From: Ian Wright (iwright@gmail.com)
Date: Wed Sep 21 2005 - 20:46:59 EDT
> > I think that to solve this one needs to follow Sraffa's suggestion that > one divides the > > wage into two parts, that necessary for reproduction, and a surplus > component. > > If you do this you then have to ask if the non basics in question enter > into > > the necessary wage bundle. If they do, then they are basics and the > problem > > is solved. > But in this case the problem does not arise: the "beans" are basic. > If not, then they still require labour inputs, and hence require necessary > wage goods as input, and are no longer self reproducing, so the > > problem goes away again. > 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. >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.
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