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

From: Fred Moseley (fmoseley@MTHOLYOKE.EDU)
Date: Tue Sep 11 2007 - 21:32:23 EDT

Quoting Ian Wright <wrighti@ACM.ORG>:

> 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

Hi Ian,

My equations are very simple.  Prices of production are determined by:

PPi =  ki +  rKi

with r, ki, and Ki taken as given.  Therefore, prices of production
change only if one of these determinants change.  These determinants in
turn depend on the productivity of labor and the real wage.  So if the
productivity of labor and the real wage remain constant, then prices of
production will also remain constant, and thus will be a
“self-replacing equilibrium", without simultaneous determination.

>> 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.

Maybe so, but that does not mean that simultaneous determination is the
best way to theorize the determination of equilibrium prices in
capitalism.  And certainly not the only possible way.

> 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,
>
> 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.

I am disappointed that you think I am “fulminating”.  I have told you
before that I think your project is worthwhile doing.  But I also argue
that the logical validity of Marx’s theory does not depend on the
outcome of your project.  The fact that Marx’s theory cannot be
translated into a different logical method does not imply that Marx’s
theory is logically invalid.  It only implies that Marx’s theory cannot
be translated into this different logical method, without producing
“anomalies”, etc.