The transformation problem has provoked controversy within Marxism and derision from without for more than a century. Bourgeois economists in particular (beginning with Ladislaus Bortkiewicz, and continuing, most notoriously, with Paul Samuelson) have seized on it to argue for…
Yup I agree it's quite interesting. I'm fairly math-oriented so I spent like 2 weeks a couple years ago reading/pondering this exact paper. I do commend the rigor of the analysis, though at points I'm wondering whether the math is actually necessary to make the arguments ... seems overly complicated to me.
Putting Marx into linear algebra terms nonetheless is quite enticing. As with all mathematical models though, the most subtle of assumptions can mean everything. And in this case I think it is a wrong interpretation of Marx to model a society as a set of simultaneous equations. It is a purely technical view of production not specific to capitalist production; such a model could be constructed for any society with a division of labor. As well, there seems to be a fusing of labor in itself and labor power which, as we know, is the essential distinction in Marx's analysis of capitalism.