[OPE-L:2813] Okishio/Kliman Part 2 "Generalization"

Duncan K Foley (dkf2@columbia.edu)
Fri, 9 Aug 1996 13:04:37 -0700 (PDT)

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Do you regard our *definitions* as different in
this case? If so, why?

Duncan now:
I've never seen a definition from Roemer or van Parijs of the profit rate
in what they would regard as transitional situations where prices are
changing, so I can't answer the question.

What could possibly justify making stationary prices
part of the *definition* of the profit rate, even the "equilibrium" profit

Duncan now:
Well, if we can define the profit rate unambiguously in nonstationary
situations, so much the better. It would help me to understand your
argument if you started with such a definition. I take it that your
definition is the same as Okishio/Roemer in the special case of stationary
prices. I don't think that in defining the profit rate in particular cases
they are saying anything about its definition in general.

But if our definitions are the same, then, at minimum, we have
produced a counterexample in the circulating capital case. Do you agree?

Duncan now:
I still don't fully understand your definition in general. As far as I
know Okishio/Roemer have not put forward any definition of the profit rate
except under the assumption of stationary prices, so I'm hard put to agree
that the definitions are "the same", or that your example is a
counterexample in the mathematical sense.

In the case of fixed capital, the level of my profit rate is identical to
Roemer's if prices are stationary (one can have technical change with
labor productivity) and, if the technical change is one-shot, I've shown
my profit rate adjusts to his over time. To me this indicates that the
*definitions* are the same, and that the results differ simply because he
illicitly smuggles in a stationarity constraint on prices. Again, how can
stationary prices be part of the definition of the profit rate? What do
think about this?

Duncan now:
I confess that I have a rather different way of understanding the logic of
the argument. I take the Okishio/Roemer results to be a partial analysis
of the problem of technical change and the rate of profit, using the
method of comparative stationary price equilibria. This certainly limits
the generality of the result, but it doesn't make it wrong. I see your
examples as striving toward a generalization of the Okishio model to take
into account nonstationary price paths. I would interpret you as claiming
that some of the theorems that are true in a comparative stationary price
context don't generalize to the dynamic behavior of the profit rate in a
model of price adjustment. I suspect that this might be true, but for me
to feel that I understand it, I'd have to see a well-specified model,
including an explicit treatment of price adjustment and expectations.

Also, how is it possible to test the claim that our definitions of the
rate differ? What is Roemer's definition of the profit rate in the
case, and not only in the special case of stationary prices? If our
definitions are precisely the same in the latter case, and he has no
definition in the general case, how can our definitions be said to differ?

Duncan now:
Isn't this an issue in all generalizations? There are many different
generalizations of any specific definition, so it doesn't seem possible to
be sure what Roemer's definition would be in general and then to compare
it with yours. I think you would be on the strongest analytical ground if
you made your definition explicit, and demonstrated that it coincided with
the usual definition in the stationary price case (as you say), so that it
is a genuine generalization of the existing theory. Then there still has
to be a discussion of whether or not your generalization is economically
relevant and analytically useful.

Moreover, with all due respect, I don't think it is enough to produce a
*possible* interpretation of the Okishio/Roemer profit rate in which its
definition differs from mine. We are discussing the *stated* premises and
conclusions of the theorem. To counter my claim to have refuted the
one must show that what they actually define the profit rate to be differs
from my definition.

Duncan now:
I think my position on this should be clear by now: I see your examples as
trying to generalize the Okishio type analysis and claiming that the
special case represented by the Okishio theorem (assuming stationary
prices) doesn't generalize. Showing that a theorem doesn't hold under more
general assumptions is not the same as exhibiting a counter-example to it
under the hypotheses it assumes.

More to come,