[OPE-L] equilibrium and simultaneous vs. sequential determination

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,

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