Allin (1620 of 28/3) writes:
"the theorem does not rule out the effect Alan is talking about
(accumulation leads to a falling rate of profit): that effect would
come about (a) if accumulation took place on an unchanged technical
basis; and/or (b) if the value of labour power rather than the real
commodity wage tends to remain roughly constant over the long haul.
"To flip that over, the proposition that capitalists can "accumulate
with a rising rate of profit" is guaranteed, on the standard
approach, only on condition that capitalists are always coming up
with sufficient "viable" technical changes, and that the real wage
does not rise."
"Am I off-base?
I don't think so, but I think you are discussing a quite special case.
First off, if the technical basis of accumulation is unchanged, then
the real commodity wage and the value of labour power are the 'same
thing' (neither changes). So we can answer the whole question by
asking what Okishio predicts if there is no technical change.
In this case, the capitalists would not adopt any new techniques,
because there are no new techniques to adopt. Therefore, only two things
can occur:
(1) the capitalists can change the scale of production, expanding
everything proportionately (proportional or balanced expanded
reproduction)
(2) the capitalists can do something like the above but can change the
proportions of different sectors.
In either case, accumulation consists in expanding variable capital
in strict proportion to the expansion of the capital stock. This is
the sort of expansion Marx discusses at the end of Volume II.
In such a case, the mass of profit also grows in proportion to the
capital stock, because the labour force is expanding at the same rate
as everything else. It may be that by a change in proportions this can
go wrong - Andrew has studied such cases and they are quite interesting
- but this effect is, I think, marginal to the analysis as a whole. The
general point is that with no technical change, you can only accumulate
by taking on more workers in proportion to the new machines and raw
material (otherwise there would be a technical change). Therefore, the
rate of profit stays constant.
But in fact there are quite strict limits on the ability of capital to
expand in this manner. There is not an unlimited supply of workers.
Moreover, technical change is taking place all the time and is
indeed imposed on the capitalists by the process of competition.
Okishio's theorem is designed to study technical change, and
fundamentally what is at stake in the FROP discussion is this:
technical change (no-one disputes) cheapens the elements of constant
capital. The question is, what is the magnitude of this effect? Is it
sufficient to offset the growth in capital stock that results from the
incessant addition to the elements of capital stock driven by
capitalist accumulation?
The core of Okishio's theorem is that it proves, in my opinion quite
irrefutably, that if you adopt the simultaneist assumption (all
capital stock is immediately devalued to the current individual value
of the most efficient producer of its components) then the cheapening
of capital stock offsets additions to capital stock so completely that
the value of capital stock *must* shrink as a result of *any*
technical innovation that permits an individual capitalist to make a
temporary surplus profit.
The core of the temporal refutation of this theorem is that the value
of capital stock taken as a whole is simply the sum of the 'historical'
values of its elements. The capitalists, having paid in money for the
machinery at the then reigning prices, must retrieve this value from
their sales, and it is this historical cost which therefor determines
the magnitude of capital stock, both in value and in price terms.
Thus, under conditions of productivity-enhancing technical change
(John's 'better machines') the Okishio theorem predicts a falling
value of capital stock and the temporal paradigm predicts a rising
value of capital stock. Moreover this temporal results extends to
almost any reasonable behavioural assumption, so it is genuinely
a result of the paradigm itself, not of any particular variant.
The only simultaneist way out of this result that I know of is to
hypothesis some special capitalist behaviour which results in them,
essentially, investing in processes that do not in fact raise physical
productivity.
The unique feature of the temporal refutation of Okishio is that it
makes no special behavioural assumptions and is valid (for example)
for *exactly* the same assumptions that Okishio makes. We simply say
that Okishio calculates the profit rate wrongly. But since Okishio
calculates the profit rate by the absolutely-standard simultaneist
method, this is the same thing as saying that the simultaneist paradigm
calculates the profit rate wrongly.
The special case of no technical change does not affect this result
because if there is no technical change, the temporal and the
sequential profit rates either coincide or rapidly converge.
This reply also relates to Paul in 1622 of 28/3 who writes
(referring to my 1580 of 27/3):
"So long as you formulate it as a conditional argument expressed at the
level of the economy as a whole you are right. But this has
nothing whatever to do with simultaneity or the TSS. The whole
argument becomes orthogonal to such disputes. "
I am interested that you think the argument is right, and this
is an area of agreement we should explor. But I don't agree that it has
nothing to do with simultaneity, as explained above.
Alan