I've now had time to take a look at Andrew's new example,
and have to say that I can't find any flaw in it. He has
succeeded in constructing an example of a set of
transformation tableaux that displays balanced reproduction,
and an equalized rate of profit each 'period', without
introducing the arbirary variation in the rate of expansion
of capital-value across the sectors that I detected in his
example for the 1996 value theory conference. I didn't
claim this was impossible, but I did privately doubt whether
it was possible; Andrew has shown that it can be done. OK,
there's the concession.
I hope this concession is sufficiently forthright; but I
also hope that its scope is noted, and that it is put in the
context of the following points (in increasing order of
importance, as I see matters):
1. It would seem that the new example Andrew has produced is
a special case. Yes, as he says, if there's one such
example then there's an infinity of them; but there's a much
larger infinity of sets of tableaux that "don't work" on his
interpretation (in the sense that they imply arbitarily
varying rates of expansion of capital-value), but that *do*
work perfectly well on the Morishima-Shaikh interpretation,
according to which the initial rounds of the iteration are
not taken as portraying actual (even 'stylized actual')
states of the economy, but merely as steps towards the
*calculation* of the characteristics of an equalized-profit
equilibrium. (For in such equilibria the arbitary variation
in rate of capital-expansion disappears.) A brief rider to
this point: Andrew complains that the balanced-reproduction
requirement is anyway something foisted on him by an alien
'simultaneist' tradition; but after a while he concedes
parenthetically that "this is a reasonable requirement,
since rates of profit will not typically be equalized if
supplies don't equal demands." Indeed. Marx's problem was
how to show the compatibility between his value theory and
the equalization of profit rates, and without supplies =
demands, equality of profit rates could only be a fleeting
random occurrence of no theoretical import.
2. A "wood versus trees" point: My fundamental objection to
the TSS conception is, and always has been, that I see it as
departing from the conception of 'value' (a) that I consider
Marx to have held and (b) that I find most scientifically
fruitful. That is, I can't accept as Marx's, or as
scientifically profound, a definition on which the value of
a commodity is the sum of the *price* of the means of
production (however determined) plus a share of aggregate
profit in proportion to the variable capital advanced -- as
opposed to the amount of labour-time necessary to produce
the commodity given technology and labour practices. We
have hashed this point over several times and I won't get
into details here; I simply want to stress that *this* is my
basic objection; discussion of the detailed characteristics
of tableaux on Andrew's pattern, while of interest in its
own right, is (even when initiated by me ;^) secondary.
Allin Cottrell.