[OPE-L:3904] Re: m in Marx's theory

From: Gil Skillman (gskillman@MAIL.WESLEYAN.EDU)
Date: Fri Sep 29 2000 - 18:39:02 EDT

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I'm writing in response to a much earlier post from Fred on this topic.

Fred writes:
>..... Marx's labor theory of value, as I
>understand it, assumes that, in a given period of time in the real
>capitalist economy, each hour of average social labor produces a certain
>amount (say, m) of money new-value (or money value added). Even though we
>don't know what m is (i.e. we can't observe m), and even though we cannot
>explain what determines m, the theory assumes nonetheless there is an
>actual, unique m in the real capitalist economy. And it is this actual,
>unique m that is taken as given in the determination of the total
>new-value produced in this period.

The measure m is real enough, but its existence does not in any way depend
on the assertion of a labor theory of value.
For example, in the NI understanding of m discussed below, m is equivalent
to what neoclassicists would immediately recognize as the average product
of labor--in this case, the average *net* product of "socially necessary"
labor. But since Marx defines "socially necessary" labor in terms of
averages in any case, the latter condition doesn't add any bite.

>>As Duncan has argued in (3761) (and elsewhere), the unique value of m in a
>given period must be equal to NV / L, i.e. to the ratio of the money
>new-value produced in this period to the average social labor performed
>during this period.

Rather, m is *defined* as NV/L. The labor theory of value itself doesn't
demand that this ratio be defined at all; we could instead follow Marx's
explicit lead in defining commodity values in terms of embodied labor time.
Then we could determine directly the average labor value of aggregate net
product, and not bring in prices at all. And the measure NV/L is only
"unique" if one can agree on how the net product vector mentioned by Fred
is valued--by labor values? current prices? inflation-adjusted prices,
relative to some base? Sraffian prices of production? Neoclassical
competitive prices?

> This does not mean that m is determined by NV / L.
>It only means that m has this unique value. We don't know what
>determines m.

Rather, m is "determined" by NV/L, but we don't know by this what
determines NV and L.

>But whatever determines m, and whatever the value of m, if
>it is assumed that NV = m L, then m must be equal to NV / L, and cannot by
>assumption be equal to anything else.

That's right: it's equal by assumption, i.e. a tautology.

>Now, let's take a quick look at how Marx determined m in Capital.
>Throughout Capital, Marx assumed that m is equal to the inverse
>of the labor-time required to produce a unit of gold, or the amount of
>gold produced per hour of average social labor, which he took as
>given. In Chapter 3 of Volume 1, Marx said: "Henceforth we shall assume
>the value of gold as a GIVEN factor, as in fact we take it at the moment
>when we estimate the price of a commodity." (p. 314) In Chapter 7, Marx
>derived his numerical example of m (0.5 shillings per hour) from gold
>production. On the assumption that it takes two hours of labor to produce
>an amount of gold equal to one shilling, each hour of gold labor produces
>0.5 shillings worth of gold, so that m in all industries (e.g. cotton
>yarn) is equal to 0.5 shillings per hour. And so on.

But clearly this *is not* Marx's determination of "m", as defined above,
and the quote from Volume I Ch. 3 does not suggest otherwise. Rather this
is Marx's determination of the value of a unit of the money commodity
(gold). This has no proven relation to the ratio of aggregates NV/L; in
general, m as defined above and the value of a unit of gold won't be equal.
 It is up to Fred, or Marx, or somebody, to explicitly demonstrate the
conditions under which this equality holds. It can't be assumed.

>So far as I know, Marx never discussed any modification to this
>determination of m at more concrete levels.

"This" doesn't determine m, as discussed above; it determines the labor
value of a unit of the money commodity, a very different thing than m.

> But gold production is also
>usually capitalist production. Therefore, the rate of profit in the gold
>industry should tend to be equalized with the average rate of profit in
>the rest of the economy.

Only under conditions of universally perfect (as opposed to either
imperfect or pure) competition.

> This seems to suggest (I could be wrong) that,
>at this more concrete level of abstraction with prices of production, m
>would no longer be determined solely by the gold produced per labor hour,

This begs the question. It hasn't yet been shown that m was determined
"solely by the gold produced per labor hour" *in any case*. And don't you
mean the direct and indirect labor time *embodied* in a unit of gold?

>but would also be affected by the equalization of profit rates across

The measure m would certainly be, *assuming* we were using hypothetical
prices, such as Sraffian prices of production, to value m. But then we
would be departing from the "real" capitalist economy to a hypothetical one
in which, contrary to fact, profit rates are equalized.

 But Marx apparently did not discuss this possibility at
>all. Nor can I think of Marxists since Marx who have discussed this
>question. If anyone knows of any discussions of this issue, either by
>Marx or others, please send me the references.

Since it's not what Marx is talking about in Ch. 3 when he refers to the
value of the money commodity, I doubt if a discussion by Marx that supports
this point can be found.

>Hence, this question - the determination of m with prices of production -
>remains an important unanswered question in Marx's theory.

Well, it's certainly an unanswered question.

>Furthermore, there is an additional important and difficult issue involved
>in the determination of m. Marx of course assumed throughout Capital that
>money was a (real) commodity (usually gold). There has been recent debate
>on OPEL and elsewhere about whether or not money MUST be a commodity in
>Marx's theory. As I have said before, I myself have not yet made up my
>mind on this issue. Either way, there are difficult questions. If money
>in Marx's theory has to be a commodity, then in what sense is money a
>commodity in contemporary capitalism? On the other hand, if money in
>Marx's theory does not have to be a commodity, but can simply be paper,
>without any automatic convertibility into a commodity, then how is m
>determined in this case, since it no longer seems linked to gold at all.

This looks easier than Fred suggests. Since it has nothing demonstrable to
do with the unit value of the money commodity in the first place, the
determination of m does not at all depend on whether money is a commodity
in Marx's sense.

Where does all this leave us? That is, if the existence of the measure m
does not depend on asserting any labor theory of value, and conversely if m
has nothing demonstrable to do with value measures developed by Marx in
Volume I (e.g., the unit labor value of the money commodity), why bring it up?

Well, here's one answer: suppose that working only with value measures
defined by Marx in Volume I, the aggregate value-price equalities asserted
by Marx in Chapter 9 of Volume III cannot be shown to hold in general. And
suppose further that for some (not particularly evident) reason, you wanted
to assure that *some* version of Marx's aggregate equalities held. Then
you might want to bring m into the picture, whether or not it has anything
to do with Marx's value categories.

More specifically:

1) In Chapter 1 of Volume I, Marx "deduces" from the fact of systematic
commodity exchange the conclusion that all commodities with positive demand
have (indeed, "are") *values*, and that their values are necessarily
measured by the socially necessary labor time respectively embodied in
them. This is a deduction, mind you: the result is claimed to follow
necessarily from the fact of systematic commodity exchange. One corollary
of this deduction is that labor values are determined independently of
commodity prices. They had better be, or else there is no meaningful,
consistent, and non-tautological sense in which prices "depend on" or
"presume" labor values.

2) Labor power is a commodity. Marx says so in Chapter 6 of Volume I.

3) Taken together, steps (1) and (2) imply that the value of a unit of
labor power is the labor time socially necessary to reproduce that
unit--that is, the labor time embodied in the subsistence wage bundle.
This is a necessary consequence of Marx's arguments in Chapters 1 and 6.

4) There are two ways of measuring the value of labor power defined above:
 one is by summing the embodied labor values of each of the goods in the
subsistence wage bundle. Denote this by the vector product b*v(b), where b
is the subsistence wage bundle and v(b) is the corresponding vector of unit
labor values for the goods in the wage bundle. Another way to measure it
is by taking the money wage rate *just necessary to ensure subsistence*,
measured in the units of some money commodity, and multiplying it by the
unit value of that money commodity, say the value of gold v(g)--thus, w*v(g).

5) The two methods will not in general give the same number for the value
of labor power.

6) Furthermore, Marx's aggregate equalities will not in general hold using
either measure for the value of labor power, along with the measures for
the values of all other commodities.

7) If these negative results matter to you, you could do the following:
define the "value of money" v(m) in a manner entirely inconsistent with
Marx's derivations in Volume I, Chs. 1 and 3--for example, as total direct
labor divided by the dollar value of net product. This requires that the
value of money depend on market prices, contrary to Marx's "deduction."
Then *define* the value of labor power as equal to the money wage rate
times the value of money, whether or not the wage rate is the level just
necessary to achieve subsistence. Again, this violates Marx's "deduction"
from the fact of systematic exchange, first by disconnecting the value of
this particular commodity from the labor time socially necessary to produce
it, and second by making its value depend on some measure of market prices.

8) Proceeding in this manner, it is readily shown that the v(m) times the
dollar value of aggregate net product is necessarily equal to the labor
value of net product.

9) This is not the same as the aggregate equality asserted by Marx, to the
effect that the labor value of *total* output is equal to the dollar value
of *total* output. But Marx's claim is invalid in general, while the claim
in (8) is tautologically true, once one abandons Marx's deductions
concerning the necessary measure of value for the specific commodities
money and labor power.

(10) It also follows from the procedure specified in (7) that total
surplus value equals (the labor equivalent of) total profits, Marx's second
aggregate equality.

(11) Question: has the foregoing procedure demonstrated a substantive
role for m in Marx's theory of the capitalist economy? Or has it
demonstrated that one can yield one (significantly modified) set of Marx's
assertions about such an economy as a tautology, but only at the cost of
violating his "deductive" conclusions about the determination of commodity


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