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2. The Relative form of value. - Karl Marx, Capital: A Critique of Political Economy. Volume I: The Process of Capitalist Production 
Capital: A Critique of Political Economy. Volume I: The Process of Capitalist Production, by Karl Marx. Trans. from the 3rd German edition, by Samuel Moore and Edward Aveling, ed. Federick Engels. Revised and amplified according to the 4th German ed. by Ernest Untermann (Chicago: Charles H. Kerr and Co., 1909).
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2. The Relative form of value.
(a.) The nature and import of this form.
In order to discover how the elementary expression of the value of a commodity lies hidden in the value relation of two commodities, we must, in the first place, consider the latter entirely apart from its quantitative aspect. The usual mode of procedure is generally the reverse, and in the value relation nothing is seen but the proportion between definite quantities of two different sorts of commodities that are considered equal to each other. It is apt to be forgotten that the magnitudes of different things can be compared quantitatively, only when those magnitudes are expressed in terms of the same unit. It is only as expressions of such a unit that they are of the same denomination, and therefore commensurable.25
Whether 20 yards of linen=1 coat or=20 coats or=x coats—that is, whether a given quantity of linen is worth few or many coats, every such statement implies that the linen and coats, as magnitudes of value, are expressions of the same unit, things of the same kind. Linen=coat is the basis of the equation.
But the two commodities whose identity of quality is thus assumed, do not play the same part. It is only the value of the linen that is expressed. And how? By its reference to the coat as its equivalent, as something that can be exchanged for it. In this relation the coat is the mode of existence of value, is value embodied, for only as such is it the same as the linen. On the other hand, the linen's own value comes to the front, receives independent expression, for it is only as being value that it is comparable with the coat as a thing of equal value, or exchangeable with the coat. To borrow an illustration from chemistry, butyric acid is a different substance from propyl formate. Yet both are made up of the same chemical substances, carbon (C), hydrogen (H), and oxygen (O), and that, too, in like proportions—namely, C4H8O2. If now we equate butyric acid to propyl formate, then, in the first place, propyl formate would be, in this relation, merely a form of existence of C4H8O2; and in the second place, we should be stating that butyric acid also consists of C4H8O2. Therefore, by thus equating the two substances, expression would be given to their chemical composition, while their different physical forms would be neglected.
If we say that, as values, commodities are mere congelations of human labour, we reduce them by our analysis, it is true, to the abstraction, value; but we ascribe to this value no form apart from their bodily form. It is otherwise in the value relation of one commodity to another. Here, the one stands forth in its character of value by reason of its relation to the other.
By making the coat the equivalent of the linen, we equate the labour embodied in the former to that in the latter. Now it is true that the tailoring, which makes the coat, is concrete labour of a different sort from the weaving which makes the linen. But the act of equating it to the weaving, reduces the tailoring to that which is really equal in the two kinds of labour, to their common character of human labour. In this roundabout way, then, the fact is expressed, that weaving also, in so far as it weaves value, has nothing to distinguish it from tailoring, and, consequently, is abstract human labour. It is the expression of equivalence between different sorts of commodities that alone brings into relief the specific character of value-creating labour, and this it does by actually reducing the different varieties of labour embodied in the different kinds of commodities to their common quality of human labour in the abstract.26
There is, however, something else required beyond the expression of the specific character of the labour of which the value of the linen consists. Human labour-power motion, or human labour, creates value, but is not itself value. It becomes value only in its congealed state, when embodied in the form of some object. In order to express the value of the linen as a congelation of human labour, that value must be expressed as having objective existence, as being a something materially different from the linen itself, and yet a something common to the linen and all other commodities. The problem is already solved.
When occupying the position of equivalent in the equation of value, the coat ranks qualitatively as the equal of the linen, as something of the same kind, because it is value. In this position it is a thing in which we see nothing but value, or whose palpable bodily form represents value. Yet the coat itself, the body of the commodity, coat, is a mere use-value. A coat as such no more tells us it is value, than does the first piece of linen we take hold of. This shows that when placed in value relation to the linen, the coat signifies more than when out of that relation, just as many a man strutting about in a gorgeous uniform counts for more than when in mufti.
In the production of the coat, human labour-power, in the shape of tailoring, must have been actually expended. Human labour is therefore accumulated in it. In this aspect the coat is a depository of value, but though worn to a thread, it does not let this fact show through. And as equivalent of the linen in the value equation, it exists under this aspect alone, counts therefore as embodied value, as a body that is value. A, for instance, cannot be "your majesty" to B, unless at the same time majesty in B's eyes assumes the bodily form of A, and, what is more, with every new father of the people, changes its features, hair, and many other things besides.
Hence, in the value equation, in which the coat is the equivalent of the linen, the coat officiates as the form of value. The value of the commodity linen is expressed by the bodily form of the commodity coat, the value of one by the use-value of the other. As a use-value, the linen is something palpably different from the coat; as value, it is the same as the coat, and now has the appearance of a coat. Thus the linen acquires a value form different from its physical form. The fact that it is value, is made manifest by its equality with the coat, just as the sheep's nature of a Christian is shown in his resemblance to the Lamb of God.
We see then, all that our analysis of the value of commodities has already told us, is told us by the linen itself, so soon as it comes into communication with another commodity, the coat. Only it betrays its thoughts in that language with which alone it is familiar, the language of commodities. In order to tell us that its own value is created by labour in its abstract character of human labour, it says that the coat, in so far as it is worth as much as the linen, and therefore is value, consists of the same labour as the linen. In order to inform us that its sublime reality as value is not the same as its buckram body, it says that value has the appearance of a coat, and consequently that so far as the linen is value, it and the coat are as like as two peas. We may here remark, that the language of commodities has, besides Hebrew, many other more or less correct dialects. The German "werthsein," to be worth, for instance, expresses in a less striking manner than the Romance verbs "valere," "valer," "valoir," that the equating of commodity B to commodity A, is commodity A's own mode of expressing its value. Paris vaut bien une messe.
By means, therefore, of the value relation expressed in our equation, the bodily form of commodity B becomes the value form of commodity A, or the body of commodity B acts as a mirror to the value of commodity A.27 By putting itself in relation with commodity B, as value in propriâ personâ, as the matter of which human labour is made up, the commodity A converts the value in use, B into the substance in which to express its, A's own value. The value of A, thus expressed in the use-value of B, has taken the form of relative value.
(b.) Quantitative determination of Relative value.
Every commodity, whose value it is intended to express, is a useful object of given quantity, as 15 bushels of corn, or 100 lbs. of coffee. And a given quantity of any commodity contains a definite quantity of human labor. The value-form must therefore not only express value generally, but also value in definite quantity. Therefore, in the value relation of commodity A to commodity B, of the linen to the cost, not only is the latter, as value in general, made the equal in quality of the linen, but a definite quantity of coat (1 coat) is made the equivalent of a definite quantity (20 yards) of linen.
The equation, 20 yards of linen=1coat, or 20 yards of linen are worth one coat, implies that the same quantity of value-substance (congealed labour) is embodied in both; that the two commodities have each cost the same amount of labour or the same quantity of labour time. But the labour time necessary for the production 20 yards of linen or 1 coat varies with every change in the productiveness of weaving or tailoring. We have now to consider the influence of such changed on the quantitative aspect of the relative expression of value.
I. Let the value of the linen vary,28 that of the coat remaining constant. If, say in consequence of the exhaustion of flax-growing soil, the labour time necessary for the production of the linen be doubled, the value of the linen will also be doubled. Instead of the equation, 20 yards of linen=1 coat, we should have 20 yards of linen=2 coats, since 1 coat would now contain only half the labour time embodied in 20 yards of linen. If, on the other hand, in consequence, say, of improved looms, this labour time be reduced by one half, the value of the linen would fall by one half. Consequently, we should have 20 yards of linen=½ coat. The relative value of commodity A, i.e., its value expressed in commodity B, raises and falls directly as the value of A, the value of B being supposed constant.
II. Let the value of the linen remain constant, while the value of the coat varies. If, under these circumstances, in consequence, for instance, of a poor crop of wool, the labour time necessary for the production of a coat becomes doubled, we have instead of 20 yards of linen=1 coat, 20 yards of linen=½ coat. If, on the other hand, the value of the coat sinks by one half, then 20 yards of linen=2 coats. Hence, if the value of commodity A remain constant, its relative value expressed in commodity B rises and falls inversely as the value of B.
If we compare the different cases in I. and II., we see that the same change of magnitude in relative value may arise from totally opposite causes. Thus, the equation, 20 yards of linen=1 coat, becomes 20 yards of linen=2 coats, either, because, the value of the linen has doubled, or because the value of the coat has fallen by one half; and it becomes 20 yards of linen=½ coat, either, because the value of the linen has fallen by one half, or because the value of the coat has doubled.
III. Let the quantities of labour time respectively necessary for the production of the linen and coat vary simultaneously in the same direction and in the same proportion. In this case 20 yards of linen continue equal to 1 coat, however much their values may have altered. Their change of value is seen as soon as they are compared with a third commodity, whose value has remained constant. If the values of all commodities rose or fell simultaneously, and in the same proportion, their relative value would remain unaltered. Their real change of value would appear from the diminished or increased quantity of commodities produced in a given time.
IV. The labour time respectively necessary for the production of the linen and the coat, and therefore the value of these commodities may simultaneously vary in the same direction, but at unequal rates, or in opposite directions, or in other ways. The effect of all these possible different variations, on the relative value of a commodity, may be deduced from the results of I., II., and III.
Thus real changes in the magnitude of value are neither unequivocally nor exhaustively reflected in their relative expression, that is in the equation expressing the magnitude of relative value. The relative value of a commodity may vary, although its value remains constant. Its relative value may remain constant, although its value varies; and finally, simultaneous variations in the magnitude of value and in that of its relative expression by no means necessarily correspond in amount.29
[25.] The few economists, amongst whom is S. Bailey, who have occupied themselves with the analysis of the form of value, have been unable to arrive at any result, first, because they confuse the form of value with value itself; and second, because, under the coarse influence of the practical bourgeois, they exclusively give their attention to the quantitative aspect of the question. "The command of quanity...constitutes value." (Money and its Vicissitudes." London, 1837, p. 11. By S. Bailey.
[26.] The celebrated Franklin, one of the first economists, after Wm. Petty, who saw through the nature of value, says: "Trade in general being nothing else but the exchange of labour for labour, the value of all things is...most justly measured by labour." (The works of B. Franklin, 8c., edited by Sparks, Boston, 1836, Vol. II., p. 267.) Franklin is unconscious that by estimating the value of everything in labour, he makes abstraction from any difference in the sorts of labour exchanged, and thus reduces them all to equal human labour. But although ignorant of this, yet he says it. He speaks first of "the one labour," then of "the other labour," and finally of "labour," without further qualification, as the substance of the value of everything.
[27.] In a sort of way, it is with man as with commodities. Since he comes into the world neither with a looking glass in his hand, nor as a Fichtian philosopher, to whom " I am I " is sufficient, man first sees and recognises himself in other men. Peter only establishes his own identity as a man by first comparing himself with Paul as being of like kind. And thereby Paul, just as he stands in his Pauline personality, becomes the Peter the type of the genus homo.
[28.] Value is here, as occasionally in the preceding pages, used in the sense of value determined as to quantity, or of magnitude of value.
[29.] This incongruity between the magnitude of value and its relative expression has, with customary ingenuity, been exploited by vulgar economists. For example—"Once admit that A falls, because B, with which it is exchanged, rises while no less labour is bestowed in the meantime on A, and your general principle of value falls to the ground...If he [Ricardo] allowed that when A rises in value relatively to B, B falls in value relatively to A, he cut away the ground on which he rested his grand proposition, that the value of commodity is ever determined by the labour embodied in it; for if a change in the cost of A alters not only its own value in relation to B, for which it is exchanged, but also the value of B relatively to that of A, though no change has taken place in the quantity of labour to produce B, then not only the doctrine falls to the ground which asserts that the quantity of labour bestowed on an article regulates its value, but also that which affirms the cost of an article to regulate its value." (J. Broadhurst: Political Economy, London, 1842, p. 11 and 14.