The labor theory of value and the problem of joint production : the failure of Sraffa's theory and Morishima's misconception

The labor theory of value has been rejected by Morishima on the grounds that it would be incompatible with joint production, which would create negative labor values. This article starts by recalling the various definitions of joint production, as well as the way they relate to the real world. For Morishima, the labor theory of value is a particular case of Sraffa's theory of production prices; it is recalled that in Sraffa's treatment of joint production the occurrence of negative multipliers and therefore of negative quantities comes from the construction of a standard commodity. Morishima extends this demonstration to labor values in the case of joint production, but the article shows that his example of giving negative labor values is absurd. Finally, using a method initially developed by statisticians to deal with joint production and simple matrix calculations, it is demonstrated that it is perfectly possible to obtain positive labor values in a theoretical but realistic model of joint production.