In ope-l 4827, Ajit writes
"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?"
Ajit's claims are false.
Sraffa's physical data are
280qr. wheat + 12 t. iron --> 575 qr. wheat
120qr. wheat + 8 t. iron --> 20 t. iron
Imagine that, at the time of input, the money price of iron is $15/ton and the
money price of wheat is $1/quarter. Thus, each ton of iron at that time is
exchangeable for 15 quarters of wheat. Imagine also that, at the time of
output, the money price of iron is $14.85/ton and the money price of wheat is
$0.99/quarter. Thus, each ton of iron is again (still) exchangeable for 15
quarters of wheat.
Given these input and output prices, along with the physical data, the rate of
return on capital advanced will be 23.75% < 25%, in both sectors. The prices
have fallen by 1%, and the profit rate is 5 0.000000e+00ss than Sraffa's.
Ajit also writes: "So this is supposed to be the *proof* that Sraffa was
wrong!"
No. It proves no more and no less that what I said it proves, namely that
Sraffa failed to *prove* that the magnitude of the uniform profit rate is
uniquely determined by physical input/output coefficients. That theory might
be right, or it might be wrong, but it has not been *proven*, contrary to what
a whole generation of economists seems to have believed. There is a
difference between "not proved" and "wrong," just as there is a difference
between "not internally inconsistent" and "true." When people start to
understand these distinctions, they get a whole different perspective on who
are the dogmatists and who are the opponents of dogma.
Ajit also says something extremely interesting about separating the theory of
accumulation from price theory. I hope to deal with this more rigorously
later, by responding both to Ajit and to the recent Dumenil/Levy paper, which
argues in a very similar manner that value theory is inherently static, and
therefore has nothing to do with the theory of accumulation. For now, I will
only note that dozens of writers have used their inherently static value and
price theories -- which have no ability to deal with accumulation and dynamic
tendencies -- to "prove" that Marx's law of tendential fall in the profit rate
is false!
Andrew Kliman