Re: [OPE-L] basics vs. non-basics

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Thu Sep 22 2005 - 05:03:27 EDT

Ian Wright wrote:

> No, that's not the meaning of "self-reproducing" in this context.
> Self-reproducing non-basics do require basics for their production
> (otherwise we have unconnected systems). But they also require
> themselves as an input. This case is precisely the problem.

Yes but any product will require labour as an input. Associated
with the labour input are two things

1. A wage w which is a share of the surplus
2. A vector of necessary reproduction commodities which will require basics

This seems to follow from the paragraph labeled 8
in Sraffa's Production of Commodities.

Thus no isolated self reproducing sections can exist
unless the workers in these sections do not consume
products that are produced in the basic sector.
That is of course possible, but that would indicate
that they lived in a different country which
had no trade relations with the basic sector, in
which case there must be some other goods
which make up the basic sector in their country - corresponding
to other previously non-basic rows of our equations.

>>I don't understand your remark about the maximum eigenvalue lying on the
> principle diagonal.
>     The diagonal is a vector not a value. Did you mean the eigenvector
>     corresponding to the
>     main eigenvalue lies on the diagonal?
> Reduce A to a block triangular form. The eigenvalues of A are then the
> eigenvalues of the square sub-matrices on its principal diagonal. To
> eliminate the problem of "beans" we must assume that the maximum
> eigenvalue of A is identical to the maximum eigenvalue of the submatrix
> on the principal diagonal that refers to the basic subsystem. On what
> economic grounds would we want to assume this? And if we don't assume,
> the Sraffian price equations are indeterminate.
> Point to bear in mind: the experts in this field recognise there is a
> problem, but have not solved it satisfactorily. And the problem has been
> known since PCMC.
> -Ian.

Paul Cockshott
Dept Computing Science
University of Glasgow

0141 330 3125

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