[OPE-L:2915] Re: Re Duncan's [2812]; Okishio 1 of 4

Duncan K Foley (dkf2@columbia.edu)
Wed, 28 Aug 1996 15:22:07 -0700 (PDT)

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A brief and partial reply to Alan's discussion of the Okishio theorem and
equilibrium methodology:

1. I think that Okishio and certainly Roemer do make the equivalent of (E)
explicit in their definition of the "general rate of profit".

2. I doubt that any of the scholars Alan criticizes as adopting the
equilibrium methodology would quarrel with his general criticism of it.
Everyone recognizes that equilibrium and stationarity assumptions do
violence to reality, and wishes for a more general dynamic theory. (Frank
Hahn, for example, has made a career out of raising this point in the
context of neoclassical theory.) I think they would adopt one or another
or a combination of the 6 "Senses" Alan lists in his 4th part as a
justification for studying the stationary case. From my experience in
having conversations with economists of various ideological persuasions, I
would expect that they would also say something like: "Of course a fully
dynamic theory would be better, and as soon as somebody produces one that
has reasonable generality and produces definite results, I'll switch over
to it as a mode of reasoning. But I don't see such a theory at present,
and so in the interests of arriving at some kind of positive results, I'll
work with the stationarity assumption, where at least I know where I stand
and I can reach mathematically clear conclusions." Much could be said
against this position, but positive results in simple models tend to hold
the field against general negative criticism in the history of thought.
The quote Alan produces from Marx (CIII p 173) in part 3 of his notes
shows, as do many other passages (such as the theory of simple and
expanded reproduction), that Marx himself was acutely aware of the
analytical advantage of equilibrium reasoning in certain circumstances and
correctly employed.

In fact, if there is a very different conclusion about the falling rate of
profit to be reached from Okishio's in the context of continuous technical
change, it will probably become influential by being put forward as a
particular carefully specified example with as much equilibrium and
stationarity assumed as possible (for example in a model with technical
change continuing at a constant rate), rather than as a very general claim
in a very general dynamic model. Andrew's examples are a step in this
direction, though they still leave some critical details of the theory of
investment and price formation unspecified.

3. In part 2 of his comments Alan says "If we agree that Okishio depends
on (E), and if we can establish that (E) is false, then it seems to me we
have a refutation of Okishio..." But this is not the usual usage of the
word "refutation" in mathematics, at least: if a hypothesis of a theorem
does not correspond to reality, it doesn't make the theorem wrong as a
logical construction, it makes the theorem irrelevant to explaining the
phenomenon at hand.