From: Ian Wright (wrighti@ACM.ORG)
Date: Sun Sep 09 2007 - 03:10:08 EDT
Hi Fred Sorry for the delayed reply. (And apologies to Jurriaan for not replying to his post as yet). I agree that Marx's prices of production (PoP) are classical natural prices, and hence are equilibrium prices (although this requires some further specification). > It seems to me that the appropriate meaning of "special case" is > "self-replacing equilibrium". Equilibrium is a special case of > disequilibrium. This special case can be theorized either with the > logical method of simultaneous determination or the logical method of > sequential determination. Simultaneous determination is not a "special > case". Simultaneous determination is a logical method. A special case > of what? All other logical methods? I think this is the crux of the issue. The equilibrium of a dynamical system is characterized by a system of simultaneous equations ("simultaneous determination"). This is true whether the dynamic system is represented by differential or difference equations. I do not think there can be another way of theorizing self-replacing equilibrium, such as your proposal of that an equilibrium is determined "sequentially". I do not know of any mathematical concepts of equilibrium that might correspond to this proposal. To resolve this matter I would need to spend some time with your mathematical model. I have read many of your papers, and find many areas of agreement, but I am sorry I have not spent time getting close to your equations. > Marx's theory does not "break down" in the special case of > self-replacing equilibrium. Marx's theory can explain self-replacing > equilibrium, as I have described. What "breaks down" is only the > misguided attempt to interpret Marx's theory, and Marx's theory of > self-replacing equilibrium prices in particular, in terms of the > logical method of simultaneous determination. Why is it "misguided"? I think that Marx's theory in Capital is essentially dynamic. Marx did not think in terms of simultaneous equations, although in places he almost did. The mathematical tools of simultaneous equations and corresponding concepts of equilibrium are major advances in scientific thought and apply generally to many kinds of material situations. The method of simultaneous determination, i.e. the study of equilibrium states, can be incredibly useful and illuminating. That there appears to be breakdown of the LTV when translated into this framework is of enormous scientific interest, since theoretical progress ultimately progresses by the resolution of well-defined anomalies, paradoxes, contradictions etc. We should understand why Marx's theory breaks down when translated into the terms of this special case, not fulminate against the legitimacy of examining it. In the abstract, the reason Marx's theory appears to break down is that his explanation of the production of surplus-value is "symmetry breaking": the labour-value added by workers exceeds the labour-value of the inputs to worker households (input labour-values do not equal output labour-values). But in self-replacing equilibrium the price system is "symmetry preserving": the price of every commodity, including labour, exactly equals the price of the inputs used-up to produce it (input prices equal output prices). Given the conditions of the problem there cannot be a conservative transform between the labour-value system and the price system in this special case. Hence the transformation problem (TP). (My recent paper goes into this in great detail). I am not interested in what Marx really meant, or whether there is a consistent interpretation of his work. I am interested in developing the critique of political economy. So the question then becomes: how does this special case further our understanding of the LTV? It's not fruitful to ignore important contradictions. I also think that when we have a complete, mathematical and dynamic interpretation of Marx's theory of the laws of motion of capitalism we will find that there are important and essential relations between the logical method of simultaneous and sequential determination. My guess is that the TSSI school, by denying the legitimacy of simultaneous determination, will be unable to arrive at a full and complete understanding of the fundamental reasons for the existence of the TP, and will be unable to develop a full and complete dynamic theory, in which the infamous special case really is a special case. Best wishes, -Ian.
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