Re: [OPE-L] Che Guevara and the Sraffian notion of profit

From: Ian Wright (wrighti@ACM.ORG)
Date: Mon May 07 2007 - 16:20:24 EDT

> von Neumann does track growth of capital stocks in a similar model of **
> proportionate **  growth using non-unitary matrices, so I infer that the same thing could
> be done with Sraffa's.

Yes it can. But the non-unitary matrix employed in proportionate
growth models (e.g., Pasinetti in his Lectures on the Theory of
Production) is merely the result of the representational choice of an
open model. One can just as easily model proportionate growth in terms
of a closed model with a unitary matrix. In this case, as before, a
surplus is produced, its scale grows exponentially over time, but its
distribution to households is specified. Per-capital consumption is

Proportionate growth is symmetry-preserving: prices are invariant
under this kind of growth. It is a special case which avoids the
necessity to formulate dynamic equations. It also lends itself to the
unfortunate Physiocratic image that the "surplus" is always a physical
surplus of additional commodities.

The interesting case is non-proportionate growth that necessarily
results in temporary out-of-equilibrium matrices that are non-unitary.

In self-replacing equilibrium, and symmetry-preserving generalisations
such as proportionate growth, there is conservation of costs and
revenues. A closed model with a dominant eigenvalue of 1 makes this
explicit. An open model hides this.

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