From: Ian Wright (wrighti@ACM.ORG)
Date: Mon May 07 2007 - 14:44:07 EDT
> I am not convinced here, the existence of a surplus allows economic > growth, this sort of growth is not possible using unitary matrices, > so in order to track the growth of capital stocks he needs non unitary > matrices. Sraffa doesn't "track the growth of capital stocks". His theoretical tools are entirely inadequate for this task. He has a one-time snapshot of the production of an undistributed surplus. But I agree that to model *non-proportionate* economic growth one must deal with symmetry-breaking technical change, which results in non-unitary matrices. But this must occur in the context of a dynamic theory, in which there are adjustment rules, expressed in terms of differential or difference equations. In such approaches, out-of-equilibrium the price and real cost matrices are non-unitary; but in equilibrium they are not. >Restoring unitarity it is not just a matter of specifying a distribution of income >one needs to track all material flows : depletion of natural resources, >creation of waste - CO2, rubbish dumps etc. Include as much of the material world as you want in the input-output matrix. It will still remain non-unitary in Sraffa's approach because it is not closed to final demand. The technique is "productive" hence its dominant eigenvalue is less than 1. The loss of non-unitary matrices in the transition from Ch. 1 to Ch. 2 in PCMC is a straightforward mathematical fact. The confusion occurs over the interpretation of this transition. Best, -Ian.
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