The standard commodity
The standard commodity, which is taken by Sraffa as an invariable measure of value, is not defined for joint production systems. As Schefold puts it:
The decisive defining property of the standard commodity (constant proportion between indirect means of production and indirect labour) cannot meaningfully be applied to joint production systems, however.
The prices of several jointly produced commodities in a ‘capital-intensive’ process may move in different directions relatively to those of other commodities jointly produced by a ‘labour-intensive process’. Hence, the thought-experiment underlying the construction of the ‘invariable measure of value’ cannot be extended to multiple-product industries. Insofar it was... a mistake of Sraffa’ s to postulate a standard commodity in his theory of joint production.(Schefold 2005: 535)
What this means is that the concept of standard commodity is not a general concept in Sraffa’s theory. The focus of normal science, therefore, cannot be on the determination of a standard commodity, but rather on systems (π, w, p) satisfying at least the fundamental law, Axiom (6) of Definition 11.3.1.
Hence, Vela Velupillai’s (2008: 326) contention that Sraffa’s mathematics in PCC did “bypass the fixed point approach and attack the equations directly to give existence of solutions, with a simpler kind of mathematics’, one with ‘algorithmic overtones’”, even if true, does not address in general the relevant issues of normal science, since it does not apply to the joint-production case. But the claim is not true even in the case of simple systems. Punzo (1986) had already proposed to interpret Sraffa’s mathematics “as constructivist; therefore, closer to mathematical intuitionism than to mathematical formalism”. But
Punzo is not correct in asserting that Sraffa does not go beyond elementary algebra. There are mathematical proofs involving problems of convergence, even if they are only sketched. Sraffa left his proofs incomplete, perhaps in
part because he lacked the training of a mathematician. But he used economic intuition as a complement and created an employment for mathematically oriented economists.
(Ibid.: 357)
At any rate, what matters is not the use of this or that mathematical method in normal science: Any method can be used if it promises to work in the endeavor to find the solution to the problems. The demand for economic theory to use only constructive methods is far-fetched: normal science is by itself sufficiently hard as to require further restrictions springing from an intuitionistic philosophical program that dislikes the axiom of choice or the law of excluded middle.
11.5