[OPE-L:2989] Re: Okishio and mathematical Economics

Bruce Robert (broberts@usm.maine.edu)
Sun, 8 Sep 1996 07:41:00 -0700 (PDT)

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This is a reply to Steve C.(#2967), with some other thoughts as well.

Steve wrote:

>1. I think it is a dodge for Wolff/Roberts?Callari, and whoever else, to
>say that an equal rate of profit condition is a structural abstraction and
>not the outcome of a process. Why this particular structural assumption?
>One can point to the literature, of course, and the fact that such an
>assumption is commonly made. But that assumption is made most often
>understood as the outcome of a competitive process. Thus, the WRC
>explanation is only a step removed from being the outcome of a process, and
>that's why it can be called a dodge.

Bruce replies:

On the contrary, an actual situation in which profit rates are uniform
across industries is not *the outcome* of any competitive process I am
familiar with, in the real world or in Marx. Rates of profit are never
actually uniform (even when we look only at the average rate within each
industry); market prices are never actually equal to prices of production.
This is the case whether there is continuous technological change or
not--even if the technology is unchanging, market prices will fluctuate
without ever actually converging to any pre-specifiable state. (This is my
own view, but it's also what I read Marx as saying.) So there's no "dodge"
here--this particular non-existent situation is not *the outcome* of a
process, it's precisely an *abstraction* from the actual outcomes that we
might observe.

What kind of abstraction is it? Well, it's not a "temporal abstraction,"
as if we are abstracting from the present to the future, abstracting
through time to a "long-run" position which will ultimately be achieved (or
would be, if only everything would stay neatly ceteris paribus)--I already
argued that, to me and to the Marx I'm familiar with, profit rate
uniformity is never actually achieved, no matter what sort of static
conditions we impose. If the notion of "the" rate of profit has any
meaning or use, it's not as a way to abstract away from the present, into
the future.

To contrast with this, I coined the term "structural abstraction." What I
think Marx is doing when he constructs production prices and "the" rate of
profit is abstracting from the ever-present reality of non-equivalent
exchange--a structure of market prices (associated with differential rates
of profit) that changes from period to period for a million reasons, among
them the responses made by buyers and sellers to the chronic absence of
equivalence in exchange. Instead he abstracts to a price structure that
*does* represent equivalent exchange: in competitive capitalism, the
equality of the rates of profit received by (average) producers of
different commodities is the *definition* of exchange equivalence.

Now Steve asks "why this particular structural assumption?" and "what is
interesting about ... these prices?" To try to briefly respond: In Marx,
I read a number of his terms as being closely linked. If prices are such
that non-equivalent exchange occurs, then that means (indeed, is virtually
synonymous with) a situation where supply and demand do not "coincide,"
which in turn means that the allocation of social labor is "wrong" in
relation to expressed social needs, and reallocation will ensue as
suppliers and demanders alter behavior, resulting in changing prices
[market output prices will differ from market input prices for these
reasons, completely independently of all the other potential
causes--accumulation, innovation, etc.--for such deviations]. Marx regards
non-equivalent exchange of this sort (and the changing prices it provokes)
as the norm. But Marx poses the conceptual possibility of equivalence:
equivalent exchange would (hypothetically) occur when supply and demand
*do* "coincide," when the allocation of social labor is "right" and, for
the time being, at least, in need of no alteration, with the implication
that there is no pressure for prices to change as an effect of
non-equivalence (even if they may well be under pressure to change for
other reasons--accumulation, innovation, etc.).

Now in Vol. 1, equivalence is identified with prices equal to values (Marx
assumes that this is what equivalence in exchange means) and in chap. 10 of
Vol. 3 most of the discussion proceeds explicitly from that assumption as
well. But Marx makes it clear, I think, that *capitalist* exchange
equivalence means an equal average rate of profit rather than equal values
changing hands. Prices of production are intended as the expression of
competitive capitalist equivalence, which is itself an abstraction from the
perpetually observable situation of non-equivalence. So why this
abstraction? Marx put it well in response (pp. 189-90 of the Int'l Vol.
3--the only version I have handy right here):

"In reality, supply and demand never coincide .... But political economy
assumes that supply and demand coincide with one another. Why? To be able
to study phenomena in their fundamental relations, in the form
corresponding to their conception, that is, is [sic] to study them
independent of the appearances caused by the movement of supply and

The phrase "political economy assumes that supply and demand coincide" is,
IMO, synonymous with saying "political economy abstracts from
non-equivalence to the structure of equivalent exchange." So I think that
the notion of equivalent exchange (not to be confused with the assumption
of prices equal to values) has a crucial role to play in the conceptual
derivation and meaning of all of Marx's value categories, and that's the
basis on which I justify this particular structural assumption.

I'm sure it's possible that Steve might respond that any invocation of
suppliers and demanders "responding" to non-equivalent exchange must be
based on an implicit appeal to their rationality. But if this is
methodological individualism, then I'm not real concerned about it. I
liked, by the way, both Paul C. and Andrew's responses to Steve on this
point, but in any case I'm pretty sure that the real methodological
individualists out there would not recognize what I've said here as having
much in common with their own views. In fact, I'd prefer to turn the
original question around: if *any* discussion of "the" rate of profit
necessarily presupposes methodological individualism, then haven't we
defined the latter term to include virtually everyone in the history of
economics (Marx and almost all of the Marxian tradition included), and
thereby made the term virtually meaningless?

Briefly, with respect to Okishio, on which I've been silent through the
recent fascinating discussions, I have never personally regarded Okishio's
result as something requiring "refutation" from my own perspective. The
premises of the theorem are unacceptable--*not* because it employs
simultaneous calculation (which is, to my mind, the only meaningful way to
approach "the" rate of profit) but because it depends on an assertion about
capitalist choice behavior in a very specific and thoroughly unreal
situation-- comparing profits *at* a uniform rate of profit calculated
using the supposedly *reigning* prices of production to profits as they
would be with a new technique but the same supposedly reigning production
prices. I have never been able to take this real seriously as having any
dynamic implications for a real capitalist economy since production prices
*never* reign in any case.

Every decision as to whether or not to implement a new technological option
is made on the basis of a ruling price structure *different* from
production prices, and thus a current profit situation that is not "the"
rate of profit in any of the senses that have been proposed. This is also
why I've never been able to take too seriously the efforts to "refute"
Okishio. As different as Andrew's conception of the rate of profit is, his
proposed counterexamples
necessarily try to occupy the same (or ar least very similar) turf as
Okishio, which leaves them open to the same objection. The TSS production
prices associated with the TSS rate of profit are not "there" for
capitalists to use in their calculations any more than Okishio's are.

So: I think simultaneous calculation is the correct basis for defining the
ratios of capitalist equivalent exchange (the basis, as I understand it,
for a Marxian concept of "the" rate of profit), but at the same time the
rate of profit so calculated is not--ever--manipulable as if it and its
associated prices were real pieces of information available to capitalists.
"The" rate of profit falls or rises depending on what capitalists (and
workers) actually *do*, but they do what they do in response to *market*
prices, not the production prices associated with equivalent exchange. And
I think that Duncan's intuition is absolutely correct--to influence those
who've been persuaded by Okishio will require "something with as much
equilibrium and stationarity assumed as possible." But for myself I'd
rather see a specific, detailed, conjunctural "story" told with numbers, in
which capitalists make what appear to be perfectly reasonable choices in
response to differential profits and prices that are not production prices,
yet in the end "the" rate of profit underlying it all ends up lower than at
the beginning.

Bruce B. Roberts
Department of Economics
University of Southern Maine
Portland ME 04104-9300
(O) 207-780-5503
(H) 207-772-7047
fax 207-780-5507-------------------------------------------------