First case. Let the labor-time required for the production of commodity B remain unchanged. In that case the exchange value of A, expressed in terms of B, rises and falls with the rise and fall of the labor-time required for the production of A.
Second case. Let the labor-time required for the production of commodity A remain constant. Then the exchange value of A, expressed in terms of B, falls and rises in an inverse ratio with the rise and fall of the labor-time required for the production of B.
Third case. Let the labor-time required for the production of commodities A and B rise and fall in equal proportion. Then the expression of equivalence of A and B remains unchanged. If through some cause the productivity of all kinds of labor were to decline uniformly, so that the production of all commodities would require an equally increased quantity of labor-time, then the value of all commodities would rise, though the expression of their exchange values would remain unchanged, and the actual wealth of society would decrease, because it would have to expend more labor-time on the production of the same stock of use-values.
Fourth case. Let the labor-time required for the production of A and B rise and fall, but not uniformly; that is to say, the labor-time required for the production of A may rise, while that required for B may fall, or vice versa. All of which can be reduced to the simple case where the labor-time required for the production of one commodity remains unchanged, while that required for the other rises or falls.
The exchange value of any commodity is expressed in the use-value of any other commodity, be it in integral units or in fractions thereof. As exchange value, every commodity is capable of subdivision, like the labor-time embodied in it. The equivalence of commodities is independent of their physical divisibility as use-values, just as the sum of the exchange values of commodities is indifferent to the change of form which use-values have to undergo when converted into a single new commodity.
So far we have considered commodities from a two-fold point of view, as use-values and exchange values alternately. But a commodity as such is a direct combination of use-value and exchange value; and it is a commodity only in relation to other commodities. The actual relation between commodities constitutes the process of their exchange. It is a social process participated in by individuals independent of each other but the part they take in it is that of owners of commodities only. Their mutual relations are those of their commodities, and thus they really appear as conscious factors of the process of exchange.
A commodity is a use-value, wheat, linen, a diamond, a machine, etc., but as a commodity it is, at the same time, not a use-value. If it were a use-value for its owner, i. e., a direct means for the satisfaction of his own wants, then it would not be a commodity. To him it is rather a non-use-value; it is merely the material depository of exchange-value, or simply a means of exchange; as an active bearer of exchange value, use-value becomes a means of exchange. To the owner it is a use-value only in so far as it constitutes exchange value.[12]
It has yet to become a use-value, viz., to others. Not being a use-value to its owner, it is a use-value to the owners of other commodities. If it is not, then the labor expended on it was useless labor, and the result of that labor is not a commodity. On the other hand, the commodity must become a use-value to the owner himself, because his means of existence lie outside of it in the use-values of commodities not belonging to him. In order to become a use-value, the commodity must meet the particular want of which it is the means of satisfaction. Use-values of commodities are thus realized use-values through a universal change of hands by passing from the hands in which they were held as means of exchange into those where they become use values. Only through this universal transfer of commodities does the labor contained in them become useful labor. In this process of their mutual interchange as use-values, commodities do not acquire any new economic forms. On the contrary, even the form which marked them as commodities disappears. Bread, e. g., by changing hands from the baker to the consumer does not change its identity as bread. On the contrary, it is only the consumer that begins to regard it as a use-value, as a certain article of food, while in the hands of the baker it was only the bearer of an economic relation, a palpable yet transcendental object. Thus, the only change of form that commodities undergo while becoming use-values, consists in the fact that they cease to be, as a matter of form, non-use-values to their owners, and use-values to those who do not own them. To become use-values commodities must be universally alienated; they must enter the sphere of exchange; but they are subject to exchange in their capacity of exchange values. Hence, in order to be realized as use-values, they must be realized as exchange values.
While the single commodity appeared from the standpoint of use-value as something independent, as exchange value it was regarded first of all in its relation to all other commodities. This relation was, however, merely theoretical, imaginary. It becomes real only in the process of exchange. On the other hand, a commodity is an exchange value in so far as a certain quantity of labor-time has been expended on it, and it consequently represents materialized labor-time. But of itself it is only materialized individual labor-time of a particular kind, and not universal labor-time. Therefore, it is not directly an exchange value, but must first become such. First of all, it is an embodiment of universal labor-time only in so far as it represents labor-time applied to a definite useful purpose, i. e., when it represents a use-value. This was the material condition under which alone labor-time contained in commodities was regarded as universal social labor. Thus, while a commodity can become a use-value only after it has been realized as an exchange value, it can, on the other hand, be realized as an exchange value only if it proves to be a use-value in the process of alienation.