[OPE-L:4768] max and actual profit rate

David Laibma (DLaibman@brooklyn.cuny.edu)
Mon, 14 Apr 1997 09:20:37 -0700 (PDT)

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Andrew says, at the IWG conference, in Allin's formulation: "with
a constant workforce and V = 0, accumulation of capital (in value
terms) is a necessary and sufficient condition for a declining
rate of profit." Allin, however, interprets this as a decline in
the maximum rate of profit and points out that this might be
consistent with a rising actual rate.

Andrew responds [4735] with two arguments, a preliminary one, and
a second, more satisfactory, one.

Preliminary: the maximum rate, L/C, falls to ZERO, so that the
actual rate must eventually turn down.

The problem with this, as I explained in detail in my paper at the
same session of the IWG conference, is that in the conditions as-
sumed, it is simply not true that L/C falls, let along falls to 0.
For a circulating capital case with L constant and material-input-
to-labor ratio and output-to-labor ratio rising at the same rate,
L/C = (Y - A)/A, or the ratio of net output to material input, and
is constant. The same embodied labor, C, is embodied in rising
flows of use values, but the profit rate (the ratio of the flow of
current labor to embodied labor) is not changing. The profit rate
is constant, not falling. If the real wage rate were positive,
the profit rate would be rising.

This conclusion is indeed qualified if one applies the historical-
cost assumption. If capitalists are maintaining scale by keeping
older vintages of capital goods in production -- and their cost at
actual valuation in time on the books -- the embodied labor, C',
will be greater than C, and the profit rate correspondingly lower.
Over time, however, loans are repaid and early vintages are
scrapped; C' thus approaches C asymptotically and r approaches
L/C. Again, r does not fall, let alone toward zero.

(Incidentally, the historical-cost argument for a falling rate of
profit sits very uneasily with the circulating capital model, in
which all capital goods are used up and replaced in each period.
I am intrigued by the way in which the TSS theorists cling to the
circulating capital case, as do their nemeses, the post-
Keynesians. When preparing an article on value theory for their
*Elgar Companion to Classical Economics,* I was told by
Kurz/Salvadori not to use a fixed capital model, as the circulat-
ing capital model alone "gives a classical price system." Why
those who reject the Marxist problematic, and those who turn that
problematic into a rigid dogma, both insist on studying a model
more appropriate for the 18th century than for the 20th (or 21st)
is something of a mystery remaining to be solved.)

Andrew's second argument is new; the historical cost stuff has now
vanished. The "temporalist" rhetoric remains, but it is not nec-
essary to the argument itself. I cannot make any sense of passag-
es like: "Roemer and Okishio aren't talking about the ACTUAL-max-
imum and ACTUAL-actual profit rates, but STATIC-HYPOTHETICAL maxi-
mum (V = 0) and actual (V > 0) rates. So, in other words, the
decline in the maximum rate of which they speak is not a decline
brought on by a *process* of capital accumulation. It is, rather,
a hypothetical series in which the simultaneist profit rate is
plotted against the A-matrix -- NOT against TIME. In that con-
text, it makes sense (as much as anything in such a context) to
say that if wages are positive, the actual profit rate will be
less." In an ACTUAL process through time, the actual rate is . .
. the actual rate. The maximum rate does not obtain (with V > 0);
therefore, it is "hypothetical" -- unless we are dealing with par-
allel universes, or Star Trek-like temporal anomalies. Can anyone
else figure this passage out? How do you "plot" something against
a matrix?

The "actual" (second) argument runs like this. r = s/(c + v), in
the antiquarian circulating-capital world. Now r(1) = s(1)/[c(1)
+ v(1)] is greater than, equal to or less than [>=<] r(0) =
s(0)/[c(0) + v(0)], iff (interchanging terms) s(1)/s(0) >=< [c(1)
+ v(1)]/[c(0) + v(0)]. With "all value reinvested," c(1) + v(1) =
c(0) + v(0) + s(0), so we have s(1)/s(0) >=< [c(0) + v(0) + s(0)]/
[c(0) + v(0) = 1 + r(0). With r(0) positive, this means the only
way s(1) can be equal to or less than s(0) is with r(1) < r(0)
(even this does not guarantee it). If, however, s were rising,
this would eventually violate s < L (which is, remember, con-
stant). So r(1) < r(0). QED.

Now the key idea here is that "accumulation" is occurring, with a
CONSTANT labor force. c(1) + v(1) = [c(0) + v(0)][1 + r(0)],
i.e., total capital invested (in value terms) is rising. If the
composition of capital is constant, both c and v are growing at
the rate r(0). Then the rate of exploitation is falling, s is
falling, and r, of course, is falling -- due to rising wages!
When did you get together with Okishio and the profit-squeeze the-
orists on this, Andrew?

The assumption of constant L is a very strong assumption, indeed.
We have s(1) = L - v(1) = L - v(0)[1 + r(0)]. Then r(1) = [L -
v(0)[1 + r(0)]/[c(0) + v(0)][1 + r(0)], < [L - v(0)][1 + r(0)]/
[c(0) + v(0)][1 + r(0)] = r(0). If, to the contrary, rising v
sets in motion a proportionally rising labor force (a reasonable
proposition, one would think), then L(1) = L(0)[1 + r(0)], and
r(1) = r(0); again, no falling profit rate.

We can make sense of the constant-L story if v is also constant.
But then all of s(0) joins c: c(1) = c(0) + s(0), c/v is rising,
and (given the constant rate of exploitation) r is falling. No
argument here. The only question is -- the one that started the
whole discussion going over a century ago: what determines a path
of technical change with a rising composition of capital? Why
would rational capitalists introduce such a change? Andrew's the-
ory is no theory at all, but a return to the starting point.

A further irony: both Andrew and Frank Thompson eventually lose
track of technical change altogether: they both focus on accumula-
tion as such, rather than on technical change, to explain the
falling rate of profit!

The key point of my critique: IF productivity and physical-input
intensity are rising at the same rate, then -- apart from transi-
tory historical-cost effects -- c(1) = c(0), and (with the rate of
exploitation constant) v(1) = v(0). (With a constant real wage
and rising rate of exploitation, v is falling, making the condi-
tions for falling r even more stringent.) There is then simply no
room for accumulation in value terms: s(0) has no place to go. If
such accumulation is nevertheless occurring, this must mean that
either or both of two crucial assumptions -- equal growth rates of
technical composition and productivity, and constant L -- must be

The value-only model of a LOGICALLY and INEVITABLY determined
falling rate of profit simply does not hold water. The falling
rate of profit issue must be analyzed in terms of the capitalist
determination of technical change: most decisively, the trend of
the composition of capital, the ratio of the labor embodied in the
STOCK of (physical) capital to the flow of current labor that sets
it in motion (alternatively, the ratio of the stock of physical
capital to net output). Trying to place the issue in "value
terms" exclusively ("It just doesn't matter how you fill in the
use-value side of the accounts") is mystifying and bogus: how (in
the name of Marx, ;-)) do you account for TECHNICAL CHANGE without
paying attention to use-values?

For OPE comrades who were not in Washington: I will send my paper,
"Okishio and His Critics: Historical Cost Vs. Replacement Cost,"
by snailmail on request.



David Laibman