Despite the somewhat sharp tone, I was very happy to get Jerry's response
(ope-l 2284) to my "model" of the rate of profit. Because the issues
were posed sharply and clearly, I can give a clear answer.
(1) Alan has previously argued, and I fully agree, that the TSS interpreta-
tion of Marx's value theory has no "model" of capitalists' behavior. Rather
it theoreizes the consequences of their behavior, whatever it might
be. Hence, the example I put forward is not meant to be a "model" of how
the economy actually works. Alan has also recently made another distinction
between a matehematical framework to represent how Marx thought the economy
operates and a mathematical framework to answer charges that this or that
aspect of Marx's value theory is logically incoherent. Again, I fully
agree with this distinction, and the mathematical framework I was discussing
in my post was the latter.
(2) The specific issue I was discussing in that post was whether the way
I *calculate* the profit rate was correct, appropriate, or whatever, not
whether my conception of the *determination* of the profit rate is correct,
consistent with Marx's or whatever. I wanted to show that I was indeed
measuring the IRR, and that the social IRR can fall under conditions in
which Roemer has said it must rise.
To do some calculations without getting into a lot of exceedingly messy
stuff, I assumed away a bunch of things to be able to get IRR's that
conform to a simple formula. I don't think there's anything wrong with
that.
(3) I have recently posted ("Moseley interpretation Pt. II") a 2-sector
model in which the actual profit rate falls while the Okishio/Roemer
rate does not. That example, too, made some simplifying assumptions, but
they can be removed. The problem, once one removes them, is how to
communicate the results. Basically, under many, many, many different
sets of assumptions, with different real wages, different numbers of
sectors, different numbers of inputs, uniform and nonuniform profit
rates, it is possible to construct examples in which the Marxian profit
rate (as I interpret it) falls while the simultaneist (Okishio-style)
rate rises.
But will a table with a bunch of numbers, or a graph, reporting such
information be meaningful (not to mention convincing)? Not very, I
think. One wants to know *why* the results differ, no? One wants to
get to the essential conceptual difference, no? And to do so, it is
legitimate, I think, to abstract from things that tend to conceal the
essential differences.
(4) I can also model depreciating fixed capital. I have used a
nondepreciating fixed capital model partly because this is what Roemer
employs to extend Okishio's theorem, and to refute Roemer it is
helpful to look at his own case. Also, IRR calculations are messy
if capital depreciates. To explain/defend my way of measuring the profit
rate, it seems legitimate to work with the simple case of fixed capital
that lasts forever.
There is a kind of physically nondepreciating fixed capital that it
seems is widely used today. Software.
If capital lasts one period, it is not fixed. If it lasts longer, it is
fixed. Thus it seems to me that it is "very" fixed if it lasts forever.
But forgetting terminology, the issue with respect to the refutation
of the Okishio theorem is to have stuff for which more value was laid
out to acquire it than would now be necessary (due to falling unit values/
prices).
(5) Marx does talk about workers living on air when discussing the
FRP. It might be when he's discussing Price's theory of interest in
Vol. III of Capital. Maybe not. Can anyone provide the citation?
Of course, Marx didn't think this was a "realistic" assumption. He employed
it in order to highlight a theoretical point.
That's basically what my unrealistic assumptions do. That's what, e.g.,
the Okishio theorem does when it assumes a constant real wage rate. I
think it is unhelpful and missing the point to critique the theorem on
the grounds that this assumption is unrealisitc. Oksihio knows this,
Roemer knows this. But they want to show Marx to be wrong when he said
that mechanization *itself* can lower the profit rate. So how to get
a test of this idea? Hold constant everything else that matters to
profitability, such as the real wage.
I think that is a legitimate and indeed an unavoidable procedure.
What seems to be emerging from all this discussion of models is that
some people take mathematical formalizations to be "models" of the
way the economy works. But others use them for other purposes, such
as a way to clarify theoretical issues. Hence, the purpose of the
formalization should be made clear by the author, and the reader should
pay attention to such statements and interpret the formalization
accordingly.
Andrew Kliman