[OPE-L:2721] Reply to Duncan (Okishio Theorem)

andrew kliman (Andrew_Kliman@msn.com)
Fri, 26 Jul 1996 04:44:05 -0700 (PDT)

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This is a very belated reply to Duncan's ope-l 2588 on the Okishio theorem and
the FRP.

Duncan wrote:
"I don't think you understand "refutation" in the same way as I do, as the
remarks above show. The theorem states its own premises and conclusion, and as
far as I can see has not been refuted yet by the production of a
counterexample that satisfies the premises and contradicts the conclusion."

What do you mean by "states its own premises and conclusion"? Are you saying
that the Okishio theorem is the same as the relevant Perron-Frobenius theorem?
Do you disagree that one "conclusion" of the theorem, and/or of its
proponents-interpreters, is that Marx was wrong to claim that
profit-maximizing firms could adopt new techniques that would lead the
"equilibrium" (equalized) profit rate to fall? Have I introduced any premises
that the theorem precludes? If so, which one(s)? Haven't I contradicted the
conclusion that "the equilibrium rate of profit" cannot be lower than the
original one? If not, why not?

What you are arguing is that the Okishio theorem is not relevant to
understanding or evaluating Marx's discussion of the falling rate of profit on
your reading and interpretation of Marx, which is a different point. The crux
of this argument seems to be the definition of the profit rate under
conditions of technical change.

Andrew: I'm certainly arguing what you say, but not only that. I'm also
arguing that (a) if the Okishio theorem is not relevant to Marx's law, it
does not refute it; (b) the theorem's proponents must *prove* that it is
relevant to his law if they wish validly to claim that the theorem refutes it;
(c) I have another defensible interpretation of Marx's argument in which
Okishio/Roemer's conclusion is not relevant (because adjustment to a
post-mechanization stationary price scenario need not occur, and will not
occur, given my premises), so that (d) the theorem's proponents haven't proved
that their interpretation is accurate, and therefore haven't proved that
Marx's law is false. Do you agree or disagree with this?

Moreover, I'm arguing that, *irrespective of its relationship to Marx's law*,
a necessary step in the proof of the theorem is omitted, which invalidates it.
Okishio/Roemer claim to *show* that the post-mechanization "equilibrium"
profit rate cannot be lower than the original one, but they only show that
this is the case *if* prices are stationary in the post-mechanization
"equilibrium." If prices are not stationary, they've proved nothing. And
thus for their claim to be valid generally, they must prove that a stationary
price scenario will result, but fail to do so. (Especially in his Australian
Econ Papers article, Roemer shows he's aware that the proof depends on dynamic
adjustment to this stationary price equilibrium. He does some hand-waving to
argue that competition will equalize profit rates, but doesn't even produce an
argument that, much less prove that, stationary prices will result.) In
short, the theorem requires a proof of dynamic adjustment, which it lacks. Do
you agree?

Is my definition of the profit rate different from theirs? I think not. If
there is no fixed capital, the definitions are the same, but my (and Alan's
and John's) rate can fall when theirs rises, due to the output prices being
lower than the input prices. Do you regard our *definitions* as different in
this case? If so, why? What could possibly justify making stationary prices
part of the *definition* of the profit rate, even the "equilibrium" profit
rate? But if our definitions are the same, then, at minimum, we have
produced a counterexample in the circulating capital case. Do you agree?

In the case of fixed capital, the level of my profit rate is identical to
Roemer's if prices are stationary (one can have technical change with constant
labor productivity) and, if the technical change is one-shot, I've shown that
my profit rate adjusts to his over time. To me this indicates that the
*definitions* are the same, and that the results differ simply because he
illicitly smuggles in a stationarity constraint on prices. Again, how can
stationary prices be part of the definition of the profit rate? What do you
think about this?

Also, how is it possible to test the claim that our definitions of the profit
rate differ? What is Roemer's definition of the profit rate in the general
case, and not only in the special case of stationary prices? If our
definitions are precisely the same in the latter case, and he has no explicit
definition in the general case, how can our definitions be said to differ?
Moreover, with all due respect, I don't think it is enough to produce a
*possible* interpretation of the Okishio/Roemer profit rate in which its
definition differs from mine. We are discussing the *stated* premises and
conclusions of the theorem. To counter my claim to have refuted the theorem,
one must show that what they actually define the profit rate to be differs
from my definition.

It is true that Roemer specifies the internal rate of return as his profit
rate. But the internal rate of return under my premises can easily be shown
to fall. Our earlier discussion of this ran into a lot of complications, so
let me try something simpler, which doesn't rely on obtaining an exact measure
of the IRR. Think of the economy as belonging to a *single* capitalist,
producing a single commodity, and imagine that workers live on air, no
material inputs are used, fixed capital is physically nondepreciating, and the
physical capital output ratio is constant. Roemer's profit rate = IRR is
constant. Mine will be, too, if labor productivity is constant. And,
importantly, the two rates will be *equal.* But imagine in the 2nd period
(initial period is the 1st), productivity rises. If this is the only period
in which technical change occurs, and production continues with the same
coefficients thereafter, the stream of returns on both investments (which
otherwise would be equal to each other and to Roemer's stream of returns) will
be lowered, and thus the IRR's on both investments must be lowered, which
makes them lower than Roemer's. But imagine a productivity rise in the 3rd
period. This lowers the stream of returns on all 3 investments. Etc. So
each new productivity rise lowers each IRR. All IRRs would be equal to each
other and equal to Roemer's in the absence of the productivity rise, so
continuous rises in productivity reduce each and every IRR and thus the
economy-wide IRR.

I had written: "my examples model precisely the phenomena that Marx said
would give rise to
a FRP--rising productivity and rising organic/technical compositions of
capital--and show that the profit rate can fall on this basis."

Duncan replied: "The example we worked through has a falling ratio of fixed
capital to output."

Andrew: Yes, but also rising productivity (output to living labor) and a
rising technical composition (fixed capital to living labor).

In reference to Duncan's suggestion that the Okishio theorem shows that the
"prospective" rate of return on investment rises, I had written: "But if
"prospective" means ex ante, then the theorem shows nothing more than that
viable technical change cannot lower the rate of return capitalists think they
will get (if real wages are constant, etc., and if the capitalists are

Duncan replied:
" think this is a recognizable statement of Okishio's theorem. The phrase
"capitalists think they will get" is taken to refer to future capitalists
correctly forecasting their revenues once relative prices have adjusted to the
technical change."

Andrew: This implies that the theorem refers to the ex ante rate only because
it is equal to the actual rate. But I've shown that it needn't be equal, if
capitalists' expectations are what the *theorem's own premises* state them to
be (techniques costed up at current prices, implying expectations of
stationary prices for all time). They don't correctly forecast their
revenues, because the unit price continuously falls. The "once relative
prices have adjusted," as I've noted above, is precisely what the theorem
needs to prove, but merely assumes. Without proving the adjustment to a
stationary price scenario, there is no proof that the capitalists' forecasts
are correct.

Duncan: "Under conditions of continuing technical change, with a finite life
of capital, there will always be a gap between historical and replacement cost
rate of profit. In a steady state, however, this gap will be constant and
could not lead to a situation where one of the profit rates
was rising while the other was falling."

Andrew: What is meant by "steady state"? Why is this case of particular
interest, instead of one in which the gap widens? Also, the result is not
obvious to me; could you explain it?

I had written: "As I understand Marx's value theory, the constant capital
transferred to the value of the product, in the case of "machines" (and fixed
capital generally), is a fractional part of the
*current* cost of the machine (the pre-production reproduction cost), not the
historical cost. See, e.g., the next to last page of Ch. 8 of Vol. I.

"For example, if the machine lasts 2 periods, and has a value of 10 at the
beginning of the 1st period, and a value of 6 the beginning of the 2d, I think
this means that (1/2)*10 + (1/2)*6 = 8 is transferred."

Duncan replied: "I'm in a summer house and don't have instant access to
Capital, but this strikes
me as wrong. In the absence of technical change, Marx uses an accounting
scheme where the whole initial cost will be written off as part of constant
capital over the life of the machine."

Andrew: I was discussing what happens when there's technical change, not when
it is absent. (I do think that Marx understood the effect of price changes on
value transferred to be the same whatever the cause, but let me leave that
aside.) So the whole value of the machine is not recovered through sale of
products when there's technical change, which lessens the gap between profit
rates when capital has a finite life and when it has an infinite life.

I had written: "...capitalists do not recover all of their initial investments
through depreciation if values are falling. This is indeed crucial, for Marx,
in explaining speedup, shiftwork, etc.
The capitalists need to recover the value they've invested in machines ASAP,
because falling values won't permit them to recover the whole thing."

Duncan replied: "Individual capitalists can't protect themselves through
speedup, and so forth,
because of competition. It's an individual capitalist who faces the losses
from competition from more advanced technology, not the system as a whole."

Andrew: If the losses to the individual aren't offset by gains elsewhere,
there is a loss to the class as a whole. Do you mean that the losses are
offset (or more than offset) by gains? If so, this is surely not Marx's
theory, for he says that mechanization lowers the *general* rate of profit. I
think the idea that gains offset or more than offset losses depends ultimately
on the proposition that only relative values (or prices) matter, not intrinsic
value. Imagine that productivity rises proportionately in *all* sectors, and
that all firms have identical technology within each sector and, for
simplicity, that compositions of capital are identical. All values fall
proportionately. All capitalists suffer losses from the moral depreciation of
their fixed capital. All fail to recover the full value of it they invested,
because what is transferred to the product is a fraction of the current
value, not the historical value, of the machines, etc. One can deny this by
saying that the exchange ratios remain unchanged, so no one suffers losses,
but then one has moved from Marx's value theory to relative price theory.
Relax the proportionality assumptions and the results differ in degree but not
in kind; there will still be a net loss (net depreciation) in the economy as a

I had written: "I don't think the import of Marx's FRP law is secular
stagnation or a secular decline in the observed profit rate. As he makes
clear in some of the passages I quoted, the tendency of the rate of profit to
fall is, in his view, continually *overcome* by crises; and the cheapening of
the elements of constant capital raises the profit rate (on new investment,
but not existing investment, of course)."

Duncan replied:
"This is a possible interpretation of Marx, but not the one that got most
people excited about the FRP, I think. This line of thinking about the
interaction of technical change and the business cycle is quite fertile:
Schumpeter and Goodwin, and their followers have developed it in a number of

"Curiously enough, it reappears in "real business cycle theory" which views
unanticipated technical changes as the origin of business cycle fluctuations."

Andrew: Well, I'm excited about the cyclical crisis interpretation of the
FRP. I don't know where the secular decline interpretation comes from. Ch.
15 of Vol. III is all about the decline resolving itself through recurrent
crises. I suspect a good deal of the confusion stems from the postulate of
simultaneous valuation. If input and output values are always the same, then
a rising composition of capital relative to the rise in the rate of
surplus-value implies a secular fall in the profit rate, with no devaluation
of capital and no collapse of old values to the new. Clearly, people were
aware of these phenomena to some extent, and that Marx referred to them, but
simultaneism always leaves a gap between models and reality. Theory never
gets concrete enough to absorb reality within itself, and instead one gets
"pure" theory on one page, description on another, but never the twain shall
meet. So when they worked out the implications of their formal models, in
which the phenomena were absent, and in which the values of inputs were *by
definition* equal to the values of outputs, "Marx's" pure theory implied a
secular decline in profitability. Temporalism itself immediately suggests a
different understanding of Marx's law, precisely because the devaluation of
capital is put into plain view.

Duncan's comment has made me wonder whether Schumpeter got some of his ideas
on innovation and business cycles from reading Marx, or perhaps Tugan. That
would account for the similarity. Does anyone know anything about this
(Riccardo, Rakesh, Michael P.)?

Sorry for the delay in responding,

Andrew Kliman