Sraffa's Incomplete Reductions to Labor

Sraffa, in part 1 of his "Production of Commodities by Means of Commodities", describes two kinds of reductions to labor. First, he reduces Classical natural prices to an infinite series of "dated" quantities of labor multiplied by a profit factor. He concludes that prices are "in proportion to their labor cost", that is Classical labor-values, only in the special case of zero profit. I show that Sraffa's reduction is incomplete in the precise sense that it ignores some actual labor supplied during the "successive stages of the production of the commodity". The complete reduction to dated quantities reveals that natural prices are, in fact, proportional to total labor costs. Second, Sraffa constructs a "standard commodity" that functions as an "invariable standard of value" in the context of changes in income distribution. Sraffa reduces the standard commodity, which he views as "a purely auxiliary construction", to the "variable quantity of labor" it commands in the market. I show that Sraffa's reduction is incomplete because it does not reduce the "invariable standard" to a real cost of production. The complete reduction reveals that Sraffa's "variable quantity" is, in fact, the total labor cost of the standard commodity. I conclude by discussing how Sraffa's incomplete reductions derive from the Classical category-mistake of conflating technical with total labor costs