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

From: Fred Moseley (fmoseley@MTHOLYOKE.EDU)
Date: Thu Sep 06 2007 - 09:28:11 EDT

```Quoting Ian Wright <wrighti@ACM.ORG>:

>> Equilibrium theorizing is not the same as simultaneous determination
>> theorizing.  One can have equilibrium (in the sense of equal rates of
>> profit and long-run center-of-gravity prices) without simultaneous
>> determination.
>
> Are you sure this is correct Fred? All equilibria of systems of
> ordinary differential equations are systems of simultaneous equations.
> An equilibrium is, almost by definition, a situation where the output
> state is identical to the input state; hence, the state of the system
> is constant over time. So if you want to develop dynamic models then
> you unavoidably have simultaneous determination in special cases.
> Although equilibrium theorizing is inherently limited it nonetheless
> is essentially related to non-equilibrium theorizing. This is a
> problem for the TSSI injunction against simultaneous determination.

Hi Ian,

equilibrium prices (i.e. “self-replacing” equilibrium prices), even
though they are not determined by the logical method of simultaneous
determination (derived from a system of simultaneous equations with
given physical quantities of inputs and outputs).

Marx’s prices of production are determined by the equation:

PPi =  Ki + r Ki

where Ki is taken as given, as the CURRENT cost of the means of
production and labor-power, and r is predetermined by the prior theory
of surplus-value.  These prices of production are NOT determined by the
logical method of simultaneous equations, and yet they are long-run
equilibrium prices,
which change only if technology changes.

This equation is not a system of equations that are solved
simultaneously for relative prices and the rate of profit.  Rather,
this equation applies to each single industry separately, with the Ki’s
taken as given and the r predetermined.

My interpretation of Marx’s theory is different from the TSSI in this
respect.  In the TSSI, prices of production are NOT long-run
equilibrium prices, because they keep changing from period to period,
even though technology remains constant.  I agree that this is
problematic.  But that is not true in my interpretation.  Perhaps you
are conflating my interpretation with the TSSI?  There are
similarities, but there is also this important difference.

> Also, regardless of the interpretative issue of whether Marx's theory
> is sequential or simultaneous there now exists a post-Bortkiewicz
> special case of self-replacing equilibrium in the  literature. Why
> does Marx's theory of value appear to breakdown in this special case?

In our discussions of the past, you have used the “Bortkiewicz special
case” with two different meanings.  Sometimes you refer to the
“Bortkiewicz special case” as “self-replacing equilibrium” (a result of
the theory), as you do here.  And other times you refer to the
“Bortkiewicz special case” as simultaneous determination (the logical
method of the theory).

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?

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.

> As far as I can tell the TSSI answer is that it is "unrealistic" to
> assume inputs prices equal output prices; and in more hyperbolic
> moments they claim that simultaneous determination and equilibrium
> theorizing belongs to bourgeois ideology. This is a totally
> unpersuasive answer to the neo-Ricardian critique. The critique must
> be met on its own ground, not by refusing to accept the terms of the
> debate or its scientific legitimacy.

I also agree that input prices are equal to output prices in Marx’s
theory, which in the absence of technological change would remain
constant over time.  This is another difference between my
interpretation and the TSSI.  But input prices are = to output prices,
not because they are determined simultaneously from given physical
quantities, but instead because the given inputs are assumed to be
equal to the CURRENT cost of the inputs, as manifested in the market,
not the original historical costs of the inputs.

And let’s not forget that the Sraffian method of simultaneous
determination of input prices and output prices from given physical
quantities is not really a viable theoretical alternative.  Because it
is based on the completely unrealistic assumption that all industries
have the same turnover period.  This is not a simplifying assumption,
that could be relaxed at a later state of the theory, but is instead a
necessary essential assumption that could not be relaxed, without which
the theory doesn’t work.  For two reasons:

(1) with unequal turnover periods across industries, the rate of profit
in the price equations would be equalized for different time periods,
which would mean that the annual rate of profit for different
industries would not be equal, contrary to the prevailing tendency.

(2) simultaneous determination requires that all commodities must be
exchanged at the same time, which means that they must all have the
same turnover period.   Sraffa’s logical method was what he described
as the “annual harvest” method, according to which it is assumed that
all industries begin the production process at the same time (as in the
Spring in agriculture), and all go through the production process over
the same period of time, and then all exchange their commodities at the
same time (“harvest time”).  The theoretical question that Sraffa’s
theory asks is:  what are the (relative) prices that will allow this
simultaneous exchange to take place and all industries end up with the
same physical inputs that they started with, so that the same
simultaneous processes can be repeated in all industries in the next
period.

Marx’s theory, on the other hand, does not require the unrealistic
assumption that all industries have the same turnover period, and
therefore is a much more promising approach to understand the
complexities of price determination in capitalism.