[OPE-L:2886] Re Duncan's [2812]; Okishio 1 of 4

Alan Freeman (A.Freeman@greenwich.ac.uk)
Tue, 27 Aug 1996 15:34:16 -0700 (PDT)

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I'd like to make a considered reply to Duncan's posts 2812,
2813 and 2814 on the Okishio theorem, because I think they
represent a considerable advance in the discussion but raise
some very deep questions. I would like therefore to inject
certain more general points, perhaps at the cost of failing
to deal directly with all the detailed issues which Duncan
and Andrew are discussing.

For me the vital advance in these posts is that they signal
agreement that the underlying assumption of 'Okishio-type'
theorems is the following postulate, which I'll call (E) for

Postulate E [OPE 2812]:
"[An Okishio-type theorem assumes] an input/output
economy in a state where input prices are equal to
output prices and profit rates are equalised. [It]
considers what happens to the profit rate if a viable
technique is introduced into the economy and the system
again achieves a stationary state"

Duncan contrasts this to a postulate I'll call (D) which he
defines as follows:

Postulate D [OPE 2812]:
"is what happens when there is continuing technical
change, so that the system cannot equilibriate at a
stationary price system"

Several approaches are rooted in this postulate including
Andrew's (1988) and mine (1996); I would also place Duncan's
own (1982, 1986a, 1986b) in this category. Hence, my
understanding of our discussion is not that Duncan supports
postulate E, but that he sustains Okishio's results to be
valid on the basis of postulate E. I thus consider us to be
'on the same side' in the discussion but with divergences
concerning how to evaluate an approach which neither of us
employs. Duncan might consider this a misreading.

I want to explain my views with respect to these two
postulates, which I argue are the foundation of two entirely
different different paradigms or systems of knowledge.

My basic points are:

1. I agree with Duncan that postulate E is the basis of
Okishio's result.

2. This is not explicit. Okishio does not state postulate
E as the basis of his result, nor does anyone else who uses
his theorem as evidence that Marx's TRPF (Tendency of the
rate of profit to fall) theory is false.

3. This should change; hidden postulates should in fact be
explicit. Economic theories should declare their hidden
content. The label of the bottle should tell us what we are
being asked to swallow.

4. I agree with Duncan that Okishio's theorem should be
refuted as stated. But I think it should be refuted as
stated by Okishio, who does not refer to postulate E. It is
therefore perfectly reasonable to refute it as Andrew has
done without assuming E, provided all Okishio's openly-
stated postulates are respected.

5. It is also reasonable to ask, as I take Duncan to be
doing, whether on some other basis, unstated by Okishio, his
theorem can be rescued.

6. D and E are mutually exclusive. They cannot both hold
as accounts of reality. In plain language, one of them is
right and the other is wrong (Most of the following posts
are devoted to explaining what I mean by this statement).

7. The basis of Marx's theory of TRPF is postulate D.
Therefore refutations of Marx on the strength of postulate E
are invalid even if postulate E is valid. Okishio should be
assessed on the basis of what Okishio says, and Marx should
be assessed on the basis of what Marx says.

8. Postulate E is in fact false: it is unusable for
science. Therefore, so is Okishio's result, even when its
foundations in postulate E are granted.

9. Any theory compatible with postulate D, leaving out
absurdities, yields conclusions incompatible with Okishio
under appropriate additional assumptions. For example,
Duncan's (1982 etc) models do so. As far as I can ascertain,
the minimum necessary postulate is the not unreasonable idea
that the money received by sellers is the same as the money
paid by buyers.

10. Since Posulate E is false, and all D-based theories
contain counterexamples to Okishio's result, this result
cannot be rescued on any basis. By the same token, none of
the reasons yet supplied by the Okishians for refuting
Marx's TRPF, can be valid.

Thus I am putting forward an extremely strong thesis: I say
that not only is Okishio's theorem wrong, but that it
*cannot* be right; there is no way to 'rescue' it.

What do the Okishians say?

In the paper generally cited as 'The Okishio Theorem',
Okishio (1961) does not as far as I can see make any
assertion concerning stationarity and does not make Duncan's
distinction. He states simply (p95)

"Our conclusions are negative to Marxian Gesetz des
tendenziellen Falls der Profitrate. Unless the rate of
real wages rises sufficiently, the technical innovations
adopted by capitalists do not reduce the general rate of
profit. Innovations in basic industries positively raise
the general rate of profit. "

He does not say, as he perhaps ought,

"On the assumption that the economy attains a new
equilibrium consequent on each individual technical
innovation, our conclusions are negative to Marxian
Gesetz des tendenziellen Falls der Profitrate. Unless
the rate of real wages rises sufficiently, the technical
innovations adopted by capitalists do not reduce the
general rate of profit which would be attained if the
economy were to attain a new stationary state.
Innovations in basic industries positively raise the
general rate of profit in the long run in this sense. "

Duncan's post allows us to agree that (E) is the fundamental
hidden postulate of all anti-TRPF theorems. That is, we
ought to be able to agree that Okishio should have written
the second statement instead of the first.

But Okishio did not write the second statement. Postulate
(E) is hidden. It is not explicit. I haven't just quoted
selectively; you can read Okishio's entire paper and not
find anything different from the idea that the real state of
the economy is directly and immediately represented, as soon
as a technical change is made, by an economy which has
entirely adopted the new technology and changed its prices
and profits accordingly.

Moreover this oversight is not confined to Okishio. The
economists of this tradition do not speak of stationary
states or how they are reached. They simply write without
proof as if the equations directly describe the underlying
real economies from the moment the first capitalists cuts
the tape on the first new machine of the new technique.

The history of the debate would otherwise be very different.
Thus Bortkiewicz (1907:466 cited in Sweezy 1942:105),
instead of

"the mistake in the proof which Marx gives for his law of
the falling rate of profit consists primarily in his
leaving out of account the mathematical relation between
the productivity of labour and the rate of surplus

would have written:

"our difference with Marx consists primarily in our
assertion of a mathematical relation between the
productivity of labour and the rate of surplus value
which holds under conditions Marx does not accept,
namely stationary prices"

Steedman (1977: 128), instead of:

"It is thus impossible for the rate of profit *after* the
technical advance to be less than that *before* the
advance, unless the real wage-rate has risen...With a
given real wage, the rate of profit can be lowered only
by technical *regress*, never by technical progress"

with a little more charity and a great deal more accuracy
would have written:

"The rate of profit after the technical advance will,
unless the real wage rate has risen, eventually exceed
that before the advance provided there is sufficient
time for the new technology to become general, for
prices to stabilise and for a new equilibrium profit
rate on the basis of this new technology to form. This
rule holds only if in the meantime no further technical
change takes place anywhere else in the economy...With a
given real wage rate, the rate of profit can be lowered
either by technical regress or by technical progress
which takes place fast enough to render our underlying
assumptions invalid"

and Brewer's recent masterpiece in the pages of HOPE might
have attracted a very different response from the editors,
never mind the respondents, had he written (1995:137):

"Nobuo Okishio showed that if it were possible for a
single technical innovation, worth adopting from the
point of view of an individual capitalist at the prices
ruling before it is generally adopted, to be adopted by
all other capitalists producing the same outputs without
any change in the rest of the economy, and if moreover
the economy could persist long enough without any
further technical change for the prices and profits
arising from this technical innovation to become
stationary, then the resultant average profit rate would
be higher than before provided the good is a non-basic.

in place of what he did write, which was:

"Nobuo Okishio has shown that any technical innovation
that is worth adopting from the point of view of an
individual capitalist, at the prices ruling before it is
generally adopted, must raise the general rate of profit
if the good concerned is a basic in Sraffa's sense or
leave it unchanged if the good is a non-basic.

If he had been exceptionally honest he could have added:

"From this, no deductions can be made about the actual
course of an actual economy in which, as is equally well-
known, innovation falls on innovation like hammer-blows
and prices never stabilise. Marx's theory, founded
unlike general equilibrium theory on this well-known
fact, is in contradiction with the predictions of
Okishio (which are as is well-known unsupported by any
empirical evidence) that the profit rate can only fall
as a result of wage rises, that technical change never
causes the profit rate to fall, and that technical
advance always and without exception mitigates any fall
in the profit rate caused by rising wages"

instead of what he did write, which was:

"If the profit rate falls, it is because wages rise.
Technical change is not the cause of any fall in the
profit rate. On the contrary, technical advance
mitigates any fall in the profit rate caused by rising

The language of Okishio himself, and almost all who have
written before and after deploying such arguments to refute
Marx, universally equate the results derived on the non-
actual assumption of stationarity with the actual movement
of the economy. This is the fundamental problem.

Moreover I don't think they are going to stop unless
somebody stops them. The minute one takes any text written
either asserting the 'truth' of Okishio's conclusions or
denying the truth of Marx's on the basis of Okishio, and
rewrite it to incorporate Duncan's postulate (E), the result
is something deprived of all its sting.

My 'rewritten' versions of the alleged refutations of Marx
do no more than make Duncan's postulate (E) explicit. But it
is as plain as the nose on your face that they no longer
stand as refutations of Marx.

That is, in my view, why these authors do not declare this
hidden postulate. In some cases this lapses into outright
charlatanry. They go to the most extraordinary lengths
either consciously to conceal this fact or subconsciously to
avoid confronting it.

This is a strong statement, but it is borne out by the
facts; at the *same* time that the statements above were
being made, there was (and remains) in existence in even
neoclassical political economy numerous traditions, backed
by leading authorities, which openly and rigorously spell
out why the categorical statements above are simply
untenable as they stand.

For example the entire Austrian tradition (see O'Driscoll
and Rizzo 1985 ch4), the Post-Keynesians (see Weintraub
1991), for that matter Kalecki, Keynes, Robinson,
Schumpeter, the dynamics of Samuelson and Dorfman,
Leontieff's own dynamics, more recently Ormerod, and so on
and so on and so on.

It is not as if the difficulties with postulate (E) are
unknown, or have not been the subject of debate or
criticism. It is not as if there is no history of discussion
on path-dependence, or stability, or the theoretical
difficulties inherent in conceptualising non-equilibrium

The fact of the matter is, at least when the order of the
day is the destruction of Marx, declaration of (E) is
treated as a statement one is not obliged to make and
conclusions drawn from it are directly and immediately
asserted as irrefutable fact.

My view is that whether or not we agree on the Okishio
theorem, this particular situation is unacceptable and we
should not accept it. The next step after stating that
Okishio-type theorems depend on postulate (E) is therefore,
whether or not we consider postulate (E) justified, to argue
and campaign intensively for it to be an explicit instead of
an implicit postulate. This is perfectly possible. For
example Alberro and Persky's articles were a model of how to
lay the question out as also, I think, was John Ernst's.

Then a future generation of students and researchers can
judge for themselves, with all the cards on the table in
front of them.

Economic theorems should carry editorial health warnings
telling us their hidden assumptions. I support 'truth-
labelling'. If the authors above could be called to account
for this lapse of scholarship, and if there were a concerted
effort even by the editors, reviewers and writers
represented on this list to make clear that postulate (E) is
in fact the hidden basis of virtually the whole Marx-
refutation industry, then in five years time we would
confront an entirely different theoretical debate.

What constitutes a refutation?

If every author were simply to mutate the assertion that
'Okishio has established Marx's error' into the assertion
that 'Okishio and Marx begin from different postulates', and
every commentator, editor and reviewer were to insist on
this necessary scholarly correction, if every author
commenting Marx from the standpoint that equilibrium is real
were actually to incorporate the wording of Duncan's
justification into their text, we could have a very
different (and much better) discussion.

At least until this is done, I think it reasonable and
necessary to define as a 'refutation' of Okishio any line of
reasoning that deduces the opposite conclusions to Okishio
from the stated postulates of Okishio.

Frankly, I don't think that vulgar economics should be
allowed to have its cake and eat it. If it is not prepared
to declare its hidden assumptions, I don't think we should
accord it the right to wave these assumptions around in its
own defence. I think this is an unnecessary and confusing

We are entitled to a level playing field. We give Okishio
much more shrift than he has given Marx, after all. Okishio
treads a familiar path, in good faith but IMHO wrongly:
along with countless others he reconstructs what he *thinks*
Marx says, refutes the reconstruction and then argues that
he has thus refuted Marx. We don't do that to Okishio and
Duncan does not really convince me that we should.

Andrew chooses to reply to what Okishio actually says. I
think he should he have the right to do so; furthermore over
the years I have come to conclude that there is something
quite fundamentally correct about this procedure. Everyone
who takes up the pen has, in my view, the right to be
answered on the basis of what they actually say and if this
right later turns to a scourge, then that is the duty that
accompanies the exercise of the right. After all we always
have the option of admitting we have changed our minds,
which is not such a terrible thing. If we don't like these
rules, then we should just be more careful about what we
say. I may be getting crusty but I have come to think these
are the only rules of the game which work.

I would not deny it is useful to read authors
sympathetically, to study their hidden assumptions,
reconstruct their logic, and examine alternative postulates;
but at the end of the day if we do not clearly distinguish
between what we have added on our own account, and what was
present in the first place, something essential to science
slips from our fingers.

I am not trying to evade Duncan's point as he poses it, and
I think it is a good one. In the next part of this post I
shall indicate why I think his reconstruction of Okishio
doesn't hold up either; in other words I want to respond to
what I perceive as the real question he poses for us.

But in the first instance, I do think it is fair that we
test Okishio, like Marx, on what he actually says. If we
*then* find a flaw which requires a more careful and
sympathetic reconstruction, well and good. But if we find
this to be necessary, we cannot simply turn round and say
that there is no problem with Okishio, any more than we can
say that a house with no foundations is a perfectly good
house once the foundations have been dug.

(References to follow)