Thus spake Andrew:
A response to Pat's comments (ope-l 2976) on my maximum rate of profit post.
Pat: "1. At what profit rate does the convergence between the maximum and
actual rate of profit occur? Presumably, convergence occurs before r(max) =
r(actual) <= 0? Is there any proof that this is the case?"
Thus spake Andrew: The difference between the two rates is due only to the
use of living labor in production. The smaller are the elements of the vector
of living labor requirements per unit of outputs, the closer are the two
rates. If the Hawkins-Simon condition is met (the amount of each good used as
input throughout the economy is less than or equal to the amount produced, and
less than in at least one case), then the maximum simultaneist profit rate is
positive. If the living labor requirements per unit of outputs become
infinitesmally small, then the "actual" simultaneist rate becomes
infinitesmally close to this positive maximum rate. (Dmitriev claimed to have
proved that the profit rate will be positive even if L is exactly zero, but as
Ted and I have shown, this proof is flawed, because it assumes non-zero
prices, which it actually needs to prove.)
Pat: "2. Maximum rate of profit FROP discussions usually contain an argument
which pinpoints the onset of a crisis. Specifically, the argument is that even
with a falling r(max) it is possible for the mass of profits to rise. However,
when the growth in capital is equal to the percentage decline in r(max) the
mass of profits stagnant. Thereafter, further reductions in r(max) lead to a
lower mass of profits and declining investment. The crisis is on. Define
r(stagnant) = the rate of profit where the mass of profits stagnants. Does the
supposed convergence between the actual and maximum profit rate occur before
r(max) = r(actual) <= r(stagnant)?
Thus spake Andrew: This can't be right. The mass of profits is, by
definition, equal to the *actual* profit rate times the capital advanced.
Apart from that, why should changes in a fictitious maximum profit rate lead
to crisis?
Pat: "3. How does one reconcile the Okisho/Roemer/Samuelson/Kliman view with
the actually existing empirical evidence which supports FROP theory?
Regardless of theoretical perspective, isn't there a basic requirement to
evaluate one's model in light of the empirical evidence?"
Thus spake Andrew: "the Okisho/Roemer/Samuelson/Kliman view" of what?
Okishio, Roemer, and I agree that the falling maximum rate argument has no
implications for the actual rate; I don't know that Samuelson has said
anything about it. Pat seems to think I said that a falling maximum rate
cannot set a declining limit on the actual equilibrium rate. I did not. I
said that *if* the Okishio theorem is true, *then* it cannot do so---one
cannot reconcile the theorem and Marx's law by resorting to the falling
maximum rate argument. But John and Alan and I have refuted the Okishio
theorem. Therefore, since it is *possible* that Marx was right, the evidence
supports his law.
Conversely, as Roemer has very rightly pointed out, if the Okishio theorem did
indeed demonstrate, as it purports to do, that it is *impossible* for
labor-saving innovation, by itself, to lead to a fall in the equilibrium
profit rate, then all the "empirical evidence" in the world could not salvage
Marx's law!!! So, no, there isn't always a basic requirement to evaluate
one's "model" in light of the empirical evidence, IMO---are we to run out and
test Arrow's impossibility theorem, or ask Arrow-Debreu to identify an
empirically existent general equilibrium? Impossible means impossible and
proofs are proofs---if they are indeed proofs.
Pat then quoted me:
>The maximum profit rate argument is the kind of thing that has led
>people like Samuelson and Steedman and Roemer to issue charges of
>obscurantism. I was initially very unsympathetic to these charges, but over
>the years I have gradually become convinced that they are justified in almost
>every case.
And responded: "4. Polemicist restrain thyself."
Thus spake Andrew: Why? Samuelson's "erase and replace" remark wasn't very
*nice*, for instance, but it was right on the mark. And why do you take the
above to be the statement of a "polemicist," and not, say, the "considered
judgment of a theorist who, in other respects, disagrees very strongly with
these guys"?
Thus spake Andrew.