# Re: [OPE-L] workers' consumption and capitalists' consumption

From: Ian Wright (wrighti@ACM.ORG)
Date: Sat Jun 03 2006 - 16:52:00 EDT

```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?

> 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.
```

This archive was generated by hypermail 2.1.5 : Fri Jun 30 2006 - 00:00:03 EDT