[OPE-L:2937] Okishio, etc.

Allin Cottrell (cottrell@wfu.edu)
Sat, 31 Aug 1996 20:00:27 -0700 (PDT)

[ show plain text ]

Sorry, I have been very much tied up with beginning-of-
semester goings-on. But herewith a few reflections on
some of the postings of the last couple of weeks.

1. I appreciate Duncan's comments on the value of labour-
power and the real wage. I think he may well be right in
his account of the tension in Marx. That is, although
(rough) constancy in the value of labour-power may be
closer to the historical reality (since the mid 19th
century), and also more congenial to the FRP thesis,
Marx had a strong political investment in the falling
real wage (and hence, a fortiori, falling value of
labour-power) thesis, based on the experience of the
earlier 19th century.

2. I agree with Alan that it is desirable that theorists
make their assumptions as explicit as possible. But
there are clearly limits to this. Every communication
has manifold tacit presuppositions, and the attempt to
spell these out fully would simply bring communication
to an end. On a related point, I don't accept his
attempted reductio ad absurdum of Okishio via the
rainfall example. The assumption of equality between
input prices and output prices is not a wild imposition
("God's umbrella") but rather a tenable reading of Marx's

3. Autobiographical notes may not cut much ice, but
when I learned my "marxian economics" it was mostly
from reading Capital, with only a small input from
interpreters such as Sweezy and Mandel. And when I
read Marx's argument about technical change and the
falling rate of profit I understood it exactly in the
sense that is vulnerable to Okishio. That is, I
thought Marx was saying that a discrete technical
change, profitable at existing prices, could -- once
generalized, and once prices had fully adjusted in the
absence of any further "disturbance" -- lead to a fall
in the general rate of profit by increasing the organic
composition of capital. I found the argument persuasive,
and when I first came across the Okishio result (as
retailed by Steedman) I thought it must involve some
sort of micro-macro confusion. But it doesn't. It
really does show that what I had taken to be Marx's
argument was wrong. Some on the list have suggested
that if the Okishio theorem is right, it is nothing
other than Perron-Frobenius. I don't agree. I
think it is a substantial intellectual achievement
to see that a certain result on eigenvalues has
definite implications for economic theory -- even if
those implications happen to be uncongenial from a
Marxist standpoint.

4. On the other hand, I think it is jumping to an
unwarranted conclusion to suppose that Okishio (if
accepted) knocks the bottom out of Marx's FRP.
Marx's argument is not limited to the particular
alleged paradox of individually profitable technical
innovations reducing general profitability. The
"bottom line" is surely that the accumulation of
capital itself tends to reduce profitability.
Let r = s/(c+v), and let's define the rate of
exploitation, s', as s/(s+v). The latter measure
is the fraction of the social working time devoted
to the production of surplus value and it ranges
from 0 to 1 (as opposed to Marx's measure, s/v,
which ranges from 0 to infinity). Then we have

r = s'/[c/(s+v) + (1-s')]

The maximum rate of exploitation (corresponding to
Andrew's "workers living on air") is 1, and as s' -> 1
we have r -> 1/[c/(s+v)]: the inverse of the ratio
of labour-time accumulated as capital to current
labour performed. *If* capital is truly accumulating,
and the total social working time is not increasing
to match, this maximum r is inevitably forced down.
(Although Paul C has reminded us that we cannot take the
accumulation of capital for granted, even if it is
supposedly "Moses and the prophets". Real-life
capitalists are sometimes inclined to consume the
loot so far as possible.)

Allin Cottrell