# [OPE-L] Free variables: was what is irrational in the functioning of capitalism?

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Wed Dec 06 2006 - 08:13:27 EST

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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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