From: Ian Wright (wrighti@ACM.ORG)
Date: Fri Jun 02 2006 - 02:49:29 EDT
Hi Allin
> Could you expand on this briefly? What is the formula you say is
> wrong (for r = 0), and what is the one you would regard as
> correct?
I'll be brief, and give assertions.
According to Sraffa, prices are proportional to labour values only
when r=0. Setting r=0 in Sraffa's dated labour representation gives
the following formula for labour values:
v = l(I-A)^{-1}
where l is the vector of direct labour coefficients, I is the identity
matrix, and A is the technology matrix (apologies if your font is not
so good at distinguishing l and I). This is the standard formula
employed by neo-Ricardian critics of Marx's value theory. For example,
Samuelson uses it in his 1971 Sraffa-inspired critique of Marx's
theory, and Steedman uses it in Marx After Sraffa.
Briefly, this formula only holds in the case of simple commodity
production, that is production absent a capitalist class. In
conditions of capitalist production, the correct formula is:
v'=l(I-A*)^{-1}
where v' is the vector of real-cost labour values, and A* is the
technology matrix augmented by capitalist consumption.
Alternatively, there is another, equivalent representation of v',
which does not require knowledge of capitalist consumption:
v' = (I-A(1+r))^{-1}l(1+r)
where r is the value rate of profit (= S/(C+V)). The value rate of
profit may be calculated from the technology A and the real wage
(i.e., it is independent of price magnitudes).
Using v under conditions of capitalist production is a real-cost
accounting error. Why? Because the formula for v fails to vertically
integrate over the whole real cost structure. In particular it does
not integrate over the real cost of the money-capital supplied to
production by capitalists. That is why labour-value is not conserved
in price in the neo-Ricardian critique. The conditions under which
Marx's assertions were considered to hold -- zero profits, uniform
organic compositions of capital, and production in standard
proportions -- are in fact the cases in which the neo-Ricardian
real-cost accounting error is accidentally consistent with the general
principle of conservation of real cost in price.
Notably, the formulae for v' can be derived from within Sraffa's
system. It turns out that prices of production are proportional to v'
under conditions of simultaneous determination. This is the case in
which the transformation problem has traditionally been discussed.
This result says very little about the stability of a state of
profit-rate equalisation or the dynamics of new surplus-value
production.
Best wishes,
-Ian.
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