The Positive Theory of Capital

CHAPTER IX

THE VALUE OF COMPLEMENTARY GOODS

IT very often occurs that, in order to obtain an economic utility, several goods require to co-operate in such a way that, if one good falls out of its place, the utility cannot be obtained, or cannot be completely obtained. Goods whose uses thus supplement each other we may follow Menger in calling Complementary goods. Thus, for instance, paper, pen and ink, needle and thread, cart and horse, bow and arrow, right and left hand gloves, and so on, are complementary goods. This complementary character obtains generally, indeed almost universally, among productive goods.

It is easy to see that the intimate co-relation of complementary goods—the co-relation in which they afford this utility—will be reflected in the formation of their value. This leads to a number of peculiarities, all, however, occurring within the limits of the universal law of marginal utility. In stating these we must distinguish between the value which belongs to the complete group, and that which belongs to individual members of it.

The total value of the complete group adapts itself, as a rule, to the amount of the marginal utility which it is capable of affording as a group. If, for instance, three goods, A, B, and C, form a complementary group, and if the smallest utility economically obtainable by the joint employment of these three goods amounts to a value of a hundred, the three goods A, B, and C taken together will be worth a hundred.

The only exception to this rule occurs in those cases where, on the general principles with which we are now familiar, the value of a good is to be measured, not by the immediate marginal utility of its own class, but by the marginal utility of other classes of goods drawn on to serve as substitutes. In the special case under consideration this will occur if every individual member of the complete group is replaceable by purchase, or production, or even by taking a substitute out of some other isolated employment, and if, at the same time, the total sum of the utility which the substituted goods would otherwise (in isolation) have had is less than the marginal utility they afford as combined. If the latter, for instance, amounts to 100, while the substitutionary value, the value of the three members individually, is only 20, 30, and 40—that is in all 90,—the thing that depends on the group of three is not the obtaining of the combined utility of 100—which is, in any case, assured by the substitutionary goods—but only the obtaining of the smaller utility, the 90, which fails of its provision when the members are taken away and become substitutes in the group. Since, however, in such cases the complementary character has, properly speaking, no influence on the formation of value, and the value is simply determined according to the ordinary laws already familiar to us, we need not give any separate consideration to this. In what follows, then, I shall give particular attention only to the normal case, where the marginal utility attainable by goods in joint employment is, at the same time, the true marginal utility.

As was before remarked, this marginal utility, first of all, determines the united value of the whole group. But in the manner in which this total value is divided out among the single members of the group, considerable differences emerge, varying with the casuistical peculiarity of the case.

First, if none of the members admits of any use other than the joint use, and if, at the same time, no one member which co-operates towards the joint utility can be replaced, then one single member has the full total value of the group, and the other members are entirely valueless. Suppose, for instance, I pay five shillings for a pair of gloves, five shillings is the total value of the pair. If I lose one of the gloves I lose the whole utility, and, with it, the whole value of the pair; and the remaining glove has no value. Of course either of the two gloves equally admits of either valuation, and it is simply circumstances that decide which of them is to rank as all, and which as nothing—the glove needed to complete the pair, or the useless single glove. Cases of this kind are relatively scarce in practical life.

Second, and more common, is the case where the individual members of the group can afford another, though a less utility, outside of their joint employment Here the value of the single member does not lie between everything and nothing, but between the amount of the marginal utility which it is capable of affording in isolation as minimum, and the amount of the joint marginal utility, after deducting the isolated marginal utility of the other members, as maximum. Suppose, for instance, that three goods, A, B, and C, in co-operation afford a marginal utility of 100; that A by itself has a marginal utility of 10, B by itself of 20, and C by itself of 30; the value of A is determined as follows. If a merchant owns this good by itself he can get from it only its isolated marginal utility of 10, and the value of the good, accordingly, is only 10. But suppose he owns the whole, group, and is asked to sell or give away the good A out of that group, what he has to consider is that, with the good A he can get a marginal utility of 100; without it, only the smaller (isolated) utility of the goods B and C, that is 20 + 30 = 50; and that, accordingly, on the having or losing of the good A depends a difference in value of 50. As complement of the group it is, therefore, worth 100—(20 + 30) = 50; as an isolated good it is worth only 10.1 Here the difference in value is not so extreme as in the first case, but still it is very considerable.

Third, and more common still, is the case where some individual members of the group are not only employed for other purposes, but are, at the same time, replaceable by other goods of the same kind. For instance, building ground, bricks, beams, and labour are complementary goods in the building of a house. But if a few carts of bricks, intended for the building, go astray in transit, or some of the labourers engaged for the job refuse to work, in normal circumstances this does not in the least hinder the obtaining of the joint utility—the built house. The labourers and materials are simply replaced by others. The consequences as regards the formation of value are as follows:—

1.   The replaceable members, even if they are needed as complements, can never obtain any higher than their “substitution value”—viz. the value conferred by the utility in those branches of employment from which the replacing goods are obtained.2

2.   This fact considerably contracts the limits within which the value of the individual good—estimated some-times as complementary, sometimes as isolated good—may be determined, particularly when it is a common marketable good. The more numerous the available goods of any kind, and the more numerous the opportunities of using them, the smaller will be the difference between the importance of that use from which a replacing sample might be drawn, as maximum, and the use next to it in rank, in which a superfluous isolated good might be employed, as minimum of value. If, for instance, besides the good A, which we shall call A1; contained in the complementary group, there are two other similar goods A2 and A3, and if the possible opportunities of use (outside of employment in the complementary group) possess an importance indicated by the numbers 50, 20, 10, and so on, only the uses indicated by 50 and 20 would be filled by the goods A2 and A3, and if one of these two were taken to replace the good A1 a utility of 20 would be lost. On the other hand, if the complementary group were broken up, and the good A1 itself obliged to seek for an isolated and inferior employment, its only chance would be the third, that indicated by 10. Thus its value would always lie between 10 (isolated) and 20 (complementary). But if, instead of three, there are a thousand goods, and a thousand opportunities of using them, the difference between the 1000th employment (from which the good required to replace the other must in case of need be drawn) and the 1001st (in which the good must look for employment if it becomes superfluous through the breaking up of the group) will certainly fall to a quite insignificant amount.

Now, of course, it is not likely that any one individual, within the limits of his own economy, will possess a thousand goods of one kind, and a thousand different opportunities of employing them. But, all the same, the efficiency of the influences just described is in no wise annulled; it is only the scene of their operation that is changed, from individual economy to the market, and that in the following way. Individuals buy what they require, and sell their surpluses in the market. Here, then, all the stocks of goods and all the opportunities of employing them over the entire field covered by the market, come together. And now—exactly as before—everything depends on whether, in the market, commodities and opportunities of employing them are scarce or not. If the commodity is very scarce, it makes a very considerable difference in the determination of price whether we approach the particular good as buyer or as seller. For instance, suppose, as before, that there are only three similar goods, and three buyers each wishing to acquire just one such good, with the view of using it in employments that will yield 50, 20, and 10. Then, if one of these goods be withdrawn from the market to serve in a complementary employment, the two remaining goods are bought for the employments indicated by 50 and 20, and—according to laws which will be explained in next book—the purchase price must be fixed between 10 and 20, say at 15. But if now the complementary employment fails, and the third good also is thrown on the market, it must—if it is to find a sale at all—fall to the buyer who can get 10 by employing it, and the result is that the market price is in all cases fixed below the level of 10. Here, then, the price—and the subjective exchange value based on it—varies not inconsiderably.

If, on the other hand, there are a thousand similar goods offered, and a thousand buyers demand them, evidently it will not make the smallest difference to the market price whether there appears a thousand and first buyer, or a thousand and first seller; the good obtains a price and value independently of whether it finds a place in the single complementary employment or not.

Thus, under the assumptions now laid down, the value of the replaceable members is fixed at a certain level independently of their concrete complementary employment, and this value they have when we distribute out the total value of the group among its individual members. The distribution, then, will be made thus: of the total value of the whole group—which is determined by the marginal utility of the joint employment—this fixed value is previously assigned to the replaceable members, and the remainder—which varies according to the amount of the marginal utility—is reckoned to the non-replaceable members as their individual value. To use our old illustration again; say that the joint marginal utility amounts to 100, and that the members A and B have a fixed “substitution” value of 10 and 20 respectively, 70 must be reckoned the individual value of the non-replaceable good C; or, say that the marginal utility of the group amounts to 120, the individual value of C will be 90.3

Of the three cases we have discussed the last mentioned is by far the most common in practical life, and, accordingly, in the great majority of cases, the value of complementary goods is determined according to the latter formula. The most important application of it is in the distribution of the product among the various productive powers co-operating in producing it. Almost every product is the result of the co-operation of a group of complementary goods consisting of uses of ground, labour, fixed and floating capital. Of the complementary members the great majority are marketable commodities, and replaceable at will; as, for instance, the labour of wage-earners, the raw materials, fuel, tools, etc. Only a few of them are non-replaceable, or not easily replaceable; as, for instance, the land on which the peasant works, the mine, the railway lines, the factory walls, the activity of the undertaker himself with his peculiar and high qualifications, and so on. It is easy to see, therefore, that here we have exactly those casuistical circumstances in which the foregoing formula of distribution obtains, and, as a fact, it is acted upon in practical life in the most accurate way. In actual business the “costs “are first deducted from the total return. If we look closer, however, we shall see that what is deducted is not all the costs—for, if so, the use of ground, or the undertaker’s activity, as both valuable goods, would come under costs—but only the expenditure for the replaceable means of production with a given substitution value, viz. the wage of labour, raw materials, wear and tear of tools, etc. The remainder, under the name of “net return,” is ascribed to the non-replaceable member or members: the peasant calculates it to his land, the mine-owner to his mine, the manufacturer to his factory, the merchant to his undertaking activity.

If the joint returns increase, it would not occur to anybody to ascribe the surplus to the replaceable members; it is always the ground or the mine that “produces more.” And, similarly, if the joint returns decrease, nobody would credit the “costs “with the reduced amount; the deficiency also is conceived as exclusively due to the diminished productiveness of the ground or the mine. And this is entirely logical and correct: on goods replaceable at any moment only the fixed substitution value is actually dependent; the entire remainder of the joint amount of utility obtainable depends on the goods that cannot be replaced.

The theory of the value of complementary goods is the key which will solve one of the most important and difficult problems of political economy—the problem of the distribution of goods as made in the present state of society, where competition is more or less free and prices are determined by free contract. All products come into existence through the co-operation of the three complementary “factors of production,” labour, land, and capital. Now our theory, in showing how much of the joint product may economically4 be considered as due to each of these, and what share of the total value may, accordingly, be assigned to each of them, lays down, at the same time, the most decisive basis for determining the amount of remuneration which each of the three factors obtains. And thus although, as we know, capital as “factor of production “does not exactly coincide with capital as “source of income,” yet this gives us at least a rough indication of the way in which the amount of the three branches of income—wage, rent, and interest—is determined.

It does not indeed do this quite directly. That quota which the workers receive, and that other quota which the owners of the co-operating ground receive, is directly identical with wage and rent. But the quota which falls to the co-operation of capital is not interest—as, in theories of distribution, economists have repeatedly assumed ever since the days of Say with fatal precipitation. It is, first, the gross remuneration for the co-operation of capital; and, out of this, interest is got, like a kernel out of a shell, because, and to the extent that, something remains over after deducting from the gross remuneration the value of the worn-out capital. To explain how this is so is a problem in itself. To make it quite clear by an illustration, suppose that a commodity, produced by the co-operation of all three factors, is worth £100. The law of complementary goods will carry us thus far; it will enable us to determine that the share of labour (the labour directly employed in the production) amounts to, say, £20, that of ground to £10, that of capital to £70. But it does not tell us what, or how much, of that £70 remains over net, as interest, after deduction of the wear and tear of capital. On the contrary, the law of complementary goods in itself would rather lead us to the conclusion that nothing remains over. For, according to it, it would be most natural to assume that the capital, to the co-operation of which the return of £70 is ascribed, and which has been consumed in obtaining that return, had already been valued at the entire £70; and, if this were the case, the return to capital would naturally be entirely absorbed by the wear and tear of the capital. That this is not the case is, so to speak, an internal matter—a matter which plays its part inside the gross share of capital determined by the law of complementary goods, and is the object of an independent problem, the peculiar problem of Interest. But before we can discuss interest there is still a great deal to be explained.5

6 Of course in this case also the peculiarities of the case decide which member is to be valued as the completing member of the group, and which as simply the isolated piece. If, for instance, the owner of the complete group is asked to sell the good A, he will value it as completing member, and the other goods B and C as isolated pieces. But if he is asked to sell C, he will value it as completing member at 100 - (10 + 20) = 70, while A and B will be valued as isolated pieces.

7 To put it concretely: although a load of bricks were absolutely indispensable to finish 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.—W. S.

8 If C also were replaceable by a substitute of less value the case mentioned oil p. 170 would emerge, and the marginal utility of the joint use would not determine the value of the complementary group.

9 Not physically. It would, in most cases, be absolutely impossible to calculate the physical share—how could one be supposed to distinguish what percentage the material and what percentage the artist had contributed physically to the making of a statue?—but it is also a matter of no importance. On the other hand it is, in most cases, quite easy to determine what share of the utility, or of the value, would have to be done without if one were not in possession of a definite individual factor, and this quota, conditioned by the possession of one factor, I call its economical share in the total product.

10 The confusion, so common in economic literature, between the gross share assigned to the co-operation of capital (Rohzins) and net interest, has been fully discussed in my Capital and Interest (see the criticism of Lauderdale, p. 146; of Carey, p. 155; of Strasburger, p. 175; of Say, p, 189, etc.) It will not be expected of me to give a complete theory of distribution in the passing, as it were. I purposely refrain from going deeper into the subject than is necessary for my special task, the development of the Interest theory. And for this it is sufficient to sketch only in the broadest lines the principles which limit the gross share of capital, as against the shares of labour and uses of land that co-operate with it: our special task will be to lay down what is the state of the case as regards the gross share of capital. Moreover I hope that on this question of the shares allotted to the various factors, which I am compelled to treat in a very cursory way, the eagerly expected work of Wieser will very shortly shed a clear light. (Wieser’s Der Natürliche Werth, Vienna, 1889, appeared while this was passing through the press.—W. S.)

• 1See Monger’s Grundsätze der Volkswirthschaftslehre, p. 93.
• 2See my Capital and Interest, 1890, p. 111.
• 3P. 219 (German edition, p. 266). See also my Hechte und Verhältnisse, p. 51. Innsbruck, 1881.
• 4See Mill’s Principles, i. 1. 2.
• 5If we were to carry our analysis of what man does in production a step further, we might appropriately distinguish three fundamental ways in which the producing man “moves things.” The first is what, for want of a better name, we may call simple movements or changes of place—where men transport entire objects from one locality to another. Thus the miner brings the ore from the depths of the shaft to the upper air; the merchant takes his goods from the place where they are produced to the place where they are demanded and used. The second embraces those movements of parts of one and the same object whereby it experiences a change of form, as when nails are made from iron, statues from marble, pipes from clay, dials from ivory, combs from caoutchouc, tumblers from glass, furniture from wood. The third, and much the most common way, is where different objects are brought together in space to form combinations of matter. These combinations may be merely temporary, or they may be lasting. Instances of the one are where the stamp falls on the coin, the chisel chips at the marble, the carving tool is applied to the wood, the ore put into the furnace, the yarn into the loom, the paper under the printing press, the stuff under the shears, the plough through the clods. Instances of the other are where we build a house out of wood, stone, lime, iron, etc.; where we put together a watch out of wheels, springs, pendula, weights, stop-action and many other things; in fact in manufacture generally. I must warn the reader that this division into three fundamental forms neither has, nor is meant to have, the character of strict scientific classification. Indeed, these forms merge in many instances into one another. Temporary combinations, for instance, are very often half-way to changes of form, and what I have called a simple change of place is at the same time, in a certain point of view, a material combination, a bringing together of the thing moved and the object (personal or impersonal) to which it is moved. This division, however, will make it easier to find our reckoning, and will prove too, if necessary, the correctness of the general characteristics which I have ascribed in the text to productive processes. I mean to say that it is easy to see that every productive activity which one can think of ranges itself under some one of these three fundamental forms, and to that extent it is proved that such an activity must, a fortiori, range itself also under the general formula given in the text, where we have described the nature and method of the production of material goods as the mastery of natural powers by means of putting objects in motion.
• 6If we try to represent the classification of our wants by a typical scheme we must, on the principles just laid down, give it something like the following shape:—
• 7When we are told that capital assists in the production of wealth, and then again that it assists in the obtaining of wealth for its owner, we are apt to jump to the conclusion that the two phenomena are intimately and essentially connected, and that the one is the immediate result of the other—that capital can bring wealth to its owner because capital assists in the production of wealth. As a fact, Political Economy has taken up this idea only too readily and too completely. Captivated by the deceptive symmetry that exists between the three great factors of production—Nature, Labour, Capital—and the three great branches of income—Rent, Wage, and Interest—the science, from Say’s day till the present, has taught that these three branches of income are nothing else than the payment for the three factors of production, and that Interest in particular is nothing else than the compensation which capital receives for its productive services when the product is divided out among society. Propounded by various interest theories in various forms this idea has found its most concise and, at the same time, its most naive expression, in the well-known “Productivity theories”—those theories which explain interest directly as the natural fruit of a productive power peculiar to and resident in capital.
• 8The theory of the use of goods I have already gone into at length in Capital and Interest. I there showed that material goods are nothing else than such distinct forms of matter as admit of the natural powers residing in them being directed to human advantage. I showed how the “use” they afford is realised through concrete activities of these natural powers, and, therefore, by real forth putting of power. I showed how a use (Gebrauch or Nutzung) cannot be made of them otherwise than by taking the peculiar forms of the energy of the good at the proper moment, supplying the conditions necessary to render them available where they previously existed in an unavailable form, and then bringing these forms of energy into proper connection with that object in which the useful effect is to take place. On these considerations I based the conception of the “Material Services” (Nutzleistungen) which I believe to be the only one that corresponds with facts, and rejected certain shadowy ideas which connected the old theory of interest with the word “Uses” of goods. What remains for us here is, on the same lines, to lay down certain fundamental ideas as to the origin of material goods.
• 9If we look more closely at the way in which man assists natural processes, we find that his sole but ample contribution consists in the moving of things. “Putting objects in motion” is the idea which gives the key to all human production and its results;—to all man’s mastery over nature and its powers. And this is so simply because the powers reside in the objects. Now when man by his physical powers—the power of moving things—is able to dictate where the object shall be, he obtains a control over the place at which a natural power may become effective; and this means broadly a control over the way and over the time in which it may become effective.
• 10Again I say a control over the time in which a natural power may become effective. This proposition, also, must not be taken too literally. It must not be imagined that natural powers work intermittently; that man can sometimes bring them to a standstill, sometimes set them working again. On the contrary, natural powers are always at work; a natural power not active would be a contradiction in terms. But it is possible that several powers may be so combined that their activities may for a time mutually balance each other, and the resultant be rest—if not complete rest, still some movement so slight that, as regards human purposes, it may be neglected. When this is the case, before any new resultant can emerge that is of interest to man, there must be an entirely different combination of materials and powers. This suggests how man may get control of the point of time at which a definite resultant emerges. It is only necessary for him, by skilful use of his power to move objects, to provide the causes of the desired effect, all but one. So long as this one is not present the conditions are unfulfilled, and there cannot be the desired result. But when at the proper moment he adds the last condition, the movement hitherto held in leash, as it were, is suddenly set free, and the desired effect is obtained at the opportune time. Thus the sportsman moves powder and lead into the barrel of the gun; he shuts the breech; he raises the cock. Each of these things has for long possessed and expressed its peculiar powers. In the powder are present the molecular powers whose energy later on is to expel the shot from the barrel. The barrel now, as formerly, exerts its forces of cohesion and resistance. The trigger which is to let the cock smash down, strains and presses against the spring. Still the arrangement, the disposition of the collective powers, is such that the resultant of their mutual energies is rest. But the sportsman covers the wild fowl with the barrel: there is a slight pressure on the tongue, a little dislocation of the arrangements, and the shot flies.