[OPE-L:2887] RE: Duncan's [2812] Okishio 2 of 4

Alan Freeman (A.Freeman@greenwich.ac.uk)
Tue, 27 Aug 1996 15:34:26 -0700 (PDT)

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Can Okishio be rescued?

In the first part of this post I expressed agreement with
Duncan's 2812 statement argued that Okishio's theorem rests on a
postulate I called E, namely

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"

I argued that though this was indeed the starting point of this
theorem that in the Okishio literature this fact is hidden.

This stated - and not to be forgotten - I then believe it is
right and reasonable to ask the next question, which I take to be
the actual thrust of Duncan's post: namely, is it possible to
'rescue' Okishio's theorem by asserting different, hidden
postulates that are *not* part of the text - for example,
postulate (E)? Perhaps more accurately, is it possible to
reconstruct a 'meaning' of Okishio's theorem that preserves its

I think this is not only an important but essential line of
enquiry. In a certain sense, what I have been trying to do for
the last five years is to demonstrate that (E) *is* a hidden
postulate of all such theorems. If we can agree that it is, we
can then have a much clearer discussion as to whether this
posulate rescues or damns the theory.

So I think Duncan's post brings closer to agreement, and brings
more clarity to the discussion. I will try now to answer his
point as I think he puts it, and hope that he will correct me if
I have misinterpreted him.

My first argument is that I don't think we can be 'neutral'
between postulates (D) and (E). I don't think they are simply
alternative good ideas to be picked up and put down at will.
Within any reasonable sense of the words, one of them is right
and one of them is wrong. I intend to show that (E) is wrong. If
we agree that Okishio depends on (E), and if we can establish
that (E) is false, then it seems to me we have a refutation of
Okishio, no? This seems a quite straightforward exercise in
ordinary logic.

Moreover, if we can show that (E) is not an hidden assumption of
Marx, then any refutation of Marx based on (E) is invalid, no?
Again, this seems straightforward to me.

The real substance of the debate is therefore: is (E)
sustainable? That is what I want to devote myself to.

The 'Equilibrium is Real' postulate: not just an axiom but a

I assert (E) is 'wrong'. In what sense? Firstly it is clearly a
simplification that does not apply to an actual economy. In no
actual economy do capitalists play 'after-you-Claude' so that
each successive innovation can stabilise before the next is
introduced. No actual economy achieves a "state where input
prices are equal to output prices and profit rates are

This is not a definitive basis for rejecting E but it is not a
small matter. The author of a new theory, especially one used to
refute Marx, is not to be given carte-blanche to introduce any
initial assumption no matter how unreal. We have the right to
interrogate the assumptions as well as the outcome. If I showed
Okishio's result is based on the assumption 2=3, then I don't
think it would be a good defence to reject me for assuming 2=2.

I would concede, though, that this error does not rule out (E) as
a starting point. There are suppositions in science, such as the
dimensionless points of the geometers or the weightless rods of
the physicists, which are technically wrong but abstractly valid;
they serve as starting point for a conception of reality which
preserves what is deduced from their supposition, even when that
supposition is negated. Their negation thus at the same time
completes them. It merely adds previously absent determinations.

I think the notion behind what Duncan says is that postulate (E)
is of this character. He writes (as many do) as if equilibrium or
stationarity were merely a suspendable supposition, an
approximation, or first abstraction.

I think it is more than a supposition or an abstraction: it is a

It is to my mind akin to the idea that the sun goes round the
earth, neither abstraction nor simplification but a definitive
assertion about the universe we live in. It therefore originates
a self-confirming, mutually re-enforcing and hermetically sealed
array of concepts, methods of argument, notions of causality and
empirical procedures. It is a concept of reality.

I will call it the "Equilibrium is Real" postulate. And this, as
we have just ascertained, is how its proponents view it. They do
not limit the applicability of their models as Duncan asserts.
They make direct, brutal and categorical statements about the
world based on these models. They treat them as an adequate
description of reality, not only for the purpose of rubbishing
Marx but in the more general case of mainstream neoclassical
economics, as a direct guide to the diagnosis and prognosis of
the economy. Is this scientifically justified? That is the
fundamental issue as I see it.

It might be argued that such a totalising hypothesis cannot be
refuted because it provides its own justification. I disagree. I
will later try to show that though superficially appealing, not
one of the claims made on its behalf hold water. It serves
neither as a useful working hypothesis, nor as a first
approximation to reality, nor as a simplified model, nor as a
source of valid abstractions, as an explanation of neither cause
nor structure, nor as a source of correct, plausible or even
possible empirical predictions.

However I would concede that to refute it we must go deeper than
normal logic or sense-data. It has to be demonstrated not just
that it is empirically absurd (which it is) or logically
inconsistent (which it is) but that the reality to which it is
alleged to correspond, cannot possibly exist. It is wrong with no
way out. It is like a carpark designed by Hieronymous Bosch in
partnership with Max Escher. Its exits are not just sealed: they
do not exist. All the 'way out' signs lead up; out there on the
street there are only ways in.

What constitutes a valid initial premise?

It is frequently said that the economy does not actually behave
in accordance with (E), but may nevertheless be explained on this
basis. (E) is therefore considered to be adequate or 'true'
because we can (it is said) deduce true things from it. It is a
valid 'beginning' or 'first approximation'; a logico-genetic
point of departure which is itself just a caterpillar but leads
to a butterfly, casting off its false shell on the way like a
discarded cocoon.

Let us put this argument around the right way. What it actually
says is that an (E)-type model can represent an (E)-free reality,
because an economy deduced from (E) need not conform to (E). I
will argue that on the contrary, the characteristic and defining
feature of postulate (E) is that an economy deduced from it can
only exist if it does actually conform to it. (E) is therefore
false because no economy deducible from it can actually exist. It
does not possess the quality of reality. Caterpillar it is and
caterpillar it remains. It will never fly. Its cocoon is its

This distinguishes it both from valid but incomplete abstractions
of science such as weightless rods, and from possible but
deniable axioms such as Euclid's axiom of parallelism. We can
validly define many properties of a real and weighty rod with the
initial assumptions of an abstract and weightless one, because we
can make deductions from these initial assumptions that remain
true when the assumption is dropped. We can investigate the
possibility of curved or uncurved universes because the concept
of parallelism includes both the possibility of its existence,
and the possibility of its non-existence. In Hegelian terms these
concepts contain their own negation.

The general notion that 'science starts with simplifications' is
not a sufficient justification for a simplification, particularly
one which appears to be negated by the deductions made from it.
There has to be some criterion for distinguishing between a good
simplification and a bad one. My argument is that if we carefully
interrogate the simplifications which science has used
effectively, we find that the simplification consists of an
absence, not a positive statement. Actually physics does not
suppose a rod with zero weight, but a rod whose weight is
undefined. In the process of developing the theory of matter it
does not use the supposition of weightlessness or we would get
all sorts of awkward things like infinite velocity with any
finite energy; what physics actually does is to make no use of
the concept of weight at all except at the logical points where
it becomes necessary to introduce it.

Such abstract concepts can be 'completed' by a negation, because
that which is to be negated consists itself of a negation, in the
precise sense of an absence. I have previously argued that Marx's
development of the concept of value and money follows precisely
this path.

Postulate (E) is not a simplification of this type. It is a very
positive statement. It says that the entire economy has to be in
a definite state before its concepts apply; that after each
change, it actually becomes stationary and actually stabilises
before further change takes place. Its concepts are therefore, so
to speak, impregnated from the outset with this state of affairs,
and lose all meaning if this state of affairs does not exist.
Postulate (E) fails to lay the basis for its own suspension. It
cannot be generalised precisely because it brooks no denial. It
is not just a first approximation but a last approximation,
because it not permit its first consequences to be forgotten in
any later stage of development.

This is in complete contrast with (D), which by definition makes
*no* positive statement about the actual course of the economy.
That is why (E) is a special case of (D) and the reverse is not
true. (D) contains its own negation, (E) does not.

How can equilibrium come into existence?

Duncan acknowledges that if we drop stationarity we can no longer
assert that the profit rate rises with technical improvements.
This should already be a warning, since stationarity is defined
as a state which arises from a nonstationary process. It follows
that even in his definition of Okishio's real meaning, there is a
transition; at one point the profit rate is lower than before,
later it is higher. At one point Okishio is wrong, at another he
is right.

Fine. So *when* does Okishio become true? How far must the
nonstationary processs proceed before we can declare it
stationary? This is not just a Zeno paradox; definite lapses of
real time are involved. In fact the lapse of time for 'Okishio-
truth' to hold is arbitrarily long. Given a lapse of time of say
T years, I can always define a technical improvement such that
Okishio's result will be false for longer than T years after the
improvement is introduced. In what sense is a theory 'true' if
there is no upper bound on the length of time before this truth
is expressed in anything observable? Actually, on this basis
*anything* can be asserted as true. All I need say is that the
universe has not existed long enough to observe it. This isn't
funny: it's the way the World Bank actually talks about
Structural Adjustment.

But the problem is much deeper; in Okishio's theory postulate (E)
furnishes the *definition* of profit. The postulate supplies not
just the theory but the concepts in which it is framed. Negate it
and we are left without the concepts with which to describe its
absence. What meaning can we attach to the prices at which goods
trade or the profits they realise before nirvana? What on earth
is an out-of-equilibrium equilibrium price? What *could* it be?
What actually 'happens' while we are waiting for the stationary
state which is required for the theory and all its concepts to
become applicable? Hence, how can we, on the basis of postulate
(E), imagine the process by which postulate (E) comes to be true?

Even religions have creation myths. But in this case, the state
of affairs which is supposed to lead to the theory, cannot be
described within the suppositions of the theory.

An (E)-economy has no history. It defines a totally self-
contained world, absolutely bounded and absolutely finite. On the
basis of (E), the conditions needed to bring (E) into existence
cannot exist. There seems to me to be a pretty clear conclusion
from this: the world of (E) cannot exist.

But it gets worse still. The moment there is any *disturbance* to
(E) - such as the introduction of a new technology - (E) no
longer holds and the whole problem is recreated. If, therefore,
the conditions that disturb (E) are actually created endogenously
by (E) - as is the case with tecnnical change in a market economy
- then at *no* point is (E) a possible or valid postulate, and
nor is anything deduced or deducible from it.

In summary;

(1) It is not actually a starting point for anything except
itself. It cannot be logically extended; all concepts and
deductions made from it are usable only when it is true;

(2) It cannot take part in a history from which it is absent at
any point. It can only apply for all of time or not at all.

A thesis of this type is not best described as a theory; it is a
self-sustaining castle in the air. It belongs, not in the sphere
of science but in the sphere of religion. The debate between
postulate (D) and postulate (E) is not a conflict between two
rival theories but a contest between rationality and myth. What
we discuss, when we examine these two postulates, is actually the
question: what is the correct foundation for the rational
appropriation of objective reality?

I would sum this up with the following proposition, an idea with
deep roots in science and philosophy and which I intend to be
taken in this deep and non-trivial sense: equilibrium has no

The 'Reality is Dynamic' postulate

In contrast, I want to argue that reality actually *corresponds*
to postulate (D), in a sense I will try to define fully later.
For now I want to point to one vital aspect only of the reality
of (D); it is not finite. It includes the possibility of its own
negation and this is what makes its infinite extension possible.

Like (E), (D) defines a world-view with its attendant concepts,
methods of abstraction, concept of causation, and procedures for
empirical enquiry.

But unlike (E) it may be suspended without damage to itself. We
may easily study equilibrium as a special case of postulate (D);
the reverse is not true. Postulate (D) sets no limits on its own
development. It has a quality of unboundedness which is totally
absent from postulate (E).

It would therefore be wrong to support (D) on the same basis as,
let us say, Kepler's laws. Many people misunderstand what we are
trying to do by likening it to a model of this type. Kepler's
laws tell us everything there is to know about the motion of the
planets. You can refer to an astronmoer to find out where the
planets will be at any time past or future. These are
'predictive' mechanical laws which exhaust the reality to which
they apply. One can use these laws to predict every eclipse there
ever was or will be. Postulate (D) is not a 'model' of this type.
We have said this before but it is worth restating in this new

Postulate (D) does not lay claim to exhaust the reality to which
it applies, only to explain the basis on which this reality is to
be investigated.

I will refer to it as the "Reality is Dynamic" postulate.

This has an important consequence for the nature of the research
that we can do. Unlike (E) which leads by all roads to general
equilibrium, (D) leads not to a single model but to a *family* of
distinct (and competing) hypothesis about reality - not only Marx
and within Marx many competing theories including ourselves and
Duncan, but also the Post-Keynesians, Schumpeterians,
Wicksellians and even Austrians. I would add one further broad
distinction within this characterisation, which is to define the
Marxian theories as 'objective', though there is not space here
to explore this concept fully.

The combination of reality and objectivity is what, in my view,
furnishes the scientific character of the tradition of Marx.
Hypotheses within this tradition may be erroneous (in some cases
extremely erroneous) but in a different sense to (E). They are
genuinely comparable with each other and with reality by the
methods of normal science. In this sense, I see them as
comparable to Euclid's parallelism postulate. We may conceive of
universes either with or without them.

They represent 'real possibilities'; it is not excluded a priori
that the universe might correspond to them. Reality is not
confined to actuality. A second Clinton presidency is a real
possibility; a socialist monarchy is not. But no real universe
could ever correspond to (E).

I can illustrate with respect to Duncan's (1982, 1986a, 1986b)
circuit model. In the 1982 paper, if I read it correctly, he
hypothesises that variable capital is a constant proportion k of
capital as a whole. However although this may be true, an
alternative hypothesis is really possible; variable capital might
be fixed. And since the employed population generally grows
according to different rules from the pace of accumulation this
is a quite reasonable hypothesis. But if we apply this hypothesis
to Duncan's model, we find that the rate of profit behaves
exactly as Marx (and Andrew and myself) predict, namely, it will
fall when a positive fraction of surplus value is invested and
rise only when the capitalists disaccumulate, that is spend more
money than their profits.

In my view this leads to a simple and genuinely testable
hypothesis; does the value of the net product expand in the
course of accumulation (1) in proportion to constant capital or
(2) in proportion to the population? If the former is true, the
rate of profit will not fall as Marx anticipated; if the latter
is true, it will. But hypothesis (1) does not rule out hypothesis
(2) ex cathedra, nor does (2) rule out (1).

On the contrary in the course of investigating (1) we are forced
to study (2) and vice versa. Our 'picture' of (1) is not complete
unless we have contemplated the possibility of (2) because this
contemplation tells us what to look for, in order to find out of
(1) is true or false.

Moreover both are *historically* possible. There might be whole
periods of history dominated by (1) - for example periods of mass
migration from the country to the town - and other periods
dominated by (2). It might be that the actual course of the
business cycle conforms to (1) during the upswing when the
reserve army is brought into employment and to (2) during the
high point of the boom when population limits act as a capacity

These types of hypothesis are genuine alternatives. They permit
their own negation and part of their determination consists in
this negation. We can explain what they are with reference to
what they are not.

Postulates (D) and (E) are not of this type at all. They are
mutually exclusive concepts of reality. Postulate (E) is to be
rejected like the idea of a socialist monarchy; there is no
possible way it could be real[1].

Those of a Hegelian bent might consider the following way of
putting it: Postulate (E)'s finitude is due to the fact that it
excludes its own negation and thereby prohibits its sublation by
excluding all further determination. Postulate (D), like reality,
posits its own further development by virtue of containing its
own negation and thereby opening the way to an infinity of
further determination. It is for precisely this reason that
reality no matter what form it takes must be expressed in
postulate (D); conversely postulate (E) cannot be real.

Those of a different philosophical persuasion might prefer the
following way of putting it; postulate (E) is an analytical a
priori falsehood.

Those of a still more positivist persuasion might prefer the
following variant: E is simply ridiculous.



[1] A socialist *monarch* is possible. One of his or her first
acts would be to abolish the monarchy. Socialism could not exist
until at least this was accomplished. Therefore, a socialist
monarchy is impossible.

References to follow