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From: owner-ope-l@galaxy.csuchico.edu on behalf of Tsoulfidis Lefteris
Sent: Thursday, January 23, 1997 6:38 AM
To: ope-l@galaxy.csuchico.edu
Subject: Re: Draft EEA paper, Part 2
I thank Lefteris for her or his comments, which give me the opportunity to
explain the methodology of the paper. That methodology is based on the
methodology of others who have studied these issues. One really needs to
understand it in order to understand what the paper does and doesn't claim,
and why.
Lefteris writes: "The first [comment ...] has to do with the realism of the
numbers used. A numerical example to have any validity must be representative
or typical of a situation and not one that will give the results that the
researcher would like to obtain."
It depends on the purpose of the numerical example. Imagine that I had
claimed that it is *likely* that simultaneist profit will be positive while
simultaneist surplus-labor will be negative, or vice-versa. Then, yes, I'd
have to produce numbers that we would be likely to observe. In fact, I'd have
to produce a large set of actual observations.
Yet this is not what I have claimed. My claim is that it is *possible* for
simultaneist profit to be positive while simultaneist surplus-labor is
negative, and vice-versa. My purpose is to refute propositions that hold this
to be impossible. To produce a successful refutation, I only need to produce
a single counterexample. This is well known.
But, you may ask, why am I *not* dealing with the likelihood that this will
occur? Answer: it is not relevant to the issue under investigation. What is
at issue is not *whether* both are positive, but *why*: is profit positive
*because* surplus-labor is positive? Therefore, I, like everyone else who
has dealt with this question, ask whether simultaneist surplus-labor
*necessary* for positive simultaneist profit to exist, and whether it is
*sufficient* for positive simultaneist profit to exist.
Here's an analogy. You see someone murmur a magical incantation and then feed
arsenic to a sheep. He does this 1000 times. Each time, the sheep
immediately dies. Thus, empirically, you are perfectly justified in
concluding that it is extremely likely that when he murmurs the magical
incantation, the sheep will die.
So what?
The real issue is *why* does the sheep die? Does it die *because* he murmurs
the magical incantation? Observation, no matter how many times it is
repeated, will not give you an answer, especially if he always murmurs the
incantation right before feeding the sheep arsenic.
What you therefore do is engage in a thought experiment. You ask, "is the
incantation *necessary* for the sheep to die?" Answer: no. If the arsenic
is administered and no incantation is murmured, the sheep will still die. You
also ask, "is the incantation *sufficient* for the sheep to die?" Answer:
no. If the incantation is murmured, but no arsenic is administered, the sheep
will not die. So, by means of this thought experiment, not by observation,
you quickly determine that the sheep does not die *because* of the
incantation.
Note that the thought experiment is not "realistic" at all! You have seen the
incantation and the feeding of arsenic coincide 1000 times in a row, but you
assume that they do not coincide! Based on past experience, the situation you
imagine in your thought experiment is definitely not typical or
representative!
Lefteris also writes: "In the case of typical numerical examples in studying
problems such as those of Kliman I think that input-output data of manageable
dimensions must be used. Perhaps super aggregated models of two or three
sectors. Once this is done then I think that it is impossible to find
situations such as those that he describes. It could be argued that the level
of aggregation might be too high but it seems to me that even more detailed
input-output tables do not convey the information that Kliman's numerical
examples claim."
I am having trouble understanding this, for two reasons. First, Lefteris'
argument was that numerical examples must be "representative or typical of a
situation." But the level of aggregation has nothing to do with the
representativeness of the *actual* situation. Aggregation is an act of
classification by the observer. However the observer chooses to classify
use-values, the actual situation remains exactly the same. So it doesn't make
sense to say that super aggregated data are more or less "typical" of
*reality* than are disaggregated data. They are two different ways of
representing the same reality. And it is reality, not the methods of
representing it, with which my paper is concerned.
Second, most of my examples are two-sector examples, just as Lefteris
advocates! See, for example, Tables 1, 2, and 3. So it isn't true that,
with a small number of use-values, or aggregates, "it is impossible to find
situations such as those that he [Kliman] describes." I've found some of
them.
Moreover, the number of sectors doesn't matter. This can be seen from the
fact that I prove my point both with a 2-sector example and with a 1001-sector
example. Also, the logic of my refutation is simple, and has *nothing* to do
with the number of use-values: the value of the positive surpluses can be
greater than the value of the negative surpluses under one price vector, and
less than the value of the negative surpluses under another price vector.
Finally, Lefteris argues: "The second problem has to do with prices, Kliman
finds negative profits
assuming prices to be of particular numerical value. Well one s[h]ould not
suppose prices but rather arrive at them."
Please also note that I find positive profit and zero surplus-labor in Table
2.
My procedure is no different from others -- e.g., Okishio, Roemer, Morishima
-- who have studied these questions. Rather than dealing with a special case
of prices, they, and I, deal with the *general case*. That is, they, and I,
ask whether it is possible to have positive profit and negative surplus-labor
(or vice-versa) under ANY set of (positive or non-negative) prices.
*If* I were claiming "these are *the* prices and *the* profits that we would
observe on the basis of these physical quantities," then Lefteris' objection
would be valid. But again, that's not my claim. My only claim is that the
examples are theoretically *possible*. And that is sufficient to prove that
simultaneous valuation and the exploitation theory of profit are incompatible.
Moreover, it is not clear to me how I am supposed to "arrive at" (derive?)
prices. On the basis of what? Physical quantities alone are insufficient to
determine the magnitudes of prices. I could introduce additional restrictions
in order to obtain determinate prices, but then I wouldn't be dealing with the
general case. If you assume equal profit rates, you are dealing with a very
special case, not with reality. If you assume prices = values, you are
dealing with an even more special case, not with reality.
Please also look at my Tables 1 and 2 again. What they show is that, even if
you *do* assume equal profit rates over two "days" (or hours, etc.), this
assumption plus the physical quantities plus simultaneous valuation is
insufficient to yield determinate prices! For instance, take Table 2, in
which good 2 is numeraire; p2 = 1 on both days. Now, you need to find p1.
But there's p1 on day 1 and p1 on day 2 -- TWO unknowns. But there's only one
equality stipulated (the two-day profit rate in sector 1 equals the two day
profit rate in sector 2). So the prices of good 1 are still not determined!
Andrew Kliman