From: Ian Wright (iwright@GMAIL.COM)
Date: Wed Sep 21 2005 - 16:46:03 EDT
> > > You can maintain this interpretation, but only at the expense of working > > with Sraffa's incomplete equation to determine prices. There are > > economic realities in which this equation either cannot determine > > prices, or cannot maintain the assumption of a uniform rate of profit > > for all sectors. This happens when the maximum eigenvalue of the i/o > > matrix A does not lie on the principal diagonal of the submatrix that > > refers to basic commodities. > > -Ian. > > Please explain why this is the case. Take a look at, for example, pages 70-73 of Kurz's & Salvadori's "Theory of Production", under the section heading "non-basic commodities reconsidered". They give a simple two sector example of the problem of indeterminacy. I am not satisifed with the general presentation of this paradox in the literature, as I think the incompleteness has not been revealed in its full glory. The problem arises due to the distinction between basics and non-basics. According to the neo-Ricardian approach to self-replacing equilibrium, the rate of profit and rate of growth is determined only in the basic sector. But what happens if the maximum rate of growth of the non-basic sector is less than that which obtains in the basic sector? This is the problem of self-reproducing non-basics, or "beans", which require themselves for their production. In such a case, we are forced to consider the physical composition of the net product. If "beans" are not consumed, then K&S say that "either their price is ignored or the free disposal assumption implies a zero price anyway", at which point one wonders what beans were doing in the technique in the first place. If "beans" are consumed, then an assumption has to be made that they are not consumed at "high prices", otherwise a "long-period" solution does not exist, i.e. uniform profit rates cannot prevail, prices are undetermined etc. Presumably this causes a feeling of consternation because K&S revisit it a number of times throughout their book, and include it as the first section in their afterword chapter on "limits to the long-period method", at which point they introduce short-period demand considerations and economies with agents with perfect foresight in order to tackle the paradox, i.e. revert to systems that are not in a state of self-replacing equilibrium. Sraffa mentions the problem in PCMC, but considers it a "freak case". Pasinetti, some years later, in his Lectures, discusses the problem, but excludes it on two grounds: empirically not very likely, and anyway the mathematics is so much easier without it, which echoes some of the defensive moves of the neo-classicals to the capital controversy. Bidard in his "prices, reproduction and scarcity" defines the problem away. By the time of K&S the "beans" are still with us, but now it is generating more pages of linear algebra. I am working on this at the moment, which is why it is on my mind. I was wondering what others, better schooled in the Sraffian/neo-Ricardian literature, might have to say. It appears that all the Sraffian price solutions that we see in the literature should be qualified with the assumption that the maximum eigenvalue of the i/o matrix A lies on the principal diagonal of the submatrix that refers to basic commodities. For the infinite set of other, logically possible, technical conditions of production, the Sraffian price equation is indeterminate. This is not a healthy state-of-affairs, to say the least. Best wishes, -Ian.
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