[OPE-L:6969] [OPE-L:461] Re: Exchange of equivalents

Gil Skillman (gskillman@mail.wesleyan.edu)
Sun, 21 Feb 1999 21:52:53 -0500

It's good to hear from Alan again. He writes:

>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.

First, it seems to me that it is Alan's burden to demonstrate the sense in
which my critique of Marx depends on the condition of "market equilibrium,"
and he doesn't even attempt to fulfill this burden.

But second, contrary to Alan's suggestion, nothing whatsoever in my two
OPE-L critiques of Marx's Volume I analysis (the first concerning Marx's
derivation in Chapter 1 of abstract labor as the basis for exchange value
and the second concerning *Marx's* insistence in Chapter 5 that surplus
value must be explained on the basis of price-value equivalence) depends on
the assumption that "the market is in equilibrium." I criticize Marx's
Chapter 1 argument in terms of *his own* premises, which include that the
exchange ratio of any two commodities "changes constantly with time and
place." The presence or absence of "market equilibrium" is thus simply
not at issue, for Marx or for me.

In Chapter 5, it is *Marx*, not me, who asserts the significance of
explaining surplus value on the basis of price-value equivalence, and he
bases this assertion only *partly* (and invalidly) on a stipulation that
*might* be read as a form of market equilibrium--i.e., that price-value
equivalence corresponds to the "pure" case of commodity exchange (I, pp.
260-61 Penguin ed.). As I've argued elsewhere this characterization is
either completely tautological and thus contentless or else demonstrably
wrong in general. But in any case, my critique of Marx's analysis in
Chapter 5 does not depend on any assumption that markets are in equilibrium.

Moreover, Alan's phrase: "...and so goods never exchange at their values,
or to put it another way, supply never equalises with demand" has the
effect of begging the central issues at hand, since in general "prices
exchanging at their [respective] values" neither implies nor is implied by
"supply equalis[ing] with demand." Thus he takes as the starting point of
his argument an invalid claim.

Consequently I cannot help but see the remaining comments in Alan's post as
a sustained _non sequitur_, at least insofar as they are held to address my
critique of Marx. I have point-by-point responses as well, but since
these are redundant, given the foregoing, I won't go into further details.


>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.