In OPE-L 290, Ajit Sinha wrote:
"If we take wheat as the numeraire, the the price of bread comes
out to be 4.04 in terms of wheat. So where is the problem? The
problem is with Andrew's meaningless imposition that prices of
the two goods happen to be $1 each (where the sign $ always
remains a mystery). One cannot do 'theory of prices' by imposing
arbitrary and m[ea]ningless prices on the system. This is the
fundamental mistake TSS makes all the time."
The "Fundamental Marxian Theorem" (FMT) is intended to show that,
given simultaneous valuation, the extraction of surplus-labor is
necessary and sufficient for the existence of positive profit.
In other words, surplus-labor is the sole cause of profit.
To restrict the scope of the theorem to the special case in which
profit rates are equalized -- the special case Ajit is
considering -- is to deprive it of significance, because then
surplus-labor is NOT necessary and sufficient for positive
profit. Rather, surplus-labor PLUS a competitive structure that
equalizes profit rates are together necessary and sufficient for
positive profit. Therefore, one has just turned COMPETITION into
a cause of profit! Ajit may be happy with that, but I am not and
I submit that Marx would not have been.
Neither is the existing literature happy with it. Because the
aim is to show that surplus-labor really is the sole cause of
profit, the most general versions of the FMT are formulated in
terms of market prices, not production prices. So if I am making
a mistake by considering market prices, it is a mistake shared by
the simultaneist literature I am critiquing. I am certainly
entitled to investigate the implications of its own assumptions,
no?
For instance, in “Three Topics on Marxian Fundamental Theorem,”
Nobuo Okishio (who first discovered the FMT) and his co-authors
give two proofs of the FMT in which the *only* restriction on
prices is that all prices are positive. In one version, they
prove that, given positive surplus-labor and some additional
conditions, "we have positive aggregate profit, WHATEVER MARKET
PRICES MAY BE" (my emphasis). In the other, they show that “If
there exist A POSITIVE p which satisfies" the condition that
profit is positive in every industry, “then there must exist
positive surplus value” (my emphasis).
Likewise, in Chapter 2 of _Analytical Foundations of Marxian
Economic Theory_, Roemer proves a version of the FMT that does
not require equalization of profit rates. He also selects
“arbitrary” prices to disprove the FMT in the case in which what
he calls “independence of production” does not exist (i.e., some
goods must be produced as joint products in fixed proportions).
Furthermore, some proponents of the New Interpretation and the
simultaneous single-system interpretations have similarly
suggested that their interpretations imply that surplus-labor is
necessary and sufficient for positive profit, whatever market
prices may be. For instance, in the post to which Ajit is
responding, Duncan notes that "the NI definition of the MELT is
supposed to work for ANY MARKET PRICES" (my emphasis).
Let me also point out that it will simply not do to argue that
market prices are "close" to production prices, so that the
latter assumption is a helpful abstraction, etc. Given only that
market prices differ from production prices, NO MATTER HOW SMALL
THE DIFFERENCE, the FMT and the related claims made for the New
Interpretation and the simultaneous single-system interpretations
do not hold up under the presence of some negative net products.
ALL of the simultaneist interpretations imply that profit can be
negative although surplus-labor is positive.
For instance, assume that
1,000,000 wheat + 100 living labor --> 1,000,001 wheat
10,000 wheat + 1 living labor --> 10,000.01 bread
Given zero wages, there are clearly 101 units of surplus-labor
extracted. The equalized profit rate would be positive (=
1/1,000,000). Letting bread be the numeriare (as we'll see, Ajit
quite wrong when he claims that my results depend on the use of
money prices rather than numeraire prices), the price of wheat in
terms of bread at that profit rate would equal 1.
Yet imagine that the price of wheat (in terms of bread) equals
1.0002. Under simultaneous valuation, profit equals
1.0002*1,000,001 + 1*10,000.01 - 1.0002*1,000,000 - 1.0002*10,000
= -0.9898. So "profit" is negative although surplus-labor is
positive AND although the relative price is *extremely close* to
the equilibrium relative price AND although the difference in
profit rates across the two sectors is very small (0.000001 in
wheat and -0.000199 in bread).
As we know, some people have been trying to argue that relative
prices are "close" to relative values, and that this somehow
disposes of the insuperable theoretical contradictions of
simultaneist value theory. But this argument doesn't hold water,
either. Given only that market prices differ from values, NO
MATTER HOW SMALL THE DIFFERENCE, the FMT does not hold up under
the presence of some negative net products. To see this, one
need only observe that, in the above example, the standard
dualist unit values of wheat and bread both equal 100, so that
the relative value equals 1. Thus, if the relative price is
1.0002 -- hardly distinguishable at all from the relative value,
and by far a much, much "better" result than any of the empirical
studies have ever obtained -- simultaneist profit is negative
even though surplus-labor is positive.
I think the conclusion is clear. Simultaneous valuation is
incompatible with Marx's theory of the origin of profit. A
choice must be made.
Andrew ("Drewk") Kliman Home:
Dept. of Social Sciences 60 W. 76th St., #4E
Pace University New York, NY 10023
Pleasantville, NY 10570
(914) 773-3951 Andrew_Kliman@msn.com
"... the *practice* of philosophy is itself *theoretical.* It is
the *critique* that measures the individual existence by the
essence, the particular reality by the Idea." -- K.M.