[OPE-L:6968] [OPE-L:460] Exchange of equivalents

Alan Freeman (a.freeman@greenwich.ac.uk)
Sun, 21 Feb 1999 17:20:18 +0000

Also responding to Jerry's request for 'new topics', I'm glad that Gil has
re-taken the fray about the exchange of equivalents because I have a
further angle on it that might clarify things. The 'old' discussion he
refers to took place around April '96, for example his OPE-1731.

My point, which features centrally in my paper to the coming EEA
conference, starts from a fact that I think the discussion has
insufficiently considered, namely, that the market is never in equilibrium
-- and when it does, this is an accident -- and so goods never exchange at
their values or, to put it another way, supply never equalises with demand.

It is precisely because of this that a 'common substance' cannot be
dispensed with: I think, moreover, that Marx considered this quite a
central issue. In my article I provide substantial textual evidence.

An analogy would be the following: consider the metaphor of the balance,
which economists are very fond of using. As long as a balance works, we do
not need the concept of mass. We can weight objects against each other and
establish 'weight' as the equivalence class of all collections of objects
that we observe balancing with each other. That's why people invented
weighing machines before they discovered the law of gravity.

This does not invalidate the law of gravity, and it does not eventually
excuse us from assigning a common substance ('mass') to all objects,
distinct from their weight and related to properties that they have quite
independent of their weight, such as attracting each other in proportion to
their mass. But it lets us get by without it, as humanity did for quite a
long period of history.

The problem is that we can actually observe balance when we weigh things.
But we can never observe the market in balance. We can never see goods
actually exchanging at their values, and so the conditions that would allow
us to define value 'purely quantitatively' do not exist.

What would you think of a grocer who used a pair of broken scales by
dumping a bag of potatoes on one pan, a pound weight on the other, and then
catching the packet as it passed the weight? You would have to ask for some
independent proof of the amount of potatoes, without resorting to the
fiction that we observed them balancing the weight. It's the same with
value. Because the market itself cannot tell us the value of a thing, you
have to find some independent way of quantifying it.

We must therefore proceed straight to the stage of Newton and relate the
fact of exchangeability to a common substance, not identical to a ratio of
use-values, which explains exchange in terms of something other than the
act of exchange, just as the concept of mass explains weight in terms of
something other than the act of balancing.

It isn't adequate, as most economics does quite dogmatically and with a
great deal less logic than the much-criticised Marx, to state that we can
proceed 'as if' the market was in stasis. Actually, there is no
justification for this at all, any more than the statement that we can
proceed 'as if' God existed. Worse still, the supposition that the market
is in stasis actually contradicts the market itself. Stasis is a
*self-contradictory* assumption.

The conditions that might establish value 'quantitatively' in exchange not
only don't exist, they can't possibly exist. This is why we can't use
analogies such as the balance or the pendulum. A balance (or for that
matter, a pendulum) can exist in stasis, or in movement. That's why we can
talk about its 'disequilibrium' and relate this disequilibrium to a static
state which we can really observe.

This is not so with the market. The market must be out of 'balance', in
order to exist. It exists because it is out of balance, just as a human
walks or runs by continually imbalancing. The word 'disequilibrium' is, as
applied to the market, an oxymoron, like speaking of life as 'un-death'.
The point is, we cannot discover in death a sufficient wealth of observable
phenomena to explain life.

We therefore need a way of talking about price which does not depend on
the relation between supply and demand. We need to enquire qualitatively
what the value of a commodity consists of, external to and independent of
any subsequent exchange relations it enters into, before and in order to
study the quantitative phenomenon of real market prices.

Think of it like this: as long as a machine works, we don't need the
manual. But when it breaks, we have to get inside the works. A market,
however, breaks in order to work. So we always need the manual. We
always need to be inside the works, because the damn thing never stays in
one place long enough to get any quantitative measurements out of its
static state. We cannot understand a waterfall by studying a lake.

If goods did exchange at values, we could use their quantitative congruity
to establish an equivalence relation of the type which Paul discusses, and
this equivalence class would in and of itself provide an adequate, though
superficial, quantitative definition of value. (Value would be a
homomorphism -- not, incidentally, an isomorphism -- between bundles of
goods exchanging with each other)

The problem is that goods don't exchange at their value. Therefore, this
equivalence class does not manifest itself in what we actually observe.
What we observe is something different, namely, price. It is therefore, I
think, completely erroneous to read Marx's derivation of value as if he
supposed it to be a quantitative relation manifested in exchange. Indeed
he explicitly polemicises against this notion in many, many places,
including Volume I. The issue for Marx is not the ratios in which goods
exchange, but what makes them exchangeable. He thus writes

"In order to find out how the simple expression of the value of a
commodity lies hidden in the value-relation between two commodities,
we must, first of all, consider the value-relation quite independently
of its quantitative aspect. The usual procedure is the precise opposite
of this: nothing is seen in the value-relation but the proportion in
which definite quantities of two sorts of commodity count as equal to
each other. It is overlooked that the magnitudes of different things only
become comparable in quantitative terms when they have been reduced to
the same unit." Volume I
(Penguin edition) p161

He is quite explicit, also in Volume I, that we cannot assume the equality
of supply and demand -- which of course means that we cannot suppose
exchange at values. He even dubs this 'vulgar':

"The vulgar economists have practically no inkling of the nature of value;
hence, whenever they wish to consider the phenomenon in its purity, after
their fashion, they assume that supply and demand are equal."
- Marx, Capital Volume I, p269

It is precisely because goods do not exchange at their values, and indeed,
do not exchange in any constant proportion -- in Marx's words they 'never,
or only accidentally' exchange at their values -- that value cannot be
calculated, and cannot arise, from the quantitative relations of exchange
but must be derived from relations external to exchange, namely production.

Ricardo spent his life trying to escape this problem and never did. This is
precisely why I think Marx was neither a Ricardian nor a post-Ricardian.
Ricardo's heirs are precisely those economists who revert to the pre-Marx
conception that we can meaningfully derive quantitative definitions by
supposing the equality of supply and demand. Samuelson, not Marx, is the
true post-Ricardian.

The problem is not averted by talking only of prices. There are things we
seek to know other than just the price at which goods exchange. Just to
distinguish, for example, between a nominal price rise and a 'genuine'
price rise, we require to define what the 'genuine' price of a thing is,
independent of its money equivalent. We can't even define inflation, or
productivity, or any of the things that economists want to talk about,
unless we can assign numerical magnitudes to vendible things that are
defined independent of the money for which they exchange.

The requirement for a concept of value arises, quite independent of its
quantitative determination, from this fact; the fact that we can't escape
this need shows in the way it enters into all economic discourse in one way
or another. If the economists choose to give it a different name, this
doesn't change the nature of the concept. When the neoclassicals speak of
the 'real-nominal' distinction', the term 'real' price is just another term
for value. The problem is not to 'prove' that value exists, since everyone
uses the concept. The problem is to clarify what value really is.

Nor is the problem averted by those economists -- including not only
Walrasians but both Sraffians and analytical Marxists -- who dogmatically
assert we can describe a real economy with reference to the ideal prices
that are established by the equalisation of the profit rate. Profit rates
never equalise; these ideal prices do not, therefore, have any necessary
relation with actually observed prices, and tell us nothing more about the
movement of a real economy than labour values. Equal-profit-rate prices are
nothing more than a disguised, alternative, value-concept. The debate is
not *whether* we need a concept of value, but whether value is best
measured by labour-content or hypothetical-equal-profit-rate prices.

The next point is then, why 'labour'? I think a lot of people make an
unnecessary meal of this. The need to quantify value in terms of
labour-time, or some function of it, arises from a need which all economics
recognises, to distinguish production from circulation. The very idea that
there are two distinct spheres of human activity, in one of which
'something' is produced and in the other of which this 'something' passes
from one human to another, demands quantitative expression. It demands
ahomogenous measure of what is produced.

The issue is then 'how do we define production, and how do we distinguish
it from circulation?' Marx's analysis of circulation, which occupies the
first five chapters of Volume I, simply recognises that circulation must,
by its very conceptual nature, be a social activity that does not modify
the amount of value in existence. I think the whole attempt to construe
this as a 'logical proof' of the existence of value is misconceived. Marx
isn't, I think, saying that he has proved the existence of value. He says,
look here, dumbos, you all talk about value, so it's stupid to try and do
without it. Let's now look at the consequences. Well, one consequence is
that if value is to have any meaning, it can't be modified in circulation.
Otherwise, circulation would include production, since production by
definition is the place where new value comes from.

That's the whole function of the chapter 5 argument; it simply says that if
you want to speak of circulation and you want to speak of value, and you
want to make your usage of the two terms coherent with each other, then you
can't have value appearing in circulation. Et voila tout. Value is simply
an invariant of circulation, and that's what the first equality is all
about. In this strict sense I agree with Paul's concept that value is
conserved in circulation, though I think he makes an unnecessarily
complicated mathematical argument, including a very odd metric indeed, to
establish the point.

The second equality indeed follows 'tautologically' from this, and moreover
chapter 5 establishes it. If no 'additional' value can arise in
circulation, then no 'surplus' value can arise in circulation. The two
words describe the same thing.

What is not tautological is to establish whether the definitions themselves
are consonant with labour-time as the measure of value, and the sale and
purchase of labour-power as a commodity; whether, when we define the
categories of labour-power, its sale and purchase, we create a
contradiction with the general considerations of chapter 5. If we did, this
would tell us that though it is reasonable to speak of value as an
invariant, we could not use labour-time as its measure. In this sense I
think that Marx's transformation has a real informational content, really
proves something -- provided, of course, the transformation is interpreted
in the single-system sense, and provided this is extended to the temporal
definition for an economy undergoing change, that is, for a real economy.

Thus the transformation problem *is* important, because if Marx's
transformation of values into prices was erroneous as alleged, then we
would find value appearing in circulation, and that is indeed incoherent
because it would mean we would be trying to make a distinction that could
not actually be made in any real world.

So why labour? Because that's what defines production. Production *is* the
application of human labour to the creation of new use-values. Capitalist
production is the same thing organised in the commodity-form.

You can define production differently. You'll then get a different
definition of value. I don't think this will necessarily be incoherent, but
it will express a different concept of production. Thus it is possible to
construct, I think, a perfectly coherent physiocratic definition of value,
provided you can get around the problem of homogenising the produce of the
land, which I guess Monsanto are working on. You'd then have some rather
strange ideas of circulation; for example,it would include everything that
happens in the towns. But that is exactly the way the physiocrats thought,
and it's completely logical internally. It's just not a very good way of
explaining the modern world, since it relegates most modern activities to
the sphere of circulation.

The classical approach moves away from this naturalistic definition of
production and *defines* production to be social. Society, however,
consists of humans. Thus, if you want to quantify the results of
production, you need a universal measure of human activity. What's the big
deal? Labour *is* what humans do when they produce. That's what we mean by
'producing'. The movement from Physiocracy, through Smith, through Ricardo,
to Marx, consists of escaping the naturalistic value definition of the
physiocrats and replacing it with a social value definition, in a coherent
and comprehensive manner. I think there is a lot less mystery in this than
is usually attached to it.

I don't think this constitutes an absolute 'proof' but merely a squaring of
concepts with each other. Science doesn't proceed by producing absolute
logical proofs. It proceeds by working out which set of concepts make the
most sense of what we see in the most elegant and comprehensive manner. It
is of course indispensible to make these concepts square with each other,
which is why one cannot proceed directly to empirical measurement and skip
the intermediate stages. But this squaring up of concepts doesn't itself
constitute proof, and I think this is one of the big mistakes that modern
economic thinking has imposed on its world, because of its Platonic method
which takes ideal and static logical forms for real and changing

Now let's consider price as such. Marx starts from price, but not from the
quantitative fact of the ratios in which goods exchange. Instead he starts
from the qualitative fact that they exchange at all. Price is indeed an
equivalence class.

However this is not a weak relation and I don't think Gil has entirely
grasped the significance of the price relation. At one point he speaks as
if price simply doesn't exist: he suggests that aRb and bRc does not imply
aRc in an 'imperfect market'. However Marx takes the commodity as
his starting point, and the commodity is defined precisely by the existence
of a set, at any given time, of mutually-compatible exchange-ratios in
which (aRb and bRc) always does imply aRc: that is, his starting point is
the law which modern economists know as the 'law of one price'. When the
'law of one price' breaks down, we do not have commodity relations and so
we do not have Marx's starting point in the commodity.

This is, moreover, not a weak algebraic relation but a very strong
one, because the price relation is not only transitive, symmetric and
reflexive, but *linear*, that is, additive. Gil constantly forgets or hides

Thus he writes: [OPE 185]:

>As a counter example, consider a preference ordering R. A preference
>relationship among bundles which satisfies reflexivity, transitivity, and
>symmetry establishes a relationship of indifference, not equality. To say
>that I am indifferent between two bundles in no way implies the two bundles
>are equal in the sense required by Marx.

But if I am indifferent between bundle A and bundle B, this does not imply
that I am indifferent between two As and two Bs. If A exchanges with B,
then two As exchange for two Bs; this is the why an exchange relation is
not the same as an indifference relation. Don't forget that; it makes all
the difference. We have more than just

aRb -> bRa

we *also* have

aRb -> (ka)R(kb) where k is any scalar.

That's an additional rule which constantly gets forgotten; it is the basis
for talking about conservation at all, since obviously if I can add
together 2 and 2, and get 3 or 5, then there isn't any conservation.

The question then is: can we, on the basis of the above *four* rules,
obtain a quantitative definition of value? Not at all, because these four
rules apply to any *arbitrary* set of prices. You need an independent
determination of value that is the same for any arbitrary R. We need a
unique and canonical mapping that takes any use-value x into its value
v(x), with the property that this mapping is invariant with respect to R.
Such a mapping is its value. There are many different possible value
measures, of course, but the choice is not arbitrary. For example a
marginal valuation does not achieve value-invariance in circulation since
if we re-assign the same use-values differently, we will increase or
decrease the total value in existence. In fact, the valuation must be
linear, or we will get value in circulation by some manipulation of prices.

This, by the way, is why we cannot suppose that the problem of defining
'real' price is solved by the index number calculation, as Steve has
in the past suggested. If we define 'real' price (that is, neoclassical
value' in terms of use, unless we have a cardinal measure of use, then
it is not additive and is altered by circulation (or there wouldn't be
any such thing as a Pareto optimum since all allocations would be
the same).

We can define value as a cardinal utility measure (that is, what Ricardo
terms 'riches' -- use-values) and in a certain sense, this is what the
Sraffian definition offers. But then we
still have a problem which applies also to ordinal utility, namely we have
to admit that the self-expansion of use-values constitutes production.

But in that case, natural production unaided by humans constitutes a
form of productive activity and we arrive at the conclusion that value
is created externally to what we normally term 'production', that is,
purposeful human activity that makes new use-values for sale. Worse
still, the self-activity of *machines* constitutes production so that
an automatic machine creates value. We have second-millenium physiocracy
-- robotocracy.

It must be repeated that there are many different linear value measures
that provide for value-conservation. However, any value measure that can
vary independent of the magnitude of labour, will permit the expansion of
value outside of production. Thus for example any definition based on the
mere self-expansion of use-values will lead back to the creation of value
in circulation.