A reply to Duncan's ope-l 2475.
Again, I really appreciate Duncan slogging through all the equations
with me. As he says, we're now agreed on the calculations.
What agreeing on the calculations implies to me is also that we should
be able to agree on the following:
(1) Given profit-maximization, viable tech. change, and a constant real
wage rate, the general rate of profit can fall even if the ratio of
fixed capital to output declines. Thus it can fall if the ratio is
constant or rising. (In an example with positive wages, the tech. change
will be viable if the cost of the additional fixed capital is less than
the savings coming from a fall in the money [or labor-time] wage rate.)
(2) This result depends crucially on commodities having an intrinsic
value, not just an exchange-value. In other words, with a commodity
numeraire, the profit rate rises under conditions in which the rate
of profit calculated on the basis of labor-time values and a constant
relation of money to labor time will fall. Thus, this result depends
crucially on Marx's value theory; Okishio/Roemer's contrary results
follow from their abandonment of Marx's concept of value in what is
alleged to be a demonstration of the theory's *self*-contradiction.
(3) Since the results do not alter any of the presuppositions of the
Okishio theorem, but come to contrary conclusions on the basis of
the theorem's own assumptions, or assumptions not precluded by the
theorem, the Okishio theorem has been refuted.
With respect to the last point, it could be claimed that the theorem
makes a claim only with respect to one-shot tech. change, not continuous
tech. change, so that examples with continuous change alter the theorem's
assumptions. However, the one-shot nature of the change is not stated
as an assumption/presupposition in any version of the theorem of which
I am aware. Second, what continuous tech. change does is to exploit a
logical flaw in the theorem: it needs to *show* that adjustment to
a post-mechanization stationary price scenario will occur, but merely
assumes this (by illicitly conflating stationary prices with a uniform
profit rate). My examples, and those of John and Alan, show that adjustment
to stationary prices will not occur, given Marx's value theory and a
constant value of money, when tech. change is continuous. Finally, if
the theorem is taken to be or explicitly restated as referring to one-
shot tech. change only, then it becomes not only uninteresting, but also
fails utterly to be any refutation of Marx's law of the FRP. He clearly
stated the law for continuous mechanization:
"... progressive decline in the variable capital in relation to the
constant capital ... progressively rising organic composition ... progressive
development of the social productivity of labour ... continual cheapening of
the product ... steadily falling general rate of profit ... tendency to a
progressive fall ... the mass of living labour applied continuously declines
in relation to the mass of objectified labour ... living labour that is
unpaid and objectified must also stand in an ever-decreasing ratio to the value of the total capital ... the rate of profit, which must therefore steadily
fall (Vol. III Vintage, pp. 318-19--3d para. of Ch. 13)."
I belabor these three points, because they were a good part of what has been
at issue. I'd be interested in knowing if Duncan and others now think these
points are resolved.
In Duncan's 2475, he takes issue with my statement that the initial investment
produces more profit relative to the investment than later investments do.
He says it employs more workers, but they're less productive, and "Marx
is pretty explicit that workers employed on obsolete capital produce less
value than those employed on the current good practice capital (and refers
to this qualification as 'socially necessary' labor)." I agree. But we
may have a difference of interpretation here, or maybe only a terminological
difference. As I interpret Marx, socially necessary labor-time is the
(weighted) *average* labor-time socially necessary. The social value of
a commodity is (total labor needed to reproduce)/(# of units of the
commodity produced). This is in fact the concept we've been working with.
What it implies is that some of the labor extracted in less productive
businesses is transferred to the owners of more productive ones. Some
get more labor than they extract, some less, and the differences cancel out
in the aggregate. In this sense, we can say that the labor extracted in
the less productive businesses *produces* profit for other ones. It
"counts" as less labor than it is to the less productive firm, and the
labor extracted by the more productive firm "counts" as more than it is,
due to a redistribution of surplus-value on the basis of the law of one price.
At the end of his post, Duncan asks whether the FRP in my scenario is a
problem for the capitalist society, whether it is what Marx was examining in
Vol. III, and whether it is the FRP that Smith and Ricardo were referring to.
Duncan's "tentative answers" are no in all cases.
My response: as for Smith and Ricardo, of course they didn't think
mechanization was a (the) CAUSE of the FRP. But a phenomenon is the same
phenomenon whatever one thinks the cause is. They observed (or thought
they did) a tendency for a FRP. My examples explain exactly that FRP, but
in a manner different from them.
The other issues can be taken together--by explaining why this is the
kind of scenario marx was referring to, it will become clear why it is
a problem for capitalist society.
One reason Duncan doesn't think this was what Marx was studying is because,
according to Duncan, Marx was studying "capital-using" tech. change. I
take this to mean a rising capital/output ratio. I know of no evidence
for this in Marx, none. I think this is a myth, albeit one with an
obvious explanation. Marx speaks of a rising technical composition. In
*simultaneism*, this basically implies a rising capital/output ratio
(K/N = pF/N = (N/X)(F/N) = F/X). So, many people have simply been unable
to understand a rising TCC except as a rising capital/output ratio, and they
thus imputed the latter to Marx. But I agree with John: to the extent that
Marx deals with this ratio, he seems to say it will fall. In Ch. 6 of
Vol. III (again, I'll be citing Vintage), he says the "size" of machines
grows, but not as much as the product, and that depreciation of machines
forms a falling part of the value of the product (though the value of raw
materials becomes an increasing part)--pp. 203-04. In Ch. 13, again, there's
a good deal of discussion of how commodities contain progressively "less
objectified labour, both in terms of the depreciation of the fixed capital
applied and in terms of the raw and ancillary materials that are consumed"
(p. 332). I don't take these statements as definitive, but they do
suggest capital-saving tech. change. (And, in any case, I have no problem
constructing viable, falling FRP examples with a rising capital/output
ratio.)
And again, I no of no textual evidence in the other direction. Nor do I
know of any textual evidence that Marx was, as Duncan says, comparing the
profitability of whole capitalist systems at very different stages of
development." Yes, whole capitalist societies (I've "modelled" a 1-sector
capitalist society), but as I cited above, he was looking at a progressive
tendency over time. More importantly, his FRP theory provides the basis
of his *cyclical crisis* theory in Ch. 15. E.g.: "the development of
labour productivity involves a law, in the form of a falling rate of profit,
that ... has constantly to be overcome by way of crises" (p. 367). Please
also see the discussion that concludes with "The devaluation of the elements
of constant capital ... itself involves a rise in the profit rate. ... The
stagnation in production that has intervened prepares the ground for a
later expansion of production--within the capitalist limits.
"And so we go round the whole circle once again. ... with expanded conditions
of production, the same cycle of erros is pursued once more" (pp. 363-64).
So I think he was not doing comparative statics here (though he did elsewhere
in places, IMO), but cyclical dynamics.
Unfortunately, very unfortunately, I cannot finish this post now. I'll post
this part and continue, I hope tommorrow, with the conclusion. Sorry
Andrew Kliman