A reply to Fred's ope-l 2712:
I continue to disagree with Fred. Nonetheless, I think this post of his was
unusually clear in its formulations, which help immensely in trying to resolve
the issues under dispute. Let me comment on the key points:
Fred: "... I assume that input prices are equal to output prices (in long-run
equilibrium)."
Andrew: What do you mean by "long-run equilibrium"? If you mean a situation
in which all profit rates are equal, then you cannot *assume* that input
prices must equal output prices in this situation. Are stationary prices
logically necessary for uniform profitability to exist? I think not, and know
of no proof that shows they are, or even any argument that indicates they are.
Will the optimizing behaviors that tend to lead to uniform profitability also
tend to make prices stationary,? Again, I think there's no necessary reason
for this, and know of no proof or argument.
This issue is important because it calls into question the ground for Fred's
(and others') stipulation that production prices must be stationary.
Production prices and uniform profitability imply one another. If uniform
profitability and stationary prices go hand in hand, then so do production
prices and stationariness. Yet if there is no necessary logical or behavioral
connection between uniform profitability and stationary prices, it is invalid
to invoke "long-run equilibrium" to justify the stipulation that production
prices be stationary.
So my 1st question to Fred---and other simultaneists---is: on what ground do
you stipulate that production prices MUST be stationary?
Fred: "I have argued that the quantitative results (rate of profit and prices
of
production) of my interpretation are different from the results of the
Sraffian interpretation because Marx's logical method of determining the
rate of profit and prices is fundamentally different from the Sraffian
logical method (the method of linear production theory).
"[... ] In his most recent post, Andrew acknowledged that, in the case of
FIXED
CAPITAL, my interpretation leads to different results for prices and the
rate of profit than the Sraffian interpretation."
Andrew: I've spliced these two passages together in order to clarify *why*
Fred's interpretation gives different results from the Sraffian one in the
case of fixed capital. It has nothing to do with "logical method." The
*sole* reason is that the Sraffians treat fixed capital as a joint product,
while Fred doesn't. Even in the fixed capital case, because Fred stipulates
that prices are stationary, his interpretation implies that
(a) the rate of profit is a function solely of the input/output and real wage
coefficients,
(b) the rate of profit can't fall due to mechanization itself,
(c) the distribution of profit affects the general profit rate (e.g., the
profit rate corresponding to the same technical and real wage coefficients is
different if commodities exchange at values than if they exchange at
production prices),
(d) technology and labor extraction in non-basic (luxury) industries doesn't
affect the general rate of profit,
(e) unit values of outputs are affected by changes in the real wage rate (per
unit of labor-power), and
(f) unit values of outputs are affected by the amounts of labor extracted
from labor-power.
All these implications contradict Marx's own results. All are due to the
stationary price postulate. (I have discussed these items in somewhat more
detail in my paper for the 1996 EEA.)
Fred: "I have also argued, responding to Andrew's arguments, that even though
the Marxian results are different from the Sraffian results, the Marxian
results can still satisfy a equation that looks like the Sraffian equation for
the determination of the rate of profit and prices:
p = (pA + pBL)(1 + R). Therefore, Andrew's argument that there can be only
ONE rate of profit and set of prices that satisfies this equation, and
therefore that the Marxian results must be equal to the Sraffian results, is
not correct. Andrew's argument assumes the Sraffian method of determination
of prices and the rate of profit and does not apply to the Marxian method of
determination."
Andrew: my argument assumes nothing of the kind. All it "assumes", i.e.,
invokes, is a well known matrix algebra proof (and I've also provided 2 proofs
in the 3-Dept. case that don't rely on matrix algebra). For given square
matrices A and BL that are irreducible (some sector's product is used directly
or indirectly by all sectors), there is one and only one solution of the above
system which satisfies the conditions that none of the elements of p are
negative and that one or more is positive. That solution gives a unique value
for R and a unique set of ratios pi/pj. One may take a different value for R
as given, as Fred does, and solve a system that will give different relative
prices, but it will be a *different* system: the technical and real wage
coefficients will not be [A+BL], but [A+BL]*.
For the *same* system, the *same* economy, in other words, there is only one
solution for relative prices and an equalized rate of profit, once one
stipulates that the p on the left and the p on the right are identical. Thus,
the only way in which Fred can get a different profit rate and different
relative prices from the Sraffians is by referring to a different economy.
This, of course, is no surprise.
This is purely a matter of math, and very well known math. Although Allin and
I don't see eye to eye on most things, he's indicated in a post on this list
that I'm right. WOULD SOME OTHER MATH WHIZZES ON THE LIST ALSO PLEASE
INTERVENE, ASSSESSING WHETHER I'M RIGHT OR WRONG ON THIS POINT? It is a
simple, straightforward point, and it is both frustrating and a very
inefficient use of both Fred's and my time for us to keep going around in
circles on this. So PLEASE, PLEASE, PLEASE will you help us out, folks? It
is a matter of efficient use of collective resources.
Fred: "I continue to think that Andrew's argument illegitimately substitutes
the Sraffian
method of determination of the rate of profit and prices of production for the
Marxian method of determination. I have been trying to think of new arguments
and numerical examples, but I haven't had much time and so far have not been
successful."
Andrew: The numerical examples are the key, because some proof is needed, and
it is easier to assess whether a numerical example proves what it is supposed
to than whether a verbal argument does so.. I'll accept as disproof of my
claims even *one* numerical example that assumes C and V are equal to the
prices of means of production and subsistence, assumes a uniform profit rate,
and assumes stationary prices, but
(1) assumes circulating capital only, and gives a different value for the rate
of profit and/or relative prices from the Sraffian ones for the same A, B and
L,
or
(2) gives two different profit rates for two economies in which all the
elements of A, B, and L, are the same, *except* in one or more "luxury"
(nonbasic) industries.
Fred: "As I have said before, if Andrew's argument is correct, then no other
theory of the rate of
profit is possible, except the Sraffian theory, as long as it is assumed that
input prices are equal to output prices."
Andrew: Well, one can revert to the apologetics prevalent in the 1970s and
claim that one has a different theory because, although the profit rate and
relative prices functionally depend only on technical and real wage
coefficients, value relations still matter, are not "redundant," since (one
can assert) value relations somehow determine the technical and real wage
coefficients. But basically the above is correct: if input prices must
equal output prices, then one necessarily gets the Sraffian numbers or, in the
case of fixed capital, other numbers that likewise imply that the profit rate
depends only on the physical input/output relations, and not value relations.
I realize Fred will be rather busy for the next couple of months, so I
certainly don't expect a reply any time soon from him. I really would,
however, appreciate responses in the interim on the uniqueness of the relative
prices and profit rate that correspond to the same A, B and L, if input prices
equal output prices.
Andrew Kliman