Marx
The study of Quesnay’s Tableau helps Marx to realize the presence, in the value not only of individual commodities but also of the social product, of a part corresponding to the value of the used-up non-wage capital goods, circulating and durable.
On this basis he develops a disaggregation of capital into constant capital c (that is, non-wage capital goods) and variable capital v (wages) (I assume the reader is acquainted with Marx’s c + v + s formulas); his reproduction schemes in volume II of Capital, where different sectors produce constant capital, variable capital, and luxury goods, are at the origin of Leontiefs input-output approach. This permits him a significant step forward relative to Ricardo: the recognition of the “organic composition of capital” c/v as a further determinant of the rate of profits besides the wage level. In Marx too the labour theory of value allows the determination of the aggregates of the “surplus equation” before the rate of profits. He reaches this conclusion before writing Capital, in the so-called Grundrisse (1858-59), on the basis of a “compensation-of-deviations” argument not unlike the one in Ricardo; this analytical motivation appears sufficient to explain his subsequent attachment to the idea that exchange value is created by labour, without need for the other motives often attributed him. Marx argues that the equalization of the rate of profits is brought about by an increase in price (relative to a starting point with prices proportional to labour-values) of the commmodities produced with a higher-thanaverage organic composition of capital, and a decrease in price of the commodities with a lower-than-average organic composition of capital; these deviations, he concludes, will compensate one another and leave the aggregate value unchanged, if one chooses asstandard of value an “average commodity” produced with the average organic composition of capital - a property enjoyed, by definition, by the total social product which is then Marx’s “average commodity” (this explains why Marx, contra Ricardo, considers the production conditions of all sectors to contribute to the determination of the rate of profits). But Marx does not realize that the same “average commodity” cannot leave the aggregate value of capital or of total profits unchanged because different aggregates have different average organic compositions, and concludes that the general uniform rate of profits is correctly determined by the “surplus equation” (assuming only circulating capital):
where N is total employment (the labour embodied in the net product) and C, V, S are the labour embodied in, respectively, the constant capital, the variable capital, and the surplus of the entire economy.
Marx also discusses durable capital and differences in rotation times, but is unable to go beyond the idea expressed by equation (2): the labour theory of value applied to the “surplus-equation” aggregates determines r correctly. Marx proceeds to argue that the r thus determined must be applied to the advanced capital of each industry to obtain the prices of production; he sees these prices as “transformed” labour values since they result from a redistribution of the given total surplus labour value. In volume III of Capital he has a numerical example of this determination of prices of production; he admits that the example needs correction because he has not “transformed” constant and variable capital from labour values to prices of production, but he argues that the question does not need further analysis because the compensation of deviations will operate for capital too, and does not attempt to implement the correction.