juliohuato at hotmail.com
Wed Sep 24 15:56:53 MDT 2003
Rakesh Bhandari wrote:
>But the whole idea of applying equilibrium thinking to of all things--the
>most dynamic mode of production in world history--is what seems to me most
A dynamical system is one whose evolution over time depends on its state
(current and/or past) as well as on "other factors." It is a very general
mathematical concept. It doesn't need to have a single "attractor," "steady
state," or "equilibrium." It may have none or many equilibria. If it has
one, the system may not converge or cycle around it. It may have no
discernible path. The possibilities are endless.
Now, when we examine a complex capitalist society as a dynamical system,
given the limitations of the mathematical analysis of dynamical systems, we
must pick the aspects of the system we wish to focus on -- and leave the
"other factors" outside of the analysis (i.e., assume their constancy).
>From a geological or astronomical point of view, the element of permanence
in capitalism may be negligible. But from the point of view of a human
lifetime or of a few generations, that is, from a reasonable historical
point of view, capitalist life has an element of permanence or stability. I
mean, capitalist production has replicated and extended itself for four
centuries already. It makes a lot of sense to study its stability or
And this is exactly what Marx does in Capital, vol. 2, part 3. He
deliberately focuses on the proportionality conditions that make it possible
for aggregate capital to reproduce itself. He is, implicitly, looking at
capitalist societies as dynamical systems, except that he uses simple
algebra and numerical illustrations while nowadays people may use more
advanced mathematical analysis. But Marx focuses there on the system's
Is Marx thereby implying that capitalist reproduction is a smooth,
harmonious, microscopically stable dynamical process? No. But to the
extent that capitalist societies do reproduce themselves, then the
conditions for their reproduction are somewhat and somehow fulfilled. Such
conditions are, implicitly or explicitly, a set of equilibrium equations.
Hence, there must exist some mechanism to enforce those conditions. Without
such mechanism, the disproportions would explode and the system would
disintegrate ipso facto.
At the stage of Marx's analysis in Capital, vol. 2, such enforcing mechanism
(the implicit "equation of motion") is assumed to be the law of value. The
concrete forms of operation of the law of value under capitalism are not yet
fully elaborated by Marx at this stage. At this stage, as it asserts
itself, the law of value corrects the disproportions and pushes the system
back to its steady state. Indeed, if the "other factors" assumed constant
were to change (and they do change all the time), then the dynamics would
adjust as well. Thus, it is trivial to say that *if* the "other factors"
(external to the system) don't change *and* the system is at a stable steady
state, *then* there are no forces *within* the system upsetting it. We need
to take the "ifs" and "thens" seriously.
In Capital, vol. 2, Marx looks at what he calls "normal" capitalist
reproduction. He assumes that capitalist reproduction happens. Now, does
he imply that the mechanism through which the reproduction conditions are
enforced (the law of value or its more concrete forms of operation under
capitalism) is smooth and nice? No. The fact is that such mechanism is not
explicitly dealt with at this stage of Marx's work. And it is obvious that
Marx doesn't conceive the law of value as a smooth, harmonious mechanism.
On the contrary, he makes it clear (somewhere else) that the law of value is
a turbulent process, beset with disproportions that pile up before they get
corrected, that even in its abstract and general form it contains the formal
possibility of crises, etc. When we consider that he has already described
how the law of value is transfigured as a result of the wealth asymmetry
between capital and labor as they face each other in the market (vol. 1,
chapter 24), the law of value is not only a turbulent mechanism but a
socially antagonistic mechanism as well. Still, Marx leaves the specific
treatment of the more concrete aspects of capitalist turbulence to further
All we can say is that Marx's analysis in Capital, vol. 2, is partial or
incomplete -- which is something he admitted. But we cannot say that his
analysis is invalid or useless because it abstracts from the crises and
fluctuations that enforce capitalist reproduction, i.e., because he focuses
on "equilibrium." This analysis is a piece in his bigger puzzle. Marx
warned the readers about his approach. The clearest defense of Marx's focus
on the stability conditions of capitalist reproduction that I know of is
given by Roman Rosdolsky in his study on the Grundrisse. In that work,
Rosdolsky refutes many common misunderstandings on the role of this abstract
analysis of capitalist reproduction in Marx's work. These misunderstandings
arise from a confusion about Marx's work plan and approach.
Again, the problem is not the use of the notion of equilibrium, but its
misuse. The problem is not the statement that capitalist societies
reproduce themselves. Obviously they do as they've been doing it for a
while. Hence, if we want to understand their fundamental dynamics, looking
at the limit case that Marx called "normal reproduction," i.e., a steady
state or equilibrium, is not a bad starting point. The problem is to imply
that *since* capitalist societies reproduce themselves, *then* the process
by which they do it is smooth and nice. That is the non sequitur.
It is of course conceivable to look at capitalist societies as dynamical
systems in a different way, so that the focus is shifted towards their
inherent instability and turbulence. As far as I know, the analysis of
complex systems is still in a state of flux. Perhaps mathematical analysis
cannot carry things further. Maybe computational simulations or other
methods will prove helpful. But my impression is that we don't get
clear-cut results in any way resembling the simplicity and generality of the
results from the mathematical analysis of simple dynamical systems.
For example, in the General Theory, chapter 12, Keynes says that long-term
investment in an "entrepreneurial economy" is a self-referential process
because it is based on expectations about what other investors might do,
investors who in turn plan their moves on what others might do, and so on in
an endless loop. As far as I know, the dynamics of self-referential systems
is not amenable to the easy mathematics of stable systems. So, here we kind
of hit a wall in terms of our ability to discern patterns in the system by
means of regular mathematical analysis. Am I right, Les?
If we think about it, it makes sense. There must be a narrow set of ways in
which a capitalist society, with its array of centrifugal forces, can
replicate itself. Yet there must be many ways in which it can go haywire.
Pinning down the turbulence of capitalist development is not an easy task.
There are, of course, other ways to look at it. I'm just alluding to the
equilibrium approach that some Marxists tend to discard offhand. IMO, given
the current state of our analytical tools, Marx's analysis of capitalist
reproduction needs to be not only developed along the mathematical lines he
sketched (there are already many formalizations that generalize Marx's
results), but also complemented. We need statistical inference and
historical analysis, inter alia, and we need to be aware of their
limitations as well. My point is that it is not acceptable to reject the
notion of "equilibrium" or to equate it with bourgeois economics,
particularly when such rejection is based on an obvious misunderstanding.
Among the heterodox economics crowd, the critique of equilibrium analysis is
the cheapest shot in the arsenal. The "equilibrium" approach is partial and
one-sided, but Marxists shouldn't draw nihilistic conclusions from that.
I don't have Carchedi and Freeman's essay at hand and my memory is not good.
So I'll appreciate it if Rakesh summarizes for us the results of their
"attempt to derive logically and formally the properties of a non
equilibrium system." I don't mean this in an ironic way. As much as my
views may diverge from theirs, my comments should in no way be interpreted
as a formal response or critique of their paper.
Finally, if Les Schaffer reads this and he gets a hold of the papers on
Marxist thermodynamics cited on the previous thread, I'd like to get a copy
of them if possible. Thanks.
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