Nonlinearity and Grossmann
cburford at gn.apc.org
Sat Feb 25 10:08:50 MST 1995
Dear All: I wonder if anyone could offer any references to
applications of non-linear mathematical models ("chaos theory") to
capitalist society (or "the economy").
The request from David Harvie, from Leeds, England
tips me over into also supporting Rakesh's diligence in promoting
Grossmann, by posting up a comment that will be published in
the small English journal "New Interventions" in the next issue.
It was in response to an informative review of Grossmann's book by
Ken Tarbuck, editor. The journal derives from the desire of a
number of people coming in the main from an ex-Trotskyist background to
re-examine and reapply Marxist ideas. Although I do not share its
background, I feel people in the UK may wish to know the
contact details: #2.50 (sterling only) single copy internal mail, from
Marken Press, PO Box 707, Worthing, West Sussex, BN11 5ZP England.
Overseas subs for 4 issues #12.65 sterling.
GROSSMANN AND NON-LINEAR MODELS OF CAPITALIST CYCLES
The cycles of capitalist production are still all too much with us. In fact
at times they seem to preoccupy capitalists and their governments even more
than they do socialists. The thoughtful review by Ken Tarbuck in New
Interventions Oct./Nov. 1994 (Vol.5, 3/4) of Grossmann's theory of
capitalist crises* does a service in bringing to the attention of readers
a creative discussion of this vital question which we might have overlooked.
I accept Ken's comments that critics such as Sweezy and Mandel may have
been over harsh. Grossmann appears to respect both the objective and the
subjective factors, which have to be held in balance on this question.
It is clear that he was making use of an abstract model to explore its
fit withreality. What we can now point out is that the model was linear,
for example positing a steady 5% increase in the available working
population each year.
Such an analysis is inherently unlikely to explain a cyclical process.
For that non-linear modelling is more likely to be relevant, that is with
terms that feed back negatively or positively on each other. (Readers will
remember how equations with squares or cubes in them - things raised to
the power of two or three, form curved rather than straight line graphs.
So will expressions with powers that are a fraction - the important thing
is a model containing feedback).
Certain models with such expressions can produce undulating wave-like
curves, which are analogous to cycles in economics. Indeed it is interesting
that in this presentation the accumulation of capital is seen to proceed in
a series of "waves" rather than a smooth upward progression, which as Ken
comments, is of course much nearer to reality.)
In fact by working it through, Grossmann shows that unless the collapse of
capitalism is predetermined, a linear model of capitalist cycles cannot
Ken's summary of all the "counter-tendencies" he lists is instructive. It
would be interesting if they could be incorporated into a working non-
linear model. Some are particularly intriguing such as "the conflict between
use value and exchange value".
The overall theme is however illustrated by the passage Ken quotes from
"The circumstances through which the crises can be overcome vary
enormously. Ultimately however, they are all reducible to the fact that
they either reduce the value of the constant capital or increase the rate
of surplus value."
Indeed the periodic destruction of sections of capital is a commonly
observed feature of capitalist crises. Redistribution of capital within a
society can occur this way. It can also occur through a shift in the
proportion of different types of capital as the total amount of exchange
value in a society increases through industrialisation, and the portion
tied up in land decreases relative to that in plant and machinery.
We need to reaffirm the overall robustness of the Marxist theory which sees
exchange value as the abstract representation of labour time necessary under
the prevailing methods of production. As Marx argued in Wages, Price and
Profit, effective resistance to the capitalist tendency to lower wages can
redistribute to some extent the total pool of exchange value of a given
society towards consumption by the workers.
Grossmann's book suggests we need to explore how during capitalist economic
cycles the division of the total exchange value of a society fluctuates
between capital and workers. (One step, is surely to try to look at this
question in terms of constant prices, as Grossmann does.) We should aim to
clarify the relevance of Marxist theory in a way that does justice both to
the changes in fortune of the workers at different stages of the cycle and,
in a non-determinist way, and if the subjective factors are also right,
leaves open the door to the revolutionary departure from this fluctuating
and self-perpetuating capitalist mode of production.
Chris Burford, London January 1995
*"The Law of Accumulation and Breakdown of the Capitalist System:
Being also a Theory of Crises", Henryk Grossmann 1929, republished
by Pluto Press, London 1992
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