[OPE-L:7111] [OPE-L:610] Re: Production relational analysis of exchange

Gil Skillman (gskillman@mail.wesleyan.edu)
Sat, 06 Mar 1999 13:25:56 -0500

Hello, Brendan. Let me say by way of preface that I also endorse a
historical materialist treatment of production and exchange relations,
and have argued in favor of same in (much) earlier rounds of this debate
as well as in print. But contrary to your view, I can see no necessary
or even coherent connection between historical materialism and the notion
of commodity value based on socially necessary abstract labor that Marx
puts forward in Chapter 1 of Volume I. I put forward some reasons for
this contrary view below.

Brendan writes:

>I am convinced by Gil Skillman's contention that if the formal
properties of the exchange relation imply the conservation of a substance
(and I think they do), then what is conserved in the actual practice of
exchange is not social labour, since non-commodities like unimproved land
have a price but no labour content.

This is not in fact my contention, since I've never suggested (and don't
believe), that there is any "substance" that is conserved in the exchange
relation. Nor has any such substantial conservation been proven, and in
light of valid counterexamples like the one I gave, I think it's highly
doubtful that there could be such a proof. I did state that whatever
Marx means in referring to an "equality" established in exchange, it
cannot be in a sense that supports his ultimate conclusion that abstract
labor is in some sense the basis of exchange value.

>He sees this as a refutation of Marx's approach, because in his view
Marx's Chapter 1 restriction of exchange to commodities i.e. products of
labour, is illegitimate, a tautology.

More narrowly, I see this as a refutation of Marx's Chapter 1 argument.
The significance of this distinction will become clear in a moment.

>I don't think this argument follows however, since it seems to me that
the elements of Marx's analysis are not the concrete acts of exchange
that take place in capitalist society, but the social relations of
exchange, "exchangeability", that is, exchange as a production

I disagree. It <italic>can't </italic>be the case that "exchange as a
production relation" is part of the "*elements* of Marx's analysis" in
Chapter 1, as Brendan contends, because it is the intended
<italic>conclusion</italic> of that analysis (specifically, the argument
beginning atop p. 127 in the Penguin or Vintage edition) that exchange
value is simply the "necessary mode of expression, or form of appearance,
of value", where "value" corresponds to abstract social labor. Brendan's
reading, then, *assumes* what Marx sets out in this argument to

Marx offers the *reverse* argument Brendan alludes to, and specifically
as an *alternative* to his Chapter 1 argument, in his famous 1868 letter
to Kugelmann.

More about this alternative in a moment.

>The chain of Marx's argument seems to me to run in the opposite
direction from the argument Gil wants to impute to him.

Not in Volume I, Chapter 1 of <italic>Capital, </italic>it doesn't. Marx
makes no mention whatsoever of "exchange as a production relation" in the
first steps of that argument. And I don't "impute" anything to Marx
here; my critique, unlike Brendan's defense, is based on what Marx
actually claims, which I quote as the basis for my critique.

>Gil wants an analysis of concrete exchanges to lead via abstraction from
troublesome details like arbitrage to a formal model of exchange, which
leads in turn to a conserved substance, which in turn is shown to be
abstract labour (of course Gil himself denies the feasibility of such an

As above, it's not at all a question of what I "want", but of what Marx
actually says in the argument I'm criticizing.

>But in Marx's argument social labour is primary and concrete exchanges
are derived. Is this valid?

That is certainly a legitimate alternative question. Alternative, that
is, to the question Marx actually poses in his analysis of exchange value
in Ch. 1. There he takes *concrete exchanges* as primary and
(abstract)*social labor* as derived (that is, as an implication of the
fact of systematic exchange).

Brendan continues:

>Let's look at this as a problem in historical materialism, a problem in
the natural history of the human race, a population of apes inhabiting
this very planet. Production is the life-activity of this population, and
undergoes a historical evolution.


>But in the social production of their life, humans enter into definite
relations that are independent of their wills, relations of production
which correspond to a definite state of development of their material
productive forces. Production of commodities is one such relation.


>Commodity production developed within pre-existing human societies and,
becoming the dominant relation of production, enabled an unparalleled
development of the division of labour. But in any form of society, the
dominant relations of production face a performance requirement: they
have to allocate the total labour resources approximately in proportion
to social needs. This constitutes fitness in the selection process of the
evolution of human social forms.


>The historical fact that exchange has rapidly expanded the division of
labour shows its relative success at this task, relative that is to other
production relations. Commodity production packages up of the products of
social labour in privately owned use-values that are then alienated,
being exchanged for others. Unless those commodities are exchanged in
proportions that correspond approximately to their labour content,
exchange would not serve to distribute social labour among different
branches of social production in proportion to social needs. Unless this
approximation to labour content was a good one, commodity exchange would
not have shown the unprecedented success it has shown, at developing the
division of labour and productivity.

As indicated in my preface, I also endorse a historical materialist
approach to production and exchange relations. But whether or not
"commodities are exchanged in proportions that correspond approximately
to their labour content," as Brendan puts it, offers no grounds
whatsoever for the explanatory significance of commodity values measured
in socially necessary (direct and embodied) labor time, the focus of
Marx's Chapter 1 argument and my critique. As I'll try to show below,
these value magnitudes are best redundant and more typically seriously
misleading when applied in attempting to explain capitalist phenomena.

But first let me note that the point Brendan is representing here is
exactly the argument Marx advances in his July 1868 letter to Kugelmann
(as part of an explanation of why he didn't need the alternative argument
he made in Ch. 1 of Vol. I). It's worth quoting the key passage from
that letter in order to demonstrate the exact correspondence to Brendan's
argument above:

" Every child knows that a country which ceased to work, I will not say
for a year, but for a few weeks, would die. Every child knows too that
the mass of products corresponding to the different needs require
different and quantitatively determined masses of the total labour of
society. That this necessity of distributing social labour in definite
proportions cannot be done away with by the <italic>particular
form</italic> of social production, but only change the <italic>form it
assumes</italic>, is self-evident. No natural laws can be done away
with. What can change, in changing historical circumstances, is the
<italic>form</italic> in which these laws operate. And the form in which
this proportional division of labour operates, in a state of society
where the interconnection of social labour is manifested in the
<italic>private exchange </italic>of the individual products of labour,
is precisely the <italic>exchange value</italic> of these products."

[Marx and Engels, Selected Correspondence 1846-1895, p. 246]

So it's *here*, not in his Chapter 1 argument, that Marx draws the arrow
from production relations to exchange relations.

But what do we make of Marx's (and Brendan's) claim here that the chain
of social causation runs from social needs to exchange values, on the
basis that a <italic>given </italic>set of social needs corresponds to a
<italic>given </italic>division of the "total labor of society", which
<italic>dictates</italic> the set of exchange values necessary to
implement this division? As a <italic>general </italic>statement, I find
this claim even more far-fetched than Marx's argument in Chapter 1.

First, Marx never <italic>proves </italic>this claim, and as I'll show in
a second, it isn't a <italic>logical </italic>necessity, even granting
the general point that labor and other resources need to be allocated in
a mutually coherent manner consistent with the fact that people need
food, shelter, etc. But second, if you think about it a bit, the claim
that social needs are somehow ontologically *prior to* and determinative
of the quantitative division of labor, and thus exchange values, in a
capitalist economy is <italic>utterly implausible</italic>. It would be
much more accurate to say that social needs and exchange values are
*mutually* determined, and in many cases the causation clearly goes the
other way--i.e., variations in exchange values may dictate the manifested
pattern of social "needs."

Specifically, I make the following 4 points against Marx's claim and
Brendan's interpretation of it.

1) Unless commodity demand is universally and perfectly price-inelastic
(i.e., all commodity demand curves are "vertical"), the realized
structure of "social needs" cannot be considered independent of (and thus
cannot be considered ontologically prior to) exchange values. Relatedly,
unless commodity demand is universally and perfectly income-inelastic,
the realized structure of "social needs" cannot be determined
independently of the (class) distribution of income, which depends in
part on a given exchange value, that for labor power. Thus, in the
absence of such incredibly restrictive (and empirically false)
conditions, Marx's "chain of argument" disintegrates at the first link.

To take just one example: after the OPEC oil price shock of the early
70s, the purchases of small cars in the U.S. went up dramatically. Does
anyone think that there was a "social need" for small cars which was in
any sense *logically prior* to the price shock? Especially given that
this relative "social need" evaporated once relative oil prices went back
down? [And conversely, does anyone assert that there was a logically
prior "social need" for mammoth "sport utility vehicles" that preceded
the recent downward trend in oil prices?]

2) Unless the ratio of input coefficients for constant capital and labor
is universally and perfectly unresponsive to input commodity prices and
the wage rate (i.e., the elasticity of substitution among inputs in all
production processes is zero), both statically and dynamically, a
realized pattern of social needs does not correspond to a *given*
division of "total labor resources", much less a given structure of
commodity values. If the elasticity of substitution is not zero,
variations in the wage rate and/or input commodity prices can create very
different quantitative divisions of labor, even for a given pattern of
social needs.

Thus, in the absence of highly restrictive (and empirically false)
conditions, the second link in Marx and Brendan's "chain of argument"
breaks, or at the very least is shown to be dependent on, rather than
determinative of, exchange values.

One needn't advert to neoclassical "production functions" to give
credence to this point. For example, we're all familiar with Marx's
argument concerning the creation of "relative surplus value" based on the
dynamic substitution of constant capital for variable capital. It is at
least plausible that the dynamic *rate* of substitution is influenced by
the wage rate or the time path of input commodity prices. But then the
quantitative division of labor cannot be conceived independently of
exchange values.

3) But suppose, for the sake of argument, that both of the highly
restrictive conditions named above are met (which is implausible, since
this suggests among other things that consumers will purchase commodities
even when they can't afford them, and nominally profit-seeking
capitalists will not seek to substitute in the direction of relatively
cheaper inputs). Then *unavoidably* the quantitative division of labor
will be dictated by the fixed pattern of commodity demands, as Marx's
argument supposes.

But the key question here is, does this have any necessary implications
for the structure of relative <italic>exchange values</italic>, the last
link in Marx's (and Brendan's) chain? Without restrictive (and
empirically unmet) additional conditions, the answer is no. First, even
under the above-named conditions, relative exchange values can vary
dramatically with the pattern of monopoly power evinced in different
markets. This leads to (empirically confirmed) variations in profit
rates corresponding to different degrees of price-setting power.
Alternatively, sectoral profit rates, and thus relative exchange values,
may vary consistently according to relative investment risk. Second,
differences in the real wage rate across markets (as in the presence of
"dual labor markets") will create variations in relative exchange values.
Needless to say, neither of these two phenomena are functions of "social
need", contrary to Brendan's schematic.

4. But finally, even if we get rid of all of these confounding factors,
and thus assume price- and income-inelastic commodity demands (so "social
needs" are determined ex ante and independently of exchange values), no
factor substitutability in production (so the quantitative division of
labor is determined by production technology and the pattern of social
needs), and uniform profit and wage rates (and thus putting aside
variations in monopoly power and the effects market segmentation,
unionization, or job conditions on relative wage rates), are we even then
compelled to accept the relevance of commodity values as Marx defines
them in Chapter 1? If not, then Marx's Chapter 1 analysis is invalid and
irrelevant, which is the point of my critique.

And again, the answer is no: consideration of exchange, even under these
incredibly restrictive conditions allowing an untangled chain to be drawn
from social needs to quantitative division of labor to exchange values,
there is no particular reason to consider the magnitude of any
commodity's value, as Marx defines it in Chapter 1. Thus this magnitude,
and this concept, is completely epiphenomenal.

For example, there is no systematic connection between relative exchange
values and relative socially necessary labor times, statically or
dynamically, even assuming uniform wage and profit rates. For example,
changes in the real wage rate will typically change relative prices of
production, but cannot, by Marx's own definition, change relative values.
Many other incongruities arise, but I won't bother going into the gory
details here.

Conclusion: the "chain of argument" that Brendan, echoing Marx in his
letter to Kugelmann, puts forward here is *at least* as problematic as
the reverse argument Marx advances in Chapter 1 of Volume I. And in no
case does it substantiate the relevance of Marx's conception of commodity
value in terms of socially necessary abstract labor. Thus, even if you
take historical materialism seriously, as I do, there are no apparent
logical grounds for pursuing historical materialist understanding of
capitalism in terms of Marx's value categories.


>This is the background that saves Marx from having to "prove" the labour
theory of value in chapter 1. His project is a different one, to analyse
the core determinations of exchange production relations to show how they
generate, "compute", this approximation to social labour contents of
commodities in the prices that are formed in exchange. Then by adding
more determinations to construct a more concrete analysis of exchange as
a social relationship, he can show how the divergence of prices from
values arises.


>Marx's abstraction from e.g. arbitrage or the positive price of
unimproved land in Chapter 1 is not a selection of a desired set of
exchanges from among all real exchanges. It's a selection among some of
the properties of the social relationship of exchange. Properties that
determine exchange's ability to generate prices embodying abstract labour
are expounded first in order, and the properties that modify this
identity to an approximation are brought in later.


>But if exchange considered as a production relation is not the set of
all concrete exchanges, then what is it? Exchange the relation of
production, exchange as a social relationship, exchangeability, is a
nexus of socially constructed roles, at base the roles of exchanger (and
later, with money), buyer and seller.


>Let's look at the "forms of value" in Chapter 1. They amount to analyses
of definite stages (or moments) of the roles of buyer and seller. In the
first "Elementary or accidental" form of value, Marx introduces the
qualitive fact of alienation of use-values. The exchanger is one who has
unwanted use-values that can be alienated in return for wanted use-values
owned by the other. This weak (and early) form of the social role of
commodity exchanger already defines some relational properties of
exchange, without recourse to generalisation from concrete exchanges. For
example, the fact of exchange directly implies symmetry, and the fact of
exchange ratios (arbitrary though they may be in this form) imposes
linearity. "It therefore follows that the elementary value-form is also
the primitive form under which a product of labour appears historically
as a commodity, and that the gradual transformation of such products into
commodities, proceeds pari passu with the development of the v!



>The elementary form of value has "relative" and "equivalent" subforms
that correspond to the two distinct roles in exchange, the one who
alienates the unwanted use-value and the one who provides the wanted


>The second, "Total or expanded" form of value corresponds to the
generalisation of the first form. The exchange relationship broadens to
the point that the exchanger sees their commodity as exchangeable with
"numberless" other commodities in definite proportions. Here
exchangeability of a particular use-value extends to a wide range
(potentially all) of other use-values, and hence the given use-value
appears as the embodiment of social labour. The value of their commodity
(embodied form not in a scalar but in the vector of exchange ratios with
other commodities) appears now to the exchanger as distinct from its


>The "General" form of value corresponds to the stage of equating the
value of all commodities through the ratios with which they exchange with
a particular commodity, a universal equivalent. It's this stage where the
social relation of exchange becomes able to enforce transitivity (more or
less successfully), and hence calculate a consistent vector of exchange
ratios. Here value begins to obey the all the 4 axioms of of RST and
composition, and thereby becomes a definite positive scalar associated
with each commodity.


>The Money form corresponds to the specialisation of a particular
commodity, money, in the role of universal equivalent. The universal
exchangeability of money now becomes its primary use-value, and the
social role of exchanger diverges into buyer and seller (the "relative"
and "equivalent" subforms of the money form).


>I won't go further with this interpretation here, it's pretty clear how
it works, and how it extends through further specification to the roles
of worker, capitalist and landowner.


>How does this reading of Marx's theory relate to our project of
formalising and developing conceptual models? To me it suggests that our
formalisation should start from a formal specification of the social
roles, as algorithms or repertoires. Our theory should start from the
simulation (and analysis) of the results of the interaction of multiple
interacting processes implementing definite (and simple) roles.


>Simulations of populations of commodity exchangers with appropriate
programs should be able to generate actual exchanges that obey e.g. the
equivalence relation laws; in particular they could evolve definite
prices. These "evolved" laws would not take the form of binding rules,
disprovable by a single counter-example. They would be attractors in the
space of possible sets of concrete exchanges computed by the simulacra.


>For example, suppose that our simulated exchangers were simple commodity
producers. The vector of values of their products would be an attractor
within the space of price vectors that they actually did compute during


>Since Marx never had a computer, the option of simulation was not
available as a way of demonstrating the implications of the social roles
he described via people's concrete behaviour to systemic properties. He
had to use analysis. We can use both techniques and use one to inform the


>To wind up, I can now return to Gil Skillman's accusation of tautology.
Marx's argument runs from a description of a subset of the properties of
the social relation of commodity exchange to the existence of commodity
fetishism, the appearance of the social labour content of products as an
"objective character stamped upon the product of that labour". That's the
kind of "tautology" that deserves the name "theorem".


>As for the relationship between actual price ratios and embedded labour,
that quite validly appears at a later stage of the analysis, after the
social relations (surrounding the commodity "labour-power") which govern
the divergence between these vectors have been added to his incremental
analysis of capitalist production relations.