[OPE-L:5077] Re: Sraffa's Non-Proof

andrew kliman (Andrew_Kliman@msn.com)
Mon, 19 May 1997 12:26:37 -0700 (PDT)

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A response to Ajit's ope-l 5071.

"Andrew insists that I should respond to this."

No. In my ope-l 5044 ("production and realization thread"), I wrote "I should
also mention that I would still be interested in Ajit's response to my ope-l
4919." I did not "insist" on anything. Had I wanted to insist, I would have
written something like "I insist that Ajit respond to my ope-l 4919."

"You made a theoretical criticism of Sraffa in his theoretical context."

No, and no. First, I made no criticism of Sraffa. I have noted this before.
In ope-l 4864, I wrote "Ajit thinks I'm suggesting that Sraffa made a 'silly
mistake.' I am not. I've merely proved that he failed to demonstrate that,
given an economy with a surplus that undergoes simple reproduction and has
stationary exchange ratios,
there is a unique rate of return on capital advanced. And that's all I've
ever claimed.

"We can debate whether Sraffa was referring to a mythical economy without
'dollars,' or whether he intended his constructions to have some bearing on
actual economies."

Let me try to be even clearer. I am not certain that Sraffa *intended* to
prove the proposition in question. He may just have been playing with the
neoclassicists' heads, showing them the problems their own theory runs into.
Both the subtitle of PCMC and the mythical nature of the economies with which
it deals are consistent with this piece of speculation.

Sraffa himself held that "The labor theory of value is absolutely correct."
This statement is, of course, open to various interpretations, but since
labor-time is redundant in the "Sraffian" system, this is an additional reason
to question whether he thought of his constructions as containing positive
propositions about actual economies. Paolo Giussani suggests the following as
a possible explanation of Sraffa's statement: "In the context of a discrete
dynamic system ... the quantities of labor performed in the various production
sectors (and thus the production of value) are absolutely essential to define
the general rate of profit. ... The fact that the equilibrium solutions of a
dynamical discrete system and the solutions of a static system are identical
when the technical coefficients are constant is of very little practical
importance and only shows that the Sraffian system of equations amounts to no
more than the static case of Marx's theory of prices of production [this last
phrase means Marx's theory of prices of production in the special static case
rather than the general case -- AJK]" ("The Determination of Prices of
Production," IJPE, 21:4, 1991-92, p. 83.)

Second, I made no criticism of Sraffa *because* I was NOT concerned with "his
[Sraffa's] theoretical context." I have also explained this to Ajit before.
As I wrote, also in ope-l 4864, "Hence, I was fully aware all along that one
can postulate imaginary conditions in which 'prices do not change unless
technology, real wages, or relative profit rates change.' My reference to
Sraffa's non-proof has been posed from the beginning as an example ('For

Let me try to make this clearer, too. If one postulates an economy without
money, and puts forth a theoretical system in which the magnitude of the
numeraire's value does not matter (or equivalently, if one stipulates that in
this theoretical system, a unit of the numeraire always has the same value, or
equivalently, if one simply postulates that input and output prices must be
equal), then Sraffa's results follow. We all know this. This does not mean
that Sraffa "prove[d] that, in an economy with a surplus, there is only one
set of exchange ratios that permits simple reproduction to take place together
with equalized rates of return on capital advanced [or] that there is a unique
uniform profit rate in such a case." The difference is that this last
statement refers to "an economy," any economy, including actual economies. In
its theoretical context, Sraffa's reasoning is unobjectionable, though perhaps
misleading. The problem comes when it is taken out of that context and turned
into an assertion concerning relations of determination in actual capitalist
economies. It is not I who started doing so, it is the "Sraffians." What I
have done is to show that the proposition in question has not been proven to
apply to actual economies.

Thus, I have absolutely no objection to any claims that the proposition holds
in Sraffa's mythical economy (*if* the exchange-ratios at time of input and of
output are equal, which he failed to stipulate). My objection is to the
"Sraffians'" implicit and sometimes explicit claims that the proposition has
been demonstrated to hold in actual economies. I therefore reiterate my
proposal concerning how to resolve the debate:

"I'm happy to let Ajit pursue his theory, in which the profit rate is
determined solely by technology, real wages, and relative profitability, given
only that he makes clear that the results of that theory do not necessarily
apply to any actual economies, and that such results cannot be used as
'proofs' that propositions concerning actual economies are false. Agreed?"

Ajit still has not addressed this proposal. I hope he will do so. Soon, I
may "insist" :-).

" I proved to you that your criticism was false."

Your "proof" in ope-l 4827 consists of an unproved assertion that if the
exchange ratio between the two commodities is the same after production as it
is before, the input and output prices of wheat must be the same.

"Then I took the rhetorical wind out of his system by showing to him that his
own prices are not 'actual' and cannot be 'actual', so his theory is also
dealing with an abstract economy, to which he now seems to agree in a
non-commital fashion."

No. Contrary to claims Ajit made, I showed that, in my interpretation of
Marx's value theory, C and V refer to actual amounts of value advanced, even
though they do not necessarily correspond one-to-one with the outlays of
individual capitals, and that prices of production are derivable from the data
of an actual economy, even though the prices at which things exchange will
differ from the prices of production. Therefore Marx is not dealing with an
"abstract" economy, i.e., a mythical, imaginary, hypothetical, counterfactual
economy, but with a real economy, according to my interpretation.

In one of Bortkiewicz's examples, he shows that the general profit rate is,
according to Marx, 29.6%. This is an *actual* profit rate. It may be the
case that no capitalist obtains a 29.6% rate of return, but it is the actual
weighted average for the economy as a whole. Accordingly, Marx's prices of
production are actual -- C + V + av. profit -- even if no one buys or sells at
those prices. The profit rate and the production prices are based on actual

What Bortkiewicz does is very different: write down the actual value
magnitudes, then erase them, then substitute mythical figures for C and V by
postulating an economy in which inputs of the period are bought at the prices
of the outputs of the period. Voila! You now have a whole new economy that
has nothing in common with the actual economy except physical data. It turns
out that, in this imaginary economy, the equalized profit rate is 25%. Big

The importance of Fred's work, in my view, is to show that you can turn the
whole procedure around: write down the value magnitudes, erase the physical
quantities, then substitute other physical quantities that yield input prices
equal to output prices. The Bortkiewiczian profit rate turns out to be 29.6%!
By the same methods that Marx was "proven" to be wrong, he can be "proven" to
be right!

BTW, it is not accurate to say that I have a "theory," much less a "system."
I have an interpretation of Marx's theory. If one wishes to critique my
interpretation, one needs to show that it fails to correspond to the original
as a whole, including concepts as well as theoretical results.

"So the argument is that since I distinguished, as every economist who was
born on this plant before me has done, NOMINAL wages from REAL wages, my
arguments against his rhetoric of 'actual' is contradictory; and so, and this
is the greatest leap of logical faith, his flawed criticism of Sraffa stands!"

No. I wrote "It thus seems to me that Ajit's objection to discussion of the
real in economics is contrary to his own practice. It also seems to me that
his objections to my demonstration of Sraffa's non-proof are
self-contradictory, so that my demonstration stands."

Note again that I did not criticize Sraffa.

Also note that I did NOT say that my demonstration stands because Ajit's
references to "real" wages is contrary to his objection to discussing the
real. I said that his *objections to my demonstration* are
self-contradictory. Neither of the objections was based on the category of
"real" wages.

One objection was apparently, that there is no "real" in economics -- so that,
apparently, one has carte blanche to present theorems pertaining to mythical
economies as referring to something real!

The other objection invoked the "real" -- but not "real" wages -- to criticize
my demonstration: "... the *real* value of 'capital' would not change, and
the profit must be calculated on the *real* value of investment and not on the
nominal value of investment." [emphases added]

I contend that these two statements are contradictory in their implications.

Ajit now claims that he was using "real" in two different senses. I have no
doubt that he *thinks* the senses are different, but I am not convinced the
difference can be sustained. Let me ask a simple question in this regard:
why MUST profit be calculated on the "real" value of investment? Can this
proposition be sustained without some reference to what is "real" is the
allegedly different sense of "objectively so, actually existing"? I doubt

Ajit has not yet proven that profit must be calculated on the "real" value of
investment (or even defined what that means). Until he does so, my
demonstration stands.

"real wages means the amount of goods and services one could buy with that

If so, it means nothing. Use-values are heterogeneous. According to this
formulation, there are an infinite number of wage vectors corresponding to any
money wage, each different from the others. So we have, for any individual at
any given moment, an infinite number of real wages.

"Now, how can REAL mean 'a quantity of "numeraire" or of the standard
commodity' is beyond my capability of understanding. A quantity of numeraire
is by definition NOMINAL and not REAL."

OK. Please explain then how one could determine whether real wages have risen
or fallen.

"Again, it is beyond my capability of understanding how a bushel of corn equal
to a bushel of corn is a 'metaphysical proposition'. What is the objection
here, that one bushel may not be equal to the other bushel? Well, then give it
a precise quantity such as one ton of corn equal to one ton of corn. Does this
become physical? "

More careful quotation may perhaps enhance your understanding. I wrote "This
is based on the metaphysical proposition that because a bushel of corn is
identical physically to a bushel of corn, a bushel of corn is always worth as
much as a bushel of corn." The metaphysical proposition is the claim that a
unit of the numeriare is always worth the same amount (because all units are
physically identical).

"One bushel of corn will always WORTH one bushel of corn as long as you cannot
distinguish one bushel from another."

Really?! (Excuse my rhetorical invocation of the real, meant to hoodwink the
feeble-minded. I couldn't help myself :-) .) The following are average
prices in the U.S. for the following marketing years, measured in dollars per

Corn for grain wheat
1989 2.36 3.72
1990 2.28 2.61
1991 2.37 3.00
1992 2.07 3.24

Of course, instead of using the dollar, I could measure the worth of corn
(wheat) bushels of corn (wheat), but that would seem to be begging the
question, wouldn't it?

But let's say I do so. Why shouldn't I then measure the worth of *everything*
in its own physical units? *Everything* would then be worth the same amount
throughout all time! The problem of the invariable measure of value has been

Perhaps we are supposed supposed to believe that the value of corn alone is
invariable. But what gives corn the magical properties that distingish it
from the myriad other commodities, which constantly vary in value? If one
thinks that a unit of a commodity might be worth less when it becomes cheaper
to produce, what in this notion allows us to say that corn is exempt?

"One bushel of corn will always WORTH one bushel of corn as long as you cannot
distinguish one bushel from another. Let us suppose I grew some gorn five
years ago and kept it in my grainary and you produced a bushel of corn this
year. Now, as long as my corn is as good as your corn, why should your corn be
more or less worth than my corn? What is metaphysical about this?"

I don't think the second and third sentences are metaphysical. However, they
do not substantiate the first sentence, which is. They do not prove that a
bushel of corn *will always* be worth a bushel of corn. The current value of
the bushel produced this year is the same as the bushel produced five years
ago. But both may differ from the value, five years ago, of the bushel
produced five years ago.

I wrote: "It is therefore not possible to show that my demonstration is
invalid by invoking this proposition [the value of the numeraire is constant],
as Ajit does. All well and good if the critics of TSS happen to *believe* in
it, but it must be recognized that no matter how much they rhetorically invoke
'objectivity,' their 'proofs' rest on metaphysical belief. So do the
objections to the TSS refutations of the Okishio theorem and vindication of
the internal coherence of Marx's law of the tendential fall in the profit

"Curiously, those who object most strenuously to Marx's view that a unit of
(insert nitpicky qualifiers here) living labor always creates the same amount
of value are almost always the ones who accept *unquestioningly* that a unit
of the numeraire always has the same value!"

Ajit replied: "This is nothing but funny. What's your point Andrew?"

My pint is that to maintain that the value of the numeriare is constant
throughout all time is a metaphysical proposition. I do not accept it. I
therefore do not accept the objections to the TSS refutations of the Okishio
theorem and vindication of the internal coherence of Marx's law of the
tendential fall in the profit rate which rest on this metaphysical

I had written:
"I do not think this was Marx's concept of real magnitudes. He does not
contrast real magnitudes to value magnitudes. For him, the real magnitudes
are themselves value magnitudes. Once one adjusts the value magnitudes
(measured in money) for changes in the monetary expression of value (MEV) or,
equivalently, measure them directly in labor-time, one has the real
magnitudes. Thus, in his discussion of the falling rate of profit, he reasons
in terms of labor-time, not money, not corn.

"This alternate concept of what is real is based on the proposition that a
unit of (insert nitpicky qualifiers here) living labor always creates the same
amount of value. This seems to be metaphysical as well, but Marx attempted to
derive it, not take it for granted."

Ajit responded: "There is supposed to be two kinds of magnitudes; "real
magnitudes" and "value magnitudes". Then we are told, for Marx the distinction

Not quite. The distinction between real and nominal is still there. Marx
contends that value measured in money is nominal, but value measured in
labor-time is real. To obtain the real magnitude of value, one thus measures
it in labor-time or, equivalently, corrects for changes in the MEV.

Ajit: "At this juncture, we need to ask: what were the units of the 'real
magnitudes' and 'value magnitudes'? If they are
magnitudes, then they must have some units. If they had two different units,
then how can one collapse them. For example, one ton of corn, most of people
would agree, is a 'real magnitude'; and five hours of labor, let's say, is its
'value magnitude', then by what magic one could say one ton of corn IS ITSELF
five hours of labor?"

The real value magnitudes are measured in labor-time, or in money that
expresses a constant amount of labor-time. Value magnitudes measured in
unadjusted money are nominal.

A ton of corn is also a real magnitude (as, BTW, 5 hours of labor is), but not
a real value magnitude. In Marx's theory, a commodity is both a use-value and
a value. So there is one measure of its real value, another real measure of
its material form.

No one says that a ton of corn is itself 5 hours of labor. Marx would say
that the real magnitude of the value of the ton of corn is 5 hours of labor.

Ajit: "But as we go on, it becomes even more interesting. The next sentence
tells us that we have to 'adjust' self-same
real-value magnitude, which is measured in MONEY."

No. The real magnitude of value is measured in labor-time or, equivalently,
in money adjusted for changes in the MEV. To obtain the real magnitude of
value, one adjusts the value as measured in money accroding to the change in
the MEV.

Ajit: "However, we do not know what this money is. Apparently, the
value-magnitude I suggested above as
hours of labor is incorrect. The value-magnitude is in terms of money."

In Marx's theory there are two measures of value, labor-time, the immanent
measure, and money, the external measure. Both are "correct," if you wish to
use such expressions, but they do not vary proportionally. So to obtain an
external measure of real value that is consistent over time, one must adjust
for changes in the MEV.

Ajit: "So now one ton of corn becomes self-same as certain amount of money,
whose unit we don't know and how we arrive at that amount of money we will
never know. This whole thing requires the knowledge of some serious voodoo."

Of course we know what the monetary unit is. I don't understand the rest of

Ajit: The adjustment, of course, had to be made for "changes in monetary
expression of value". Now, we get into another trouble. First the "value
magnitude", which we are told is the self-same "real magnitude" is measured in
money. Then we
are told the "value" must be "adjusted" for changes in its monetary
"expression". Then we are told, "equivalently measure them directly in
labor-time". How does "equivalently" arise there is only god knows!

I hope my explanations have helped. I might note that, rather than trying to
make a mockery of what I wrote, you could simply have asked for clarification,
and I would have been happy to oblige, Ajit. Your tone at times seems to
suggest that you are interested in ridiculing rather than understanding, which
I hope is not the case.

Ajit: "Then we are given the final conclusion, 'Thus' Marx's discussion of
FROP is in terms of labor-time!!"

To be precise, I wrote that his "reasoning" is in terms of labor-time. And
the concept of value magnitudes as real magnitudes helps explain how this is

Ajit: "If Andrew does not think that what he wrote is simply gibrish, ..."

No, it isn't gibberish, though I agree that Ajit's version of it is. I don't
blame him for that; he just didn't understand. Again, however, it might have
been better to have sought clarification before resorting to ridicule.

Ajit: "... then I, for one, can't help him. My only request to Andrew is that
please remove Marx's name from what you write."

We've been through this before. I do not attribute my own views to Marx, and
I try to make very clear that what I say about his work is an interpretation,
to be assessed on the basis of textual and other evidence.

Ajit: "Marx did not write such gibrish."

Nor did I.

Ajit: " Do him a favor. Don't put all this stuff in his name."

See above.

I had written: "This alternate concept of what is real is based on the
proposition that a unit of (insert nitpicky qualifiers here) living labor
always creates the same amount of value. This seems to be metaphysical as
well, but Marx attempted to derive it, not take it for granted."

Ajit: "'Derive' it from what? The 'nitpicky qualifiers?"

No, from the concept of value. See _Capital_ I, Chapter 1, sections 1 and 2.

Andrew Kliman