This subsection is “Quantitative determination of Relative value”
Page 53: “Every commodity, whose value it is intended to express, is a useful object of a 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 labour. 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 coat, not only is the latter, as value in general, made the equal in quality of linen, but a definite quantity of coat (1 coat) is made the equivalent of a definite quantity (20 yards) of linen.”
This is a restatement and summary of the earlier subsections: the equivalent form asserts qualitative equality in that human-labor = human labor, and quantitative equality (x of commodity A = y of commodity B).
“The equation 20 yards of linen = 1 coat, or 20 yards of linen are worth 1 coat, implies that the same quantity of value-substance (congealed labor) is embodied in both; that the two commodities have each cost the same amount of labour of the same quantity of labour-time. But the labour-time necessary for the production of 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 changes on the quantitative aspect of the expression of relative value.”
If the amount of labor embodied in a commodity determines the value of the commodity, then we need to determine how changes in the productivity of labor affects the value.
“I. Let the value of the linen vary, 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 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 one 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 = 1/2 coat. The relative value of commodity A, i.e., its value expressed in commodity B, rises and falls directly as the value of A, the value of B being constant.”
As productivity increases, less labor is required to produced commodity A, therefore the value of A falls compared to B.
“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 = 1/2 coat. If, on the other hand, the value of coat sinks by one-half, then 20 yards of linen = 2 coats. Hence, if the value of commodity A remains constant, its relative value expressed in commodity B rises and falls inversely as the value of B.
The obvious corollary to the above.
“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, or because the value of the linen as doubled.”
“III. Let the quantities of labour-time respectively necessary for the production of the linen and the coat vary simultaneously in the same direction and the same proportion…”
Well, yeah, double them both, and there’s no change. Cut them both in half, and there’s no change. Seems clear enough.
“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.”
This seems pretty obvious. It also gladdens my heart to see that old Marx was a believer in the serial comma.
“Thus real changes in the magnitude of value are neither unequivocally nor exhaustively reflected in their relative expression, this 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 variation in the magnitude of value and in that of its relative expression by no means necessarily correspond in amount.”
This is a straightforward extension of the two theses: value of a commodity is determined by the amount of labor, and value is expressed relative to other commodities.