[OPE-L:2950] Re: In Search of (E)

Duncan K Foley (dkf2@columbia.edu)
Tue, 3 Sep 1996 12:40:29 -0700 (PDT)

[ show plain text ]

On Tue, 3 Sep 1996, andrew kliman wrote:
(in part)
> The Kliman Theorem
> ----------------------------
> The equilibrium rate of profit is determined by
> e = mc^2
> (1)
> where e is the equilibrium profit rate, m is a positive constant, and c is the
> sum of costs of production throughout the economy.
> Now, if a cost-reducing technical change, evaluated at current prices, is
> introduced anywhere in the economy, then
> c' < c
> (2)
> where c' is the new sum of costs of production, and
> e' = m(c')^2
> (3)
> is the new equilibrium profit rate.
> Since c' < c, e' < e. Q.E.D.

In my view, it is a true mathematical theorem that if e = mc^2 and c
falls, then e falls.

> >From the above, it should be clear that those authors who have denied the law
> of the tendency of the profit rate to fall were simply wrong.
> Questions:
> Is this proof valid, or is it hogwash because the equilibrium profit rate is
> NOT determined by e = mc^2?

The proof is valid, but the interpretation of it as applying to an
economically meaningful profit rate is hogwash.

> Did I *define* "the equilibrium profit rate" in (1) or (3), or did I make a
> falsifiable (and false) *claim* concerning the determination of its magnitude?

You did both. Mathematically you defined it. Interpretatively you made a
falsifiable claim.

> Is my conclusion, that "those authors who have denied the law of the tendency
> of the profit rate to fall were simply wrong," a valid one?


> Are we living on planet Earth, or in a Wonderland in which I'm allowed to use
> words to mean whatever I want them to mean?

On Earth words often mean different things in different contexts, which is
the cause of much dispute and misunderstanding. For example the word
"refute" has the technical mathematical meaning of providing a
counter-example that meets the hypotheses of a theorem and is inconsistent
with the theorem's claims. It also has the meaning of "refuting an
argument", which could take place at the level of interpretation, or
empirical fact, or whatever. I think that when you say you have "refuted
the Okishio Theorem" most economists who know anything about it will
assume that you're an incompetent mathematician, which isn't true, because
they will hear you claiming to have a counterexample to the theorem. I
think what you mean to say is that you believe you have refuted the
argument that the Okishio Theorem shows that Marx was wrong in his
analysis of the falling rate of profit. Of course, argument type
refutations are subject to a great deal more dispute than mathematical

> Gil (and Duncan, it seems) thinks that invocation of the term "equilibrium
> rate of profit," together with the writing of an equation such as p =
> p(A+bl)(1+r), constitutes an explicit statement of (E) or an equivalent of it.

I do.

> Jerry and I (and, I presume, Alan and John) do not. One may discount my
> reading by saying that I have an ax to grind on the issue, but does Jerry?
> No. He went on a painstaking and time-consuming search for (E) or its
> equivalent and, although he surely noticed the equations and terms like
> "equilibrium profit rate" used in connection with r, didn't find it stated
> explicitly. So we have a disagreement here. But that doesn't mean that it
> is a matter of "opinion" whether (E) or its equivalent is stated explicitly.
> The very fact that there's a disagreement on this issue is a *demonstration*
> that (E) or its equivalent is *not* stated explicitly.

At this point, however, the issue is about the drafting of the papers, not
about the results or their scientific importance. Maybe it would have been
better if a referee had insisted that (E) be stated explicitly in the
original papers, but I don't think it would make much difference to
anybody's opinion about the result.

I think it would be more fruitful to focus on the problem of theories of
profit rate determination and competition under conditions of continuing
technical change (a constellation of questions that we are far from having
any agreed-on answers to).