Thursday, August 30, 2012

Sraffa Solves Marx's Transformation Problem

"if we want to follow in Marx's footsteps and pass from values to prices of production and from rate of surplus value to rate of profits, the Standard System is a necessary adjunct: for that passage implies going through certain averages and if these are calculated without weights (or with the weights of the real system), a result which is only approximately numerically correct is obtained. If an exact result is wanted the proportions of the St[andard] Syst[em] of eq[uation]s q's [quantities] must be applied as weights. - This is not stated explicitly in the book, but is implied. " -- Piero Sraffa (as quoted by Heinz D. Kurz. "Obituary: Aiming for a 'Higher Prize': Paul Anthony Samuelson (1915-2009)", European Journal for History of Economic Thought, V. 17, n. 3 (August 2010): pp. 513-520.)


Anonymous said...

Is there a relationship between Sraffa's standard commodity and Marx's theory of money as the form of appearance of value (and, extending this, modern conceptions of the MELT)? It seems like there may be some conceptual similarities, but I'm not sure I understand the former well enough.

Ian Wright said...

Hi Robert,

Unfortunately a false claim by Sraffa here. To relate the rate of surplus-value and the general profit-rate the net product must be composed (not measured) in units of the standard commodity, as per your previous post. Hence we get an approximate relation between real-costs, measured in labor-time, and money-costs. Neither Ricardo or Marx were satisfied with an approximate relationship between labor-time and money-costs. Ricardo wasn't satisfied because he understood that any mismatch, however numerically small, indicates "another less powerful cause" of the variation of relative prices, other than labor-time. Hence his measure of value was imperfect. And, in some passages, he was open to the idea that reward for "waiting" was the other, less powerful determinant of profit. Marx wasn't satisfied because his understanding of the relationship between labor-time and money-costs is fundamentally different from Ricardo's (and Sraffa's). The key is the opening three chapters of Volume 1 of Capital where Marx attempts to argue that exchange-value in the market represents labor-time in virtue of the causal regularities of the social practice of commodity exchange. In other words, the economy, objectively, measures labor-time. Ricardo believes the economic theorist should choose the best standard of value. Marx says that the economy, as an objective social practice, has a standard of value, whether we are theoretically conscious of it or not. This is why Marx states his three invariances between labor-time and money-costs and attempts to show they are satisfied in Volume 3 of Capital.

Sraffa's standard commodity, then , being a approximation, even in theory, therefore does not solve the transformation problem, nor does it solve Ricardo's problem of an invariable measure of value. I would say Sraffa merely restates the problem.

Best wishes,

Matias Vernengo said...

Sraffa's standard system allows to determine the rate of profit without explicitly determining prices, in the same way that Ricardo's corn model. In that sense, it makes the problems of an absolute measure of value and of transformation irrelevant.

Robert Vienneau said...

I am ambivalent on the use of Sraffa's standard system to solve Marx's transformation problem. He does say that propositions regarding the standard system are not "central points" of his book.

I think propositions regarding the standard system and the Monetary Expression of Labor Time are analogous. They both relate labor time to an abstract measure of value, where that measure is related to net national income, in some sense. Real wages are then a proportion, not a fixed, temporally unchanging, basket of goods.

By the way, Ian argues, in his ROPE 2008 article, that certain propositions about the MELT are empirically true, not tautologies.