously satisfied are still satisfied with the exception of this last one, and thus none of them depended on having or losing the shilling. Again, all wants under this, just as before, remain unsatisfied whether the shilling is there or not. Only this marginal want is satisfied if the shilling is present and unsatisfied if absent: it alone, then, is the dependent want.
ITV-E1-5.8 To recur to our illustration. So long as the sailor had the two biscuits, one of them would go to satisfying the higher want (his own), and the other to satisfying the lower want (the dog’s), and either biscuit was capable of satisfying either want. But, when one biscuit was lost, the one that remained was instantly elevated to satisfying the higher want only: it rose, literally, in value because then it was not a man’s or a dog’s life that depended upon it but a man’s only; what was lost was the means of satisfying the dog’s want: the less important of the two wants was the dependent one; and it is the relation of dependence, as we said, that determines value. We may formulate the proposition thus. The value of a good is measured by the importance of that concrete want which is least urgent among the wants satisfied. And we find that what determines the value of a good is, not its greatest utility, not its average utility, nor yet its least conceivable utility, but its marginal utility in the given circumstances. Jevons called this the Last or Final Utility. We shall follow Wieser literally in calling it the Marginal Utility. Simple as this proposition is, my experience in teaching tells me that it is not easily retained so as to be used. For this reason I do not consider it superfluous to confirm its truth by testing it in various circumstances. I cannot improve on Böhm-Bawerk’s admirable illustration, and only modify it in non-essential particulars.
ITV-E1-5.9 A modern Robinson Crusoe has just harvested five sacks of corn. These must be his principal maintenance till next harvest. He disposes of the sacks, according to the scale of his wants, in the following way. One sack he destines for his daily allowance of bread. Another he devotes to cakes, puddings, and the like. He cannot use more than these in farinaceous foods, so he devotes a third to feeding poultry, and a fourth to the manufacture of a coarse spirit. With these four sacks, we shall say, he is able to satisfy all the wants that occur to him as capable of being directly satisfied by corn, and, having no more pressing use for the fifth sack, he employs it in feeding dogs and cats and other domestic animals whose company is a solace to his lonely life. The question is: What to him is the value of a sack of corn? As before, we ask: What utility will fail him if he lose one sack? It is inconceivable that Crusoe should have any doubt as to his answer: he will, of course, apportion out the sacks that remain as before; – two to food, one to poultry, one to spirits, and he will give up only the feeding of the domestic animals. This is seen to have been the Marginal Utility – the utility on the margin of economic employment or use. What he loses, then, by losing one sack is his former Marginal Utility; and this marginal utility undoubtedly determines the value of a single one of the five sacks. But here we come upon another feature of this valuation. If the marginal utility determine the value of one, it must determine the value of all, as, by hypothesis, all sacks were alike, and therefore all interchangeable. Thus we obtain the universal formula for the valuation of goods in stocks. The value of a stock of similar goods is the value of the marginal good multiplied by the number of goods in the stock.2
ITV-E1-5.10 To follow the illustration out. If another sack gets lost, the marginal utility is found to have been that of the making of spirits: if still another, the feeding of poultry. Finally, suppose Crusoe to be reduced to the one sack: the satisfying of all lesser wants is out of the question: the losing of it means death to him: the marginal utility and the highest utility are one.
ITV-E1-5.11 Again, suppose Crusoe as merchant bargaining, say, with the Spaniards. If he have five sacks he will sell one at a low rate; if he have four, he will ask a higher price; if he have only one, he will not part with it for any money. Extend this to the phenomena of an industrial community. The five sacks represent a larger supply than the four, the four than the three, and so on; and, as the supply decreases, the value of the single sack rises. Now one of the commonest phenomena of a market is that, ceteris paribus, increase of supply brings down value and decrease of supply sends it up. To put it in terms of our theory: When the quantity of any good produced is increased, the good is put to lower levels of use; the last want supplied determines the last satisfaction; and this last satisfaction determines the value of all the stock. Here we have the explanation of the old paradox of value. If any commodity is available in such quantity that all possible wants for that commodity are supplied, and yet there is a surplus of the commodity, the marginal utility is zero, and the value of the entire stock is nil. And it is also explained how diamonds have a high value compared with bread. The quantity of diamonds available is never sufficient to satisfy more than a fraction of the desire for them: the marginal utility, then, is high. Bread again is, happily, to be had everywhere at a comparatively small expenditure of labour, and the immense supply, as compared with the limited wants, puts the marginal utility low.



NOTES:
ITV-E1-5.n1.1 1 There are two typical cases where valuations are made: – where a man values something he has, with the view of parting with it (in selling, giving, lending, etc.), and where he values something he has not, with the view of acquiring it. As will be seen from above, the two methods of valuation come practically to the same result.
ITV-E1-5.n2.1 2 The reader will understand that, in an illustration like this, it is unsafe to use definite figures to express subjective estimates. The above formula is quite familiar in ordinary exchange where, as we shall see on p. 49, purely subjective valuations have been corrected and leveled by social and commercial valuations. If stocks of entirely similar articles are sold openly in a market, the calculation of the total value is; – units of stock  last price obtained per unit. But, if we were to represent the decreasing (subjective) values, as we should be apt to do, by the figures, per sack, of 5, 4, 3, 2, 1, we should conclude that the value of a stock of one sack and that of a stock of five sacks is the same (5 = 5  1). But in a case like Crusoe’s, or in similar economic circumstances – say in a sieged town – the subjective value of one sack, a sole stock, is infinity.



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