Most of this post will be a reply to Duncan's ope-l 2534, but first a
brief comment on the exchange between Paul C. and John: whether it is
the physical output or the value of output that is relevant depends on
the question one asks. To produce an example of "capital-using" technical
change, as I understand the term, one must show that physical output
declines relative to the physical means of production or, since this
involves index number difficulties, as John notes, the constant-price
value of output must decline relative to the constant-price value of means
of production.
Duncan writes that my examples push the divergence between historical and
"prospective" rates of profit "to its most extreme form by assuming no
depreciation at all." This is true, but I must point out that it isn't
something I used to stack the deck against the Okishio theorem. It was
John Roemer who used to case of fixed capital that lasts forever to
extend the theorem to fixed capital-using economies.
Duncan denies that my examples refute the theorem. "What has happened is
that you have changed the profit rate from the one Okishio was looking at
(the prospective internal rate of return) to the ratio of surplus value
to historical cost of capital. A 'refutation' is a counterexample that
meets all of the hypotheses of the proposed theorem. Your example obeys the
Okishio theorem, because the internal rate of return is rising."
I understand "refutation" to mean the same thing as Duncan does. I think
my examples (and those of John and Alan) do refute it. First of all, as
to the internal rate of return (IRR). I showed that at least under certain
conditions, my measure of the profit rate, which falls, is equivalent to
the economy-wide weighted average of actual, realized IRRs. Duncan agreed
with this. What he seems not to agree with is that this weighted average is
the economy-wide IRR. That conclusion, however, seems unavoidable to me.
So the *actual* economy-wide IRR under certain conditions is falling, not
rising.
Secondly, even *if* my measure of the profit rate differs from Okishio's
(actually, its identity with or difference from Roemer's is what is at
issue)--which I'll discuss in a moment--my argument serves to refute the
Okishio theorem if I can show that the theorem's measure of the profit
rate doesn't necessarily to conform to the one for which Marx stated his
law. (To be precise, at issue is not the "measure" of the profit rate--
Okishio clearly says Marx's is wrong because of price-value differences,
basically--but the *terms* of the profit rate.) Part of what we mean by
the Okishio theorem is an argument that disproves Marx's claim that mechan-
ization itself can cause the rate of profit to fall. The theorem is not
just a mathematical result; the interpretation of this result is what is
at issue; and the proponents of the theorem has always asserted that the
results refute Marx's law. For instance, the first sentence of Okishio's
"Tecnical Changes and the Rate of Profit" is "In this note, we shall comment
on Karl Marx's _Gesetz des tendenziellen Falls der Profitrate_." The
first sentence of the concluding section (except for Appendix) states "Our
conclusions are negative to Marxian _Gesetz des tendenziellen Falls der
Profitrate_." The first sentence of Roemer's "The Effect of Technological
Change on the Real Wage and Marx's Falling Rate of Profit" states: It is
now well-known that the 'tendency for the rate of profit to fall' which
Marx predicted as a consequence of technical change is nullified by
'countervailing factors', those effects Marx seemed to think were not
predictable or consistent." The second sentence of his conclusion reads:
"While Marx's original conclusion was incorrect--that the rate of profit
could fall with cost-reducing technical changes and constant real wages ...."
Let's assume for the sake of argument that the terms of my profit rate
measure differ from those of the theorem. Does that make the theorem--as
understood by its key proponents--valid? I think not. They would need to
prove that their profit rate is the one to which Marx's law refers. Have
they done so? No. Is there any evidence that my profit rate is the one
to which the law refers. Yes: (a) I measure surplus-value relative to
capital *advanced*, which is how Marx defines the profit rate; (b) in
Ch. 15 of Vol. III, in a passage I quoted in ope-l 2520, Marx refers to
the purpose of the capitalist mode of production as being to "maintain the
existing capital value and to valorize it." This indicates even more clearly
that he was referring to profit relative to historical investment; (c) 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. This, I
think, is the strongest evidence that my profit rate is the one to which the
law refers. Other concepts of the profit rate fail to replicate Marx's
argument, while mine (and John's and Alan's) does. Since we our able to
interpret the text in an internally coherent manner, while other interpre-
tations can't, it seems to me that this implies that our interpretation is
superior, as interpretation; and (d) the reason my profit rate falls is
devaluation of capital, which Marx likewise emphasizes in Ch. 15, and the
results and/or implications of my examples correspond closely with the
crisis of devaluation argument of Ch. 15.
One doesn't even have to accept all of the above in order to recognize that
the theorem is refuted. Even if (a)-(d) only imply that it is *possible*
that Marx's law refers to profit relative to historical costs, then the
theorem is refuted. If the theorem is referring to profit relative to
historical cost, or the IRR, then its mathematical results are false. If
the theorem is not, but Marx was or even may have been, then it is not
proved that Marx's law is false, because a contrary interpretation of his
profit rate concept vindicates the internal coherence of his law of the FRP.
A separate question is whether the Okishio thorem refers to a profit rate
different from the one our examples show can fall, as Duncan suggests.
He refers to the "prospective internal rate of return" and the "prospective
rate of return to new investment." I'm not sure what this means. One thing
it might mean is the actual, realized, ex post, rate of return on new
investment, rather than the rate of return on past investment. If so, my
examples show that the prospective IRR can indeed fall. If new entrants
don't come in later, the rate of return on the latest investment would be
no lower than the rate of return on the next-most recent investment. But
when new entrants come in, the unit price continues to fall, which
lowers the rate of return on all investments. And the economy-wide IRR
(weighted average of actual IRRs) can fall.
Another thing "prospective IRR" may mean is the rate of return that firms
which make a new investment THINK THEY WILL GET. If they have ultra-myopic
expectations, it is true that this ex ante rate rises. But this is clearly
*not* what Marx's law refers to. Nor do I think this is what the Okishio
theorem is meant to refer to. Duncan writes that "I think most people working
on this problem ... have ... taken the prospective internal rate of return
as the relevant variable ...." 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 ultramyopic). This is the import
of the celebrated Okishio theorem, as understood by those who accept it?
This is the result that lets them think Marx's law has been refuted, and
that gives them the right to claim he was simply wrong? I don't think so.
First, this is too implausible to be believable (which is why I don't think
this is what Duncan meant, but I'm covering all bases), and second, as I've
discussed in earlier posts, Roemer especially is very clear that, although
the capitalists make decisions on the basis of current prices and profit-
ability, their expectations are wrong. Prices fall, capital mobility occurs,
etc. But the mutatis mutandis *effect* is (allegedly) a higher or equal
*actual* profit rate. This is what we've shown is not necessarily true.
Again, I think Duncan meant not this, but the rate of return on *new*
investment. But, again, this can fall (both when profit produced and when
profit realized are used as the denominator). What is now past investment
was once new investment, and what is now new will someday be past. So I
don't think there's any difference between the "prospective" and the
historical rates of profit, as long as we're referring to results, what
actually occurs.
I agree with Duncan that other theorists have been aware that the rate of
profit measured on historical costs can diverge from the prospective IRR
(meaning the actual rate on new investment). So why have they failed to
recognize the kind of results we show? Duncan thinks it is because they
think that the prospective rate is the relevant one and because they think
the difference is small. All that may be true, but it doesn't explain why
they think a rate of profit that ignores devaluation of capital (or, more
precisely, uses the devaluation inappropriately to lower the denominator
of the profit rate retroactively) somehow refutes Marx's law. I've never
seen it stated explicitly, but I'm pretty sure the reason they think it
refutes Marx's law is that the theorem examines an "equilibrium" rate of
profit. (Marx does refer to the innovator being subjected eventually to
the general rate of profit.) Here we see THE KEY confusion of simultaneism:
the false belief that equal rates of profit and stationary prices imply
one another, or at least the dependence of equal rates of profit on
stationary prices. This false belief is at the root of Bortkiewicz's
erroneous "proof" of error in Marx's transformation, as I've discussed, it
is at the root of the false Sraffian claim that a unique price vector ensures
the reproduction of the economy; and it is at the root of the false belief
that the equal-rate-of-profit condition implies the postmechanization
tableau of the Okishio theorem. (This is especially clear when one reads
the Roemer article I quoted from above, and which I "deconstructed" a few
months ago on ope-l.)
I agree with Duncan, in general, that the difference between historical and
replacement cost rates of profit is less the shorter the lives of capital
investment. But I do not understand how they ever become equal, if prices
(values) are continually falling. Duncan writes that "If, for example, the
original factory ... lasted a finite time, sooner or later it would be
amortized, and the 'general rate of profit' would become equal to the IRR
on current investment." First of all, *which* IRR on current investment--
the one computed at stationary prices, the actual one using profit produced,
or the actual one using profit realized? Second, why the scare-quotes
around GROP? Third, doesn't this statement either presume that prices stop
falling, that capital goods on average are amortized before they wear out,
or both?
Duncan asks: "Don't capitalists recover the initial investment through
depreciation? ... The value doesn't 'vanish', but is recovered in the
ordinary course of business." 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. (Of
course, this raises a number of difficulties concerning the life of
machines, depreciation rates, etc.) But what this means--to me (not to
other temporalists, necessarily)--is that capitalists do not recover all
of their intial 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. So
I do think that value vanishes, in the system as a whole, when values fall
generally. This often isn't "recognized" until a financial crash, or
something like that. But a portion of capital has been turned into
"ficticious capital," as Michael Perelman has explained to us.
In response to my quotes and comments on the link between the FRP, devalua-
tion of capital, and crisis, Duncan notes that the disruption in reproduction
to which Marx refers is "short-run." Marx is referring to "short-run ...
crises, and the business cycle." I'm not sure what Duncan means by
short-run here. In any case, 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). So
the FRP law leads to a cyclical crisis theory, not the "long-run
evolution" of the system. I do agree with Duncan that a necessary, though
not sufficient, condition for devaluation of capital to lead to crises is
that price and payment expectations are not fulfilled. I don't think this
implies that Marx's law of the FRP therefore refers to a fall in an
expected rate of profit rather than the actual rate.
Both John and Duncan think there is evidence in Vol. I that Marx was referring
to capital-using technical change. Maybe; I'll have to go back to it and
see what I think. In any case, what has emerged from this discussion, a
point John Ernst was the first to made back in 1982, is that a rise in the
technical (or organic) composition of capital is not equivalent to a rise
in the capital/output ratio. So any evidence of capital-using tech. change
in Marx, to be valid, cannot rely on his mention of a rising TCC or OCC.
Andrew Kliman