Thanks to Alejandro for his replies. Here are brief responses.
Alejandro:
I think that, given that all these quotations come from a draft,
Allin's hypothesis ("Marx is assuming that the *inputs* are sold at
their values, not at prices of production that deviate from values.")
is perfectly reasonable.
However, it seems to me that Allin does not wish to quote the lines
following the piece in p. 164-5 (Moscow edition) that he quotes.
"It is necessary to remember this modified significance of the cost-
price, and to bear in mind that there is always the possibility OF AN
ERROR IF THE COST-PRICE OF A COMMODITY IN A PARTICULAR SPHERE IS
IDENTIFIED WITH THE VALUE OF THE MEANS OF PRODUCTION CONSUMED IN IT.
Our present analysis does not necessitate a closer examination of
this point" (In my "Moscow Edition", this lines, as well as those
quoted by Allin, are in p. 162)
So, Allin's hypothesis is reasonable, but if we identify the COST-
PRICE with the value of the means of production (i.e. as Allin says,
if "the inputs are sold at their values") WE ARE SIMPLY MAKING A
MISTAKE.
Allin responds:
I'm happy to discuss the chunk Alejandro cites.
Sure, given that inputs are sold at prices of production that may deviate
from values, "there is the possibility of an error" if cost-price (= sum
of prices of production of inputs) is identified with the value of the
means of production consumed. (The error is "possible" not inevitable,
because, for instance, the price-value deviations among the inputs might
cancel out.)
This doesn't undercut the point I was making, which I can perhaps state a
bit more clearly here: After re-examining Chapter 9 (yet again!) it seems
to me that Marx is assuming -- in all the tables including the "hidden"
one, and also in a good deal of the accompanying discussion -- that the
inputs to production are purchased at their values. Of course, he's
perfectly entitled to do so, for heuristic purposes, despite the fact
that making this presumption in any _real_ case would be to court
"error". It is only on this condition -- p=v for the inputs -- that
Marx's "k" can do double duty (value = k+s and price = k+p, on the output
side). Otherwise we'd have to write something like: value = c+v+s, price
= k+s, allowing that k might not equal c+v. Remember, "the value of a
commodity is equal to the value of the constant capital contained in it,
plus the value of the variable capital reproduced in it, plus the ...
surplus value" (Moscow, p. 150).
Alejandro:
The decisive point in the definitions "dropped by Engels" is that
COST-PRICE, "k" is COMMON for both, VALUES and PRODUCTION
PRICES. Now then, if we think that "k" corresponds to the the "value
of inputs", it is clear that there would be an error.
Allin:
I don't think that "k" (necessarily) corresponds to the value of the
inputs, and I don't think that Marx did either. But I think he assumed
this for simplicity in his tables. In fact, you could say he had to, in
the first instance at least, since he was trying to show how you could
get _from_ values to prices of production. And under that assumption, of
course, there's no error.
Alejandro:
So, I think that we could concentrate our efforts, in a first stage,
in the interpretation of what we can call the "traditional framework"
of the transformation. For instance, let us take the single-table
of Penguin p. 264, where Marx does not consider "changes" of any kind.
What are, there, the definitions of "value" and "production price"
suggested by Marx?
Have we, in this table, any element to think that the magnitude
"k", cost price is different, regarding, on the one hand, the
calculation of prices and, on the other, the calculation of values?
Allin:
Briefly, value = total labour-time embodied, contained in, or required to
reproduce, the commodity, while price of production is that price which
yields a uniform rate of profit on capitals, regardless of their
composition. In the table, k is taken as equalling c+v, even though Marx
is aware that these magnitudes may differ in practice.
Alejandro:
I would wish to ask Allin in which kind of "iterative
transformation" is he thinking?. We can have a "dualistic" or a "non-
dualistic" iterative transformation, depending, precisely, on the
definition of value we use.
Allin:
The iteration I have in mind is as follows: You start with inputs selling
at their values, then compute the prices of production (first
approximation) of outputs just as Marx does. Then you feed those
first-round output prices back into the calculation as the prices of the
inputs, and equate the rates of profit with respect to the resulting
cost-prices (which k's are no longer equal to c+v). This gives you a
second approximation to the price of production vector, and so on...
There is a parallel iterative procedure for calculating values. Start by
reckoning values as just the direct labour-times entering the production
of the various commodities. Then evaluate the indirect labour-time
flowing from the non-labour inputs at their first-round values and
recompute the output values. Then feed these back in as the new input
values, and so on...
But in my opinion it would be a grievous mistake to "mix" the two, and to
contaminate the idea of the "labour-time contained in" or "required to
produce" a commodity -- a phrase Marx repeats literally hundreds of times
in Capital as what determines value -- with magnitudes derived from the
level of inter-capitalist competition and profit-rate equalization,
magnitudes from the "surface" of capitalism. Labour-times are part of
the "deep structure" of the capitalist economy.
Allin Cottrell.