[OPE-L:3676] Re: equality of cost-prices

Allin Cottrell (cottrell@wfu.edu)
Sun, 17 Nov 1996 20:54:59 -0800 (PST)

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I've been bogged down with work recently. Meanwhile several interesting
threads have started up, on which I'd like to comment, but for the moment
I'm returning to the unfinished business of the discussion of cost-prices,
values and prices of production, mostly between Alejandro, Fred
and myself.

This posting is in four parts: two brief rejoinders to points made
recently by Alejandro and Fred; a relatively substantial discussion of
a section of Capital, III, ch. XII; and a concluding challenge.

1. Alejandro [3675] cites the following passage from Capital III, ch. 1:

If we call profit p, the formula C = c+v+s = k+s
is converted into the formula C = k+p, or commodity
value = cost-price + profit. (Penguin, p. 127)

I think this passage supports my reading. The point is this: I don't
think that any party to the current debate would hold that "value = cost
price + profit" is a proper expression for the value of a commodity *in
the general case*. In the single-system approach, value = cost-price +
surplus value, where surplus value can diverge from profit. So, either
Marx is 'talking loosely' here, or, if you prefer, he is assuming in
context that profit = surplus value. But my claim is that "value =
cost-price + surplus value" has the same sort of status. Marx may say it
(or imply it) in some places, but it is not correct *in the general case*
either -- again, it is either a loose formulation, or it is based on the
assumption that cost-price equals the sum of the values of the inputs.

2. Fred [3644] cites the concluding paragraph to ch. XI of
vol. III (in which chapter Marx analyses the impact on
prices of production of a change in the wage). The relevant
passage is on p. 204 of the Moscow edition:

"In this entire chapter, the establishment of the general rate of profit
and the average profit, and consequently, the transmutation of values
into prices of production, are assumed as given. The question merely was,
how a general rise or fall in wages affected the assumed prices of
production of commodities."

Fred wants to use the fact that the transformation is taken by Marx as
"given" to argue against my point that -- in certain aspects of his
argument -- Marx is assuming that input prices are equal to values (which
makes it possible to explain, without giving up 'dualism', why Marx
sometimes says, or implies, that value = cost-price plus surplus value.)
But it seems clear to me that in the above quotation, all that Marx is
saying is that the transformation of *outputs* is taken as already
accomplished in ch. XI. He's just warding off the potential
misunderstanding, that what he's just been doing in the chapter is somehow
essential to the value/price-of-production transformation itself, when in
fact it is, in Marx's view, merely a subsidiary exercise.

This interpretation squares with section II of the following chapter (XII)
where Marx introduces -- N.B. *as a new consideration* -- the possibility
that "the cost-price of commodities produced by capitals of average
composition may differ from the sum of the values of the elements which
make up this component of their price of production."

3. In a previous posting I admitted puzzlement over part of Marx's
argument in the aforementioned section II ("Prices of Production of
Commodities of Average Composition") of ch. XII ("Supplementary Remarks").
(The bit that gave me trouble was the third full paragraph.) Although I
offered an argument against Fred's interpretation I was not able to offer
a very satisfactory interpretation myself. Having puzzled over this
section for some time, I think that I now understand Marx's argument.
Here it is in my own words.

i. By the basic transformation postulate, all capitals earn the same
rate of profit, which equals the rate of profit on the total social
capital. Clearly, as one instance of this, individual capitals that
happen to be of average composition earn the average rate of profit.

ii. By the result (which Marx reckons he has established by this point --
correctly or not, it doesn't matter here) that the sum of prices equals
the sum of values, conjoined with the basic premise that a change in the
wage rate does not affect the values of commodities, the sum of prices is
invariant with respect to changes in the wage rate. ("Other things
equal", of course -- in particular no change in the value of money.) That
is, if the wage rate rises, the general rate of profit must fall by just
enough to preserve the original sum of prices, given that the total
cost-price increases.

iii. For a capital of average composition (in price terms), an increase
in the general wage rate (ceteris paribus) will generate an increase in
cost-price of the same percentage as the *aggregate* increase in

iv. By point 1 above, the rate of profit on a capital of average
composition must fall in step with the average rate, in case of a rise
in the wage rate. By 2 and 3, this fall will be just enough to
preserve the original price of the commodity produced by that
capital. And this argument goes through irrespective of any
price-value deviation in the means of production.

A bit more formally, we can say that for any capital x, the price of its
product is p(x) = (1 + r)[c(x) + v(x)], where c(x) and v(x) are measured
in price terms. Given an equalized rate of profit, the general rate of
profit may be written (using upper-case letters to refer to aggregates)
as P = (1 + r)(C + V). Thus the ratio of the price of the output of
capital x to the aggregate price of output is given by

p(x)/P = [c(x) + v(x)]/(C + V)
= [v(x)/V]*[c(x)/v(x) + 1]/(C/V + 1)

If c(x)/v(x) = C/V, i.e. capital x is of average composition (in price
terms), we have p(x)/P = v(x)/V. But v(x)/V is invariant with respect
to a uniform change in the wage. Therefore p(x)/P is invariant with
respect to a uniform change in the wage, for any capital that is of
average composition. [And of course, if a capital is of average
composition at some given wage, it is of average composition for any
wage: if c(x)/v(x) = C/V = m at some wage w, then a y percent change in
the wage alters both the composition of x and the aggregate composition
to m/(1 + y/100).] It follows that *if the sum of prices is unaffected
by a change in the wage, so is the price of the output of any capital of
average composition*.

The idea can also be illustrated with a numerical example of the sort
Marx uses. Take the 'c' figures below as being in price terms.

A. With a rate of surplus value of 100 percent:

sector c v s k profit p. of p.

1 70 30 30 100 20 120
2 80 20 20 100 20 120
3 90 10 10 100 20 120
--- -- -- --- -- ---
240 60 60 300 60 360

B. After an increase in the wage such that s/v falls to 2/3 (but holding
constant the sum of prices, and the prices of the non-labour means of

sector c v s k profit p. of p.

1 70 36 24 106 16.31 122.31
2 80 24 16 104 16.00 120.00
3 90 12 8 102 15.69 117.69
--- -- -- --- ----- ------
240 72 48 300 48.00 360.00

As Marx stresses, it doesn't matter -- for the result that the price of
production for sector 2 (of average composition) remains unchanged when
the wage rises -- whether or not the 'c' figures truly represent values.

Whether or not the c figures correspond to values will make a difference
to a magnitude not shown in the tables, namely the value (in the standard
sense) of the outputs. If the c prices equal values, we have an output
value vector of (130, 120, 110) and the price of production for sector 2
equals value. Suppose on the other hand that the actual values of
constant capital consumed in sectors 1 and 2 are not equal to 70 and 80
respectively, but 75 and 75. Then (on the standard view) one would
compute the output values vector as (135, 115, 110). In that case the
`average' sector 2's price of production no longer equals value (120
versus 115).

*But that doesn't alter the point Marx is concerned with in this context*
-- namely the invariance of price with respect to a change in the wage.
As he puts it, "the practical result is therefore the same as it *would*
be *if* [the products of the capital of average composition] were sold at
their real value" (Moscow, 207, emphasis added) -- since "under all
circumstances a rise or fall in wages can never affect the value of
commodities, but only the magnitude of the surplus value" (208). This
formulation makes good sense to me now.

Then what of the earlier statement, which Fred stresses, that (given
profit = surplus value for a capital of average composition) "price of
production = cost-price plus profit ... i.e., in practice it is equal to
the value of the commodity" (207)? I don't know German well enough to
evaluate this as a translation from the original, but I'm a bit suspicious
-- either of the translation, or of the clarity of the original sentence.
The statement I quoted in my previous paragraph, which echoes "in
practice" with "the practical result", seems to me clearer: for practical
purposes (and in context, where we are interested in the effect of a
change in the wage) it as *as if* the commodities in question exchanged at
their values.

4. Neither Fred nor Alejandro has yet addressed what I regard as a key
statement of Marx's on this whole matter, namely that a price/value
deviation among the non-labour inputs to a given commodity is a cause from
which arises "a deviation in prices of production from values" on the
output side (Moscow, 206-7, plus a few other locations). How can they
make sense of this? On their reading -- where, *in the general case*,
value = cost-price plus surplus value, and price of production =
cost-price plus profit, with only one "cost-price" in the picture -- there
should be only *one* source of such deviation, namely a divergence between
profit and surplus value, not two as Marx states.

Allin Cottrell