[OPE-L:2925] Re: Okishio theorem

Gil Skillman (gskillman@wesleyan.edu)
Fri, 30 Aug 1996 09:21:08 -0700 (PDT)

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What the heck, I'll take a shot at this. Andrew writes:

>A reply to one issue addressed in Duncan's 3-parter, Alan's 4-parter, and
>Duncan's response (ope-l 2915) of this evening. There is obviously more that
>I need to and want to say, but the following can be discussed in independence
>from the rest, and it is all I have time for before leaving town (and the
>list) for the long weekend.
>I think it is *the* single most crucial issue under discussion at this moment.
>Duncan's latest post states: 'I think that Okishio and certainly Roemer do
>make the equivalent of (E) explicit in their definition of the "general rate
>of profit".' "(E)" stands for the following postulate (which I've edited
>slightly for concision): "an input/output economy [considered] in a state
>where input prices are equal to output prices and profit rates are equalised"
>both before and after "a viable technique is introduced into the economy."
>I *think* Duncan's statement indicates that we have come to a very important
>agreement in this discussion. That is, *if* Okishio or Roemer state (E) or the
>equivalent explicitly in their major presentations of the "Okishio Theorem,"
>then the theorem has not been refuted in the narrow sense. However, *if* they
>do not state (E) or the equivalent explicitly, then the theorem has been
>refuted, even in the narrow sense.

The question is whether Okishio or Roemer state condition (E) or its
equivalent "in their major presentations of the "Okishio Theorem". My
answer is that Roemer certainly does, and therefore in my understanding
Andrew has not refuted the theorem "in the narrow sense" (or indeed in any
sense that I understand the notion of "refuting a theorem").

In his 1977_ Journal of Economic Theory_ article, Roemer states the theorem
this way:

"Proposition 5 (Okishio). If technical change is introduced by capitalists
only when it is cost-reducing at current prices, then the equilibrium rate
of profit will rise."

What Roemer means by the "equilibrium rate of profit" is stated explicitly
in equations 1.3-1.4, which specify prices of production equations for "an
input/output economy [considered] in a state where input prices are equal
to output prices and profit rates are equalised", that is, condition (E).

Lest there be any doubt here, in support of this specification Roemer refers
the reader to Morishima's _Marx's Economics_, where on p. 62 the equivalent
of Roemer's equations (i.e., those requiring that input prices=output prices
and that the rate of profit is equalized across sectors) is characterized as
a representation of "long-run equilibrium." So it seems legitimate to say
that the term "equilibrium" invoked by Roemer in his statement of the
Okishio theorem is equivalent to condition (E).

I'd add that this is the only reasonable interpretation of "equilibrium" in
the theoretical world specified by Roemer, i.e. a static model with no
monopolies, mobility barriers, transaction costs, or heterogeneous goods.

I'd add further that by allowing equilibria in which input and output prices
diverge other than by a given time discount factor, Andrew is implicitly
assuming a form of market incompleteness which requires explicit
justification, since futures markets do in fact exist in the real capitalist
world. Thus in my reading Roemer's assumptions are more clearly spelled out
than Andrew's.

Bottom line: much as I like the *issues* that the TSS approach has
introduced into Marxian analysis, I have to agree with Duncan: in my
understanding, Andrew has not in any standard sense provided a "refutation"
of the Okishio theorem.

In solidarity, Gil