From: Philip Dunn (hyl0morph@YAHOO.CO.UK)
Date: Sat Jun 03 2006 - 18:15:38 EDT
Hi Ian
On Sat, 2006-06-03 at 13:52 -0700, Ian Wright wrote:
> Hi Phil
>
> > 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."
> >
> > Rewrite them as:
> >
> > v = l(B-A)^{-1}
> > v'= l(B-A*)^{-1}
> >
> > where the output matrix B = I.
> >
> > Consider:
> >
> > v'= l(B*-A)^{-1}
> >
> > where B* = B - (A* - A).
>
> This gives
> v'=l(B-(A*-A)-A)^{-1}
> v'=l(B-A*)^{-1}
> v'=l(I-A*)^{-1}
>
> ie. we're back to the real-cost definition of labour values. Maybe
> there's a typo in your message?
No typo. I am saying that leaving capitalists' consumption out of what
labour produces is equivalent to the real cost definition. The value of
capitalists' consumption is immortal in these circumstances. It just
goes round and round. Labour creates only the value of workers'
consumption.
Similarly, if workers' consumption transfers to the commodity produced,
labour creates only the value of capitalists' consumption. The value of
workers' consumption is then immortal.
>
> > This removes capitalist consumption from gross output for the purpose of
> > calculating value. Gross output is x = Bx where x is the output vector
> > but we only consider x* = B*x
>
> OK, but that's not what your algebra says, unless I've missed something.
> > Ian says:
> >
> > "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)"
> >
> > If this is correct it seems to be saying that Sraffian prices are the
> > same as values when capitalists' consumption is removed from gross
> > output.
>
> If I understand you correctly -- then yes. Removing capitalist
> consumption from simple reproduction gives us simple commodity
> production.
>
> In this case, simple commodity prices are proportional to Sraffian
> labour values. Most people agree on this point.
>
> The Sraffian definition of labour value is a special case of the
> real-cost definition. The real-cost definition yields Sraffian values
> under these equivalent conditions:
> (i) profits are zero
> (ii) capitalist consumption is zero
> (iii) money-capital is absent
> In other words, the Sraffian definition of labour values is correct
> only for simple commodity production.
> > This significance of this is probably zero.
>
> I hope not! :)
>
> -Ian.
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