An Introduction to the Theory of Value

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

Second Edition – 1910

by William Smart (1853-1915)

Chapter VII
Complementary Goods

ITV-E2-7.1 As the ultimate goal of economic effort is not the obtaining of goods but the satisfaction of human want, we are not finished with our subject till we have traced the finished good to its end and raison d’être in affording this satisfaction. In the present chapter we have to consider cases where several goods contribute to one satisfaction, and to find what influence this has upon their separate values. In such cases the “good” we have to value is, properly speaking, a group, and in the various forms taken by these groups, we meet with some puzzling and far-reaching peculiarities.
ITV-E2-7.2 The class of Complementary goods, to use Menger’s term, is much wider than we are apt to suppose. In consumption goods, it tends to increase with the variety of modern wealth and the development of new tastes. Many of our enjoyments depend on the co-operation of a great many factors, of which usually one is prominent, and the others only assert themselves on rare occasions. Thus the part played by that insignificant commodity, salt, in most of the pleasures of the table, is never appreciated till the want of it – say, at a pic-nic – suggests how indispensable a complement it is. Among productive goods, again, where the division of labour is constantly adding to the number of factors which work together in the making of any good, the complementary character becomes even more apparent. The first thing to be noticed here is that the value of a group, as a group, is determined by the marginal utility of the group, not of the separate members. But, as each group may on occasion be broken up, the interesting question is as to the distribution of value among the members, the difference in value between goods as complements and goods as isolated articles.
ITV-E2-7.3 The simplest case is where the single members of a group are all useless in any other form but that of a group, and are at the same time economically irreplaceable. In valuing boots, for instance, the “good” is the pair; if I lose one, I lose the entire utility. In such cases – which are, of course, comparatively rare – if I have had the pair and lose one, I lose the entire value of the pair: if I have one and obtain another, I gain the entire value of the pair. Here, then, the value of one single member of the group is the same as the value of the whole group.
ITV-E2-7.4 This case, however, is really of importance only as introducing the others which follow; under the assumed conditions we are dealing with a good similar, say, to a pair of compasses or a pair of spectacles, which we can divide in two only at the cost of the compasses or spectacles; that is to say, it is only externally a group.
ITV-E2-7.5 A more common form is where the group can afford one utility, and the individual members of it in isolation can afford another but a less utility. Thus the utility of a well-matched pair of roans will be valued at a figure much higher than would be realised by selling the horses separately. Suppose that the utility of the pair is represented by 100, and that of A roan and B roan separately by 50 and 40: what is the value of A? To calculate it from the side of the owner: if he has A and B, he has a value of 100; if he lose A, he has only B, and B separately has a value of only 40. What he has lost is the difference between 40 and 100. Or, from the side of the buyer: if he gets B he obtains 40; if he gets A in addition he obtains 100; the value of A, as before, is the difference between 40 and 100. Here, then, A has a different value as complement and as isolated good: in the one case it is worth 60, in the other 50. If we take the case of a well-matched four-in-hand team we have a more complicated instance of the same; the whole team makes the most highly valued group, but each pair within that again has a higher group value than the sum of the isolated values which would be attached to each single horse. This case of valuation holds in the very numerous cases where goods are in sets: if we “break the set,” the separate members have a less value than they had as complements.
ITV-E2-7.6 A third case is, where, as before, the group can afford one utility, and the individual members of it separately can afford a less utility, but where some members are replaceable and some are not. In this case the replaceable members can never obtain any other than the one value: however indispensable they may be to the making of the group, goods that can be easily replaced cannot rise higher than the competition of all other uses allows. Although a load of bricks, for example, were absolutely indispensable to finish the building of a house, the load could never obtain any higher value than that determined by the marginal utility of bricks generally: that is, as determined by all the uses to which bricks generally are put. To the irreplaceable member, on the other hand, falls the remainder of the value of the group. Thus suppose a group A, B, and C, with a group value of 100, and isolated values of 10, 20, 30. If A and B are articles of large manufacture and great demand, while C is a monopoly good, A and B will get 30% of the value, and C the other 70%, although, if the other members were not present in the group, the only value C could realise would be 30.1

ITV-E2-7.n1.1 1 How far the theory of Complementary Goods admits of being applied directly to the problem of distribution of product among the various factors is matter of controversy. Böhm-Bawerk considers that it is the key which will lead to its solution. The line which this suggests would be something like the following. Labour and Capital enter into the composition of all productive groups: in proportion as they are abundant and mobile do they enter into competition with all labour and all capital, and become perfectly replaceable. In entering into products, then, they can never secure more than their outside value – that fixed by all their employments or uses. The surplus in the price of each product goes to the monopolist factor, whether that monopoly be caused by natural and site advantages of land, mental and technical qualities of undertakers and workers, peculiar conditions of process, or the like. And in proportion as these factors lose their monopoly, does the value of the group shrink; if all the members were to become replaceable, as when first-class land in other countries becomes available through rapid and cheap carriage, or education makes unskilled labour the exception, the group value, as distinct from the combined isolated values, would disappear.
ITV-E2-7.n1.2 Wieser, again, considers that this is no more than a valuable suggestion. What guidance, he asks, will this law give where there are several irreplaceable members, and how is the outside value of replaceable members given if not in other combinations of complementary goods which in turn require to be split up into their factors? He points out acutely, in reply to Menger, that, to estimate the proportion contributed by any factor by the loss which would accrue if that factor were absent, is to reckon too much to it, as the loss of a factor from a co-operation will generally disorganise the group and cause more damage than its presence would cause gain. Instead of using the doctrine of Complementary Goods in this way, he proposes to find, by a series of equations, what each factor positively contributes; not, of course, the physical share, but the proportion of value which may be economically “imputed” to it. A great part of the Natürlicher Werth is taken up with this doctrine of the “Zurechnung,” which is treated in Wieser’s usual strong and graphic manner.

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