[OPE-L:2982] Re: Math Theorems, Economic Theorems

andrew kliman (Andrew_Kliman@msn.com)
Fri, 6 Sep 1996 20:15:35 -0700 (PDT)

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A response to Allin's ope-l 2978.

In response to my ope-l 2971, Allin wrote:
4. Andrew on Okishio and Perron-Frobenius: I don't think
you can say that the "economic content" of Okishio is just
an arbitrary assignment of economics-sounding strings to
mathematical objects. For one thing, it seems clear that
thinking about Okishio has forced greater explicitness regarding
certain economic matters.

Allin, you've misunderstood me. I began that post "by agreeing with
something Allin wrote in ope-l 2937. He notes that the Okishio theorem
rightly demolished a lot of pro-FRP thinking." I continued that "*Some* valid
inferences can be drawn
from the exercise; among them is the inference that *if* there is full
adjustment to a post-innovation stationary-price/equal-profit-rate state,
*then* the new profit rate cannot be lower than the initial one (given the
theorem's assumptions)."

More importantly, the whole point of my post was to *repudiate* the idea that
the theorem is true by "definition"; i.e., by virtue of the "assignment of
economics-sounding strings to mathematical objects." I wrote:

"I of course do not think that Okishio or Roemer were doing anything as silly
as comparing the size of yellow logarithms. But the only reason I don't is
because I think, and have some strong evidence, that they were *not* defining
the pre- and post-innovation equilibrium profit rates as r and r*. Rather,
they were letting r and r* represent externally defined economic concepts, and
making an argument concerning the relative magnitudes of these nonmathematical

In a somewhat different vein, Allin continued:
Are we sure that Marx had a definite
assumption in mind regarding whether or not input prices
equalled output prices? Surely it is reflection on Okishio
that has made this appear as an issue.

Actually, Ted and I began thinking about (in)equality of input and output
prices in connection with Bortkiewicz's "proof" that Marx's Ch. 9
transformation was logically inconsistent because input and output prices
differed. Only later did I turn to the Okishio theorem. In a 1995 ASSA
paper, Eduardo Maldonado-Filho gave a TSS defense of Marx's transformation
formally identical to ours (though with a different numerical example) without
having seen it, and he made only a passing reference to the tendency of the
profit rate. It also seems that Mino Carchedi began questioning the
stationary price postulate in connection with the value/production price
transformation, not Okishio. John, on the other hand, started with the
Okishio theorem directly, abstracting from value/price differences. I think
Alan and Paolo Giussani also began with Okishio and worked backward (from the
historical standpoint) to the transformation.

I for one am sure Marx didn't think input and output prices had to be equal.

First, there's Marx's critique of Torrens. Marx says the value of 100
quarters of corn advanced can exceed the value of the 120 quarters produced.

Second, throughout Marx's work, he discusses changes in productivity causing
values to change over time.

Third, there is NO evidence, to my knowledge, that he ever assumed they were
equal, and none of his theoretical results depend on this equality.

Fourth, a lot of his results that are otherwise valid get messed up the moment
stationary prices are postulated.

Fifth, Garegnani--certainly no TSSer---has studied this issue in great detail,
and has concluded:

"...in order to avoid a frequent misunderstanding, it may perhaps be stressed
that changes in normal prices over time were ignored in traditional theory
because they were considered sufficiently _small_, and not because of any
assumption of stationary or steady growth of the economy .... That no such
assumption was made should be clear already from the fact that the normal
positions were meant to be centres of gravitation of the actual economy, and
this could not have been the case for a stationary or steady-state position of
the economy."

Sixth, Marx lacked the mathematical sophistication to assume input and output
price equality ;-). I find it very difficult to imagine the notion arising
in anyone's head who wasn't faced with the problem of eliminating n unknowns
in order to solve some simultaneous equations.

Seventh, as Bortkiewicz himself noted, and Michele, Alan, and Ted have
stressed, determination in Marx's work is "successivist," not simultaneous.

Eighth, the postulate is ridiculous, and I don't assume people think
ridiculous things until I have strong evidence to the contrary. And, as a
general rule, one needs *positive* evidence to impute a special-case
assumption to someone. I've noted this recently in connection with Gil wanting
me to spell out that I am not assuming complete futures markets. To infer
they assume it unless the contrary is proven is completely backwards, a
license for wild speculation. It is the theoretical equivalent of "when did
you stop beating your wife?" It is those who think that Marx assumed
stationary prices who bear the burden of demonstrating it.

Allin also wrote:
I wonder, though (I haven't yet
attempted to think this through in detail) to what extent the
counter-argument (i.e. that what happens to r-max cannot be
used to make non-trivial inferences about what happens to r)
depends on r-equalization? That is, on everything being
measured in prices of production. If -- as Paul C and I have
urged -- we conceive of prices as being stochastically
distributed around values, exactly what difference does that
make to the argument?

Well, the inability to *infer* the tendency of r from the tendency of r-max is
obviously still true as a logical stricture. The only issue is whether viable
technical change could lead to a fall in the general simultaneist profit rate
under non-uniform profitability. I haven't investigated this either, but my
intutition is that prices of production vs. values wouldn't make much
difference. One thing Sraffa's and post-Sraffian work shows is that, in a
simultaneist context, variations in relative prices have a rather limited
impact and role; the physical input-output relations reign.

Andrew Kliman