From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Wed Dec 06 2006 - 08:13:27 EST
Further to the discussion between Ajit and I about whether there are counter factual assumptions in Sraffa. In the Sraffian system you have n prices and the rate of profit r as unknowns to solve one has n production equations plus a final equation dividing the social product between labour and capital. However when one observes an actual i/o table one sees that there are n prices and also n rates of profit, one for each industry. The system is thus underdetermined. The Sraffian equations as with the Marxian equations for the transformation equation implicitly assume the existence of n-1 auxiliary equations of the form r0=r1, r1=r2, r2=r3,.... where rx is the rate of profit of the xth industry. If one takes a simple labour theory of value model one introduces and analogous set of equations which predict the mass of profit in each industry as the product of the rate of surplus value and the wage bill. In deciding between the two models one is in the end making an empirical judgement - which is the more realistic assumption - that the rate of profit is the same in all industries, or that the profit is a fixed mark-up on labour costs. Both the labour theory of value ( unaugmented by other data to predict rates of exploitation ) and the theory of production prices make counter factual assumptions. One has to assess which gives the better fit to reality. Ones metric for quality of fit should probably be some metric on the vector space formed by concatenating the price and profit rate vectors. One should compare the vector of length 2n formed by n prices and n rates of profit, that one gets from the theory with what is actually observed. It is not clear what is the appropriate metric here, whether it should be the normalised inner product of the vectors, the angle between them, the correlation between them or what. But it is worth noting that the existing literature on comparing these models only takes into account the first n elements of the vector - the price elements. The predictions on the rate of profit are typically disregarded.
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