I have decided not to go into line by line critique of what you have
written, because I have a feelin that would end up being waste of time. So
I'll just point out what I think is the basic flaws in your examples:
First of all, in the example you give below, the production price ratio of
the two commodities is not 1:1 as you suggest, but it is: the price of
bread in terms of wheat is equal to 1.00009.
In both the examples, that is the example in this post as well as the
earlier one, your given systems are irreproducible, and that's the source
of your results. For example, in your earlier example, the system needs 104
units of wheat for simple reproduction but produces only 101 units of
wheat. The system cannot go on reproducing itself. Similarly, in your
current example your system needs 20,000 units of wheat as input but
produces only 10001 units of wheat (I have scaled down your first equation
by 100 to make it clear--in your original example it will take a bit longer
time for the wheat sector to wind down to nothing). Nobody works out
properties of an economic system which is structurally irreproducible.
You have a tendency to use non-basics as numeraire as you have done below.
Only basics should be accepted as numeraire since equations for non-basics
can be simply removed without having any impact on the system, but the
equation for the numeraire commodity cannot be removed. Cheers, ajit sinha
_________
At 15:06 5/11/98 -0500, you wrote:
>It will take me a while more to think through Duncan's welcome
>and thoughful post (OPE-L 283). In the meantime, I'll take the
>opportunity to clear away some confusions.
>
>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.
>
>
>
>