[OPE-L:4827] Re: Sraffa's Non-Proof

Ajit Sinha (ecas@cc.newcastle.edu.au)
Mon, 21 Apr 1997 00:42:39 -0700 (PDT)

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At 10:59 AM 4/16/97 -0700, Andrew Kliman wrote:
>A response to one aspect of Ajit's ope-l 4677. I may have time to
>address the rest soon.
>I had written "Sraffa fails to prove 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. Nor does he prove that there is a unique uniform
>profit rate in such a case. I demonstrated this in my paper 'The
>Okishio Theorem: An Obituary,' which I know that Ajit knows, because
>he was a presenter on the same panel at the ASSA in January at which
>I presented it."
>He responded: "I haven't read your paper. But your claim sounds
>Here's what I wrote. Whether or not is it "outlandish," let us see
>you -- or anyone else -- disprove it.
>* * * * * * * * *
>Yet, contrary to the apparent belief of the proponents of the Okishio
>theorem (and most readers of Dmitriev and Sraffa), it is simply not
>true that the magnitude of the uniform profit rate is uniquely
>determined by physical input/output coefficients. To demonstrate this
>crucial point, let us turn to the example in which Sraffa (1960:7)
>supposedly proves that the uniform profit rate is uniquely determined.
>He posits the following input/output relations:
> 280qr. wheat + 12 t. iron --> 575 qr. wheat
> 120qr. wheat + 8 t. iron --> 20 t. iron
>and immediately concludes:
>"The exchange-ratio which enables the advances [on the left-hand sides]
>to be replaced and the profits to be distributed to both industries in
>proportion to their advances [so that the rate of return on capital
>advanced is equalized] is 15 qr. of wheat for 1 t. of iron; and the
>corresponding rate of profits in each industry is 25%."
>To obtain 15:1 as the unique exchange ratio, Sraffa implicitly assumes
>that the exchange ratio between wheat and iron at the time of input is
>equal to the exchange ratio at the time of output. This will not
>necessarily be the case, but even if it is, the uniform profit rate is
>not uniquely determined by the data above, as we shall see presently.
>Letting Pw[t] and Pi[t] be the input prices, and Pw[t+1] and Pi[t+1]
>be the output prices, of wheat and iron, respectively, Sraffa's
>exchange ratio implies that Pi[t] = 15 Pw[t] and that Pi[t+1] =
>15 Pw[t+1]. The rate of return on capital advanced in the wheat
>sector is therefore
>(575 Pw[t+1])/(280 Pw[t] + 12 Pi[t]) - 1 =
>(575 Pw[t+1])/(280 Pw[t] + 180 Pw[t]) - 1 =
>1.25(Pw[t+1]/Pw[t]) - 1
>and the rate of return on capital advanced in the iron sector is
>(20 Pi[t+1])/(120 Pw[t] + 8 Pi[t]) - 1 =
>(300 Pw[t+1])/(120 Pw[t] + 120 Pw[t]) - 1 =
>1.25(Pw[t+1]/Pw[t]) - 1.
>The constant exchange ratio of 15:1 thus guarantees that the two rates
>of profit are equal. Yet the level of the equilibrium profit rate is
>still not determined. It depends as well on the ratio of the output
>to the input price of wheat, and it can vary, theoretically, from
>-100% to + infinity.
>* * * * * * * * *
>Andrew Kliman (AX)

So this is supposed to be the *proof* that Sraffa was wrong! Anderw, look at
your both the final equations, eg. 1.25(Pw[t+1]/Pw[t]) - 1. Now, as you say
above "...Sraffa implicitly assumes that the exchange ratio between wheat
and iron at the time of input is equal to the exchange ratio at the time of
output, ..., but even if it is, the uniform profit rate is not uniquely
determined by the data above,...". As long as "even it is" the case, your
Pw[t+1]/Pw[t] must be equal to one. That's what even it is would imply. In
that case your equation turns out to be equal to 0.25, exactly Sraffa's
result. So what the hell have you proven here?

So your whole proof rests on the notion that Pw[t+1]/Pw[t] is not equal to
one, ie. even it is clause do not apply. First of all, it could vary from
"100% to + infinity" is something I cannot figure out. What would 100% mean
here? And infinity is possible only when Pw[t] would be equal to *zero*.
Now, only in your theoretical world, which I think is more like Alice in
Wonderland, prices of all the basic goods in the beginning of the period
could equal zero, ie. you start of with all free goods!

Now, for your general case where Pw[t+1]/Pw[t] is not equal to one, as I
have already suggested in the earlier post, your theory of prices leads to
absurdities. Sraffa is on quite stron ground in assuming that Pw[t+1]/Pw[t]
= 1, because what he is saying is that *given* production conditions these
prices would hold time after time (it is not necessarily a static model).

Your proofs of Sraffa, Okishio, and most of the great 20th century
economists being wrong reminds me of an old Hindu story. One character asks
another character, so what does earth rests on? the other character answers,
it rests on the hood of a cobra. The first character asks, and what does the
cobrs rests on? The second character responds, it sits on a turtel. The
first character asks, and what does the turtle rests on? The first character
responds, it sits on an elephant. End of the story. Marx talks about this
story and says that at this point the critic got satisfied. My
interpretation is that the critic got the idea that it was pointless going
on and on and on. In any case, if you believe that elephants can stand on
nothing, the above story would convience you. Now, on the basis of this
theory, ie. elephants can stand on nothing, you could prove all the modern
theories of astronomy wrong. And that is exactly what you have been doing.
Your theory of prices is absurd. And on the basis of an absurd theory you
could prove all reasonable theories to be wrong. I urge you, and all the TSS
people, to rethink the whole issue. Nobody is against dynamics. The whole
theory of accumulation has to be a dynamic theory, and that is the center of
Marx's analysis of capitalism. A theory of prices does not have to be
formulated in dynamic context, unless you are working on a theory of
inflation. Sraffian system is open to all kinds of dynamics. So don't think
Sraffa has nothing to offer here, he has to offer a lot. I suggest this
point in my 'Althusser-Sraffa connection' paper. Cheers, ajit sinha