[OPE-L:2924] Re: Okishio and the poverty of mathematical economics

Stephen Cullenberg (Stephen.Cullenberg@ucr.edu)
Fri, 30 Aug 1996 09:09:42 -0700 (PDT)

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Jerry asked the following in the context of a debate over equilibrium and

>If a hypothesis that purports to explain reality is incapable of
>explaining reality, then what use is it? Using the above test, I could
>develop a mathematical theorem that would have no relevance for life in
>this or any other potential galaxy, yet could still not be refuted (even
>though it was developed as a theorem to explain life in *this* galaxy)!

I think we might all agree that the relationship between theory and reality
is not a trivial question, nor is what is meant by "explanation," and I
don't want to address that issue directly here. Having said that, I don't
think that all mathematical models need to "explain" reality in a
positivist sense to be useful.

I think much of the modern microeconomic theory that I find useful, doesn't
address reality at all, but is constructed in a very explictly
counter-factual way. I am thinking here of general equilibrium in the
Arrow-Debreu tradition, and of social choice theory. The organizing
question of this research is not, "What is the world like", but rather
"what would have to be true if such and such a result were to hold."

Frank Hahn in his short book "On Equilibrium" is very clear on this point.
For Hahn, the importance of A-D type models is not as an approximate
description of reality (whatever that is), but to rule out unwarranted
theoretical claims made on behalf of free markets, etc.

As Garegani argued long ago in his paper in Zarembka's book on capital
theory, "On the Change in the Notion of equilibrium" (or something like
that), the equilibrium project of Classical theory was/is fundamentally
different from that of Walrasian/A-D theory. Or, as Steedman puts it in
the first pages of "Marx after Sraffa", Classical theory was looking for
"necessary" conditions for an equal-rate-of profit model, whereas
Walrasian/A-D models are looking for "sufficient" conditions for existence,
etc. That is, the A-D model is operating within a counterfactual
problematic (is the existence of an equilibrium price vector even
possible), whereas the Classical model is taking its cue from an insight
from reality (whether correct or not) and asking what must necessarily hold
if there is to be a uniform profit rate across the economy.

So, even if mathematical models don't explicitly make reality-claims, I
think they have great, and progressive (in a political sense), potential
for helping us organizing our thoughts.

Steve C.

Stephen Cullenberg office: (909) 787-5037, ext. 1573
Department of Economics fax: (909) 787-5685
University of California Stephen.Cullenberg@ucr.edu
Riverside, CA 92521