A comment on Jerry's ope-l 3007.
Jerry quoted Duncan's ope-l 2950:
> 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.
and asked: "I may have missed something, but has anyone answered the above
argument?"
Not yet, as far as I know. Since Jerry has asked, however, let me do so now.
(1) Duncan's statement was made in response to a comment of mine in ope-l
2949. I wrote that since he and Gil thought (E) was stated explicitly, while
others of us did not, "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."
(2) I interpret Duncan's response as follows. His previous claim that (E)
was stated explicitly meant that Okishio and especially Roemer *intended* (E)
to be understood as a premise. However, to explain the existence of a
contrary interpretation of the theorem, Duncan acknowledges that (E) was
actually not stated *explicitly*.
(3) This last point was what had been in dispute, beginning with Alan's ope-l
2886 and Duncan's response in ope-l 2915. Alan wrote: "1. I agree with
Duncan that postulate E is the basis of Okishio's result. 2. This is not
explicit. ... 3. This should change .... The label of the bottle should tell
us what we are being asked to swallow. 4. It is ... perfectly reasonable to
refute [the Okishio theorem] as Andrew has done without assuming E, provided
all Okishio's openly-stated postulates are respected." As Alan's point 3.,
especially, makes clear, the issue was whether Okishio and/or Roemer labeled
(E) as a premise of the theorem, not whether they intended it to be understood
as such.
(4) Duncan's statement in ope-l 2950 indicates that he concurs with Alan,
Jerry, and me that (E) was not stated explicitly, i.e., labeled as a premise.
(5) I wonder whether Gil also concurs.
(6) As Alan noted, if (E) was not stated *explicitly*, the Okishio theorem,
as put forth by Okishio and Roemer, has been refuted in what I called the
"narrow" sense and Duncan, with more precision, has called the meaning of
"refutation" in mathematics and logic. That is, counter-examples have shown
that the conclusion of the theorem does not follow from its explicitly stated
premises.
(7) This refutation of the theorem is *sufficient* to establish that the
theorem does not demonstrate any "logical" error in Marx's law of the FRP.
(8) Proponents of the theorem have thus claimed too much when they have
claimed that it refutes Marx's law _and_ when they have claimed that it shows
that technical innovation itself cannot cause the "equilibrium" or "general"
rate of profit to fall (given the theorem's premises). Beneath these
excessive claims, however, I believe that Okishio and Roemer *do* derive a
valid result, and I agree with Duncan that the refutation of the
theorem-as-stated is not a negation of this result or its scientific
importance.
(9) The valid result, as I stated way back when (March 22; ope-l 1533), in a
reply to Gil, is this: "I would suggest that a valid English translation of
the demonstration would be: 'Assume a static equilibrium at stationary
prices, with an equalized profit rate. Assume a technical change that lower's
some producer's costs at current prices. Use the new input coefficents to
compute an imaginary set of prices and the imaginary profit rate associated
with it, given the further assumptions that the profit rate is again equalized
and that stationary prices then prevail. The latter, imaginary, profit rate
must be greater than the initial one.'"
(10) If one finds this wording too biased, the following is equivalent:
"... Assume a technical change .... If both an uniform rate of profit and
stationary prices are again established after this change, the magnitude of
the resulting rate of profit cannot be lower than the initial one."
(11) One's evaluation of the scientific importance of this valid result
will clearly depend on one's view of (a) the likelihood that *both* conditions
will be established, whether exactly, or tendentially, or as centers of
gravity (average of oscillations); and (b) the permissibility of using the
result to draw inferences about the real world when *either* condition is
violated, whether exactly, or tendentially, or as a center of gravity.
(12) My own view concerning (a) is this: Stationary prices are extremely
unlikely to be established in *any* sense, even as a center of gravity, in
part because technical changes come one after the other rapidly enough to more
than counteract any tendency toward stationary prices. To my knowledge, no
behavioral models that show convergence to stationary prices supply any reason
to alter this view, because convergence is far from guaranteed, because they
abstract from technical change, and, perhaps most importantly, because they
show only convergence of *relative* prices to a stationary state, whereas the
valid result of Okishio and Roemer requires stationary *absolute* prices.
Concerning (b): If the conditions under which a result holds are not present,
even in any approximate sense, then the result is irrelevant to the real
world. The contrary view allows us to conclude that it rains because we fail
to do God's work and His umbrella thus fails to cover us.
(13) My comments in (12) are strictly separable from the issue of whether
the Okishio theorem has been refuted and from the issue of whether it
disproves Marx's law of the FRP. One may think the valid result of Okishio
and Roemer is of great scientific importance, but for the *Okishio theorem*
and its purported disproof of Marx's law to be true, it would also have been
necessary that (E) had been stated explicitly.
(14) I do not think that Okishio or Roemer even *intended* (E) to be
understood as a premise of the theorem. Although Gil and Duncan both seem to
think Roemer does a better job than Okishio of calling attention to the role
of (E) as a premise, I am convinced that Roemer does more to make (E) seem to
be a RESULT.
In his June 1978 _Australian Economic Papers_, v. 17 article, "The Effect of
Technological Change on the Real Wage and Marx's falling Rate of Profit,"
Roemer presents the theorem by means of a 2-sector example. After positing a
viable technical change, but *before* writing down the post-innovation,
stationary price, uniform profit rate equations, he writes (p. 154): "If such
a technique appears and is adopted, the profit rate *will immediately rise* in
sector 1 [the innovating sector]. This *will encourage* more firms to enter
sector 1 from sector 2; prices *will be cut* in competition and *eventually* a
new equilibrium tableau *will emerge* [my emphases]." He then writes down the
equations and comments: "It is a theorem that if (2.5) [the viability
condition] holds then pi* > pi: which is to say that if the real wage (b)
remains fixed then cost-reducing technical innovations *give rise,
eventually*, to a rise in the equilibrium rate of profit in a competitive
situation" [my emphasis]."
Similarly, on pp. 114-15 of his _Analytical Foundations of Marxian Economic
Theory," he presents an n-sector model under the heading "_Okishio's
theorem_." After presenting the viability condition, he writes "If and only
if the innovation is viable, it will be introduced. After its introduction,
*there will, for the time being, be* a higher rate of profit earned by the
innovators in sector i; *eventually*, through entry and price cutting, a new
equilibrium *will be arrived at* ... [my emphases]."
How is it possible to interpret any of this as a statement that (E) is a
premise in the theorem? Not only is there no explicit statement that the
proof presupposes (E) as a premise, but the nonconditional, declarative
language and the temporal language do state explicitly that a stationary price
tableau "will be arrived at," "will emerge," "eventually," through competition
of capitals. A CLAIM is being made concerning what would be the real world
"in a competitive situation."
Nor is it tenable to separate the English from the algebra. In AFMET, both
the English and the algebra come under the heading "_Okishio's theorem_."
The most charitable reading of all this I can give is that Roemer was assuming
that competition would eventually give rise to a uniform rate of profit and
(wrongly) thought that uniform profitability presupposes stationary prices,
and therefore (validly but wrongly) concluded that the establishment of a
uniform profit rate would necessarily result in stationary prices.
(15) Duncan suggests that it would not have made "much difference to
anybody's opinion about the result" of the Okishio theorem had (E) been stated
explicitly. Well, there's no way of knowing, but I suspect the opposite is
true. Certainly an explicit statement of (E) would not have allowed Roemer to
tell everyone that the theorem constitutes a result concerning the real world
in a competitive situation.
Certainly, when I learned about the theorem as a graduate student, I would
have laughed it away, instead of spending countless hours doing the work
myself of figuring out that the result depends crucially on stationary prices.
Moreover, what did people who didn't like the result do? They scrutinized the
theorem to see which assumptions they could relax in order to arrive at a
different result. Salvadori and Giussani relaxed the single-product
industries assumption, Anwar and Nakatani relaxed the viability condition,
Hunt relaxed the no-land assumption, Duncan, Laibman and others relaxed the
constant real wage assumption. Why did no one other than John Ernst call
attention to, or even seem to recognize, the fact that the result doesn't hold
unless input and output prices are equal? Might it not be because this was an
"unobtrusive postulate," an assumption which, unlike the others, Okishio,
Roemer, and van Parijs did not lay bare? Might it not be because they all
also wrongly thought that the establishment of a uniform profit rate would
necessarily result in stationary prices?
So I suspect that had the opposite been more widely understood, and had the
proponents of the theorem called attention to the fact that the result
requires stationary prices as a postulate, a lot of critical attention would
have been concentrated on this problem very early on. Since, moreover, the
disruption of stationary prices is a consequence of technical change *itself*,
whereas the other conditions that were relaxed are independent of technical
change, I suspect it would have become clear very early on, at least to some
folks, that the theorem treats the problem in a ridiculous way. Its lack of
implications for Marx's law would have also been a lot clearer, I suspect,
because falling values are part and parcel of the law.
And if the fact that uniform profitability and stationary prices don't go hand
in hand had been understood, I suspect that the Bortkiewiczian "transformation
problem" would have come under attack a lot earlier, too, and it would be more
widely questioned than it is now. With these two pillars of the "logical"
critique of Marx's value theory in question, people like Anthony Brewer would
have had a much harder time with their campaign to consign Marx to the dustbin
of history.
(16) But again, all this is speculation (as is Duncan's contrary guess).
What matters at the present moment is whether the explicit statement of (E)
NOW will make much difference to anybody's opinion about the result. Let
there be the truth-in-labeling for which Alan pleaded. How can this possibly
be objectionable? How about if we take on as an ope-l group project the task
of making clear to everybody that the theorem as stated is false, that it
doesn't refute Marx's law, that the result would be valid were stationary
prices made a premise, but that uniform profitability doesn't ensure
stationary prices. Then let's take the discussion of the implications of the
result, and the implications of stationary prices in general, out into this
newly-informed environment and see whether opinions are changed.
(17) As the Brewer attack and many others like it make clear, the Okishio
theorem is not, historically, just a scientific model, but a powerful weapon
against Marx's Marxism. This is the main reason I do not want to turn my
attention solely or even mostly to "the problem of theories of profit rate
determination and competition under conditions of continuing technical change"
(Duncan, ope-l 2950). I want to keep combating the ideological attack on
Marx's body of ideas and try to get the historical record corrected.
(18) Duncan's project is an important one nonetheless. I don't presume to
have identified many questions in the constellation, much less answers. I
have tried to investigate one question that I consider extremely
important---what are the implications of stationary prices?---and will
continue to do so. I do not think our attention should be drawn solely, or
even necessarily mostly, to behavioral and empirical questions. It is also
important to understand, for instance, why certain postulates give certain
results. Why, for instance, does the Okishio/Roemer result depend on the
postulate of stationary prices? Is it (only) because there are too many
degrees of freedom otherwise? How many degrees of freedom would be added?
(19) We haven't had a quiz in awhile. I'm starting a new one, consisting
of these three questions.
Andrew Kliman