[OPE-L:6980] [OPE-L:472] Postscript on exchange of equivalents

Gil Skillman (gskillman@mail.wesleyan.edu)
Mon, 22 Feb 1999 12:14:05 -0500

Here's a postscript on my earlier reply to Alan. Recall that the theme of
his argument is that "the market is never in equilibrium,", which while
completely unprovable (the economy could be following a dynamically
volatile equilibrium path, for example) is certainly plausible. Toward the
end of his post he writes:

>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 characterization is doubly puzzling to me, first because of Alan's
suggestion that the definition of a commodity implies that the "law of one
price" obtains. I don't see this. A commodity is defined as a good
produced explicitly for exchange. This in no way dictates the *conditions
under which* it will exchange.
I don't see Marx suggesting anywhere in his Chapter 1 argument that the
existence of commodity exchange rules out such phenomena as price
discrimination or transaction-specific bargaining, which preclude the
transitivity condition mentioned by Alan from obtaining in general. And
saying that price discrimination (for example) exists is obviously not
tantamount to arguing that "prices simply don't exist", contrary to Alan's

Second, the "law of one price" is a condition which only makes sense in the
context of market equilibrium, and not just any old equilibrium, but as
indicated above, a special animal known as *perfectly (or purely)
competitive equilibrium*. Absent the market conditions necessary to
achieve this form of equilibrium, there is no basis whatsoever for thinking
that the "law of one price" obtains. Thus I find this a very strange
interpretation for Alan to insist on, given that he is putatively arguing
that markets are fundamentally in disequilibrium!

>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

I forget many things and hide some others, but not in this case. The price
relation Alan invokes here only makes sense in a market economy that is in
competitive equilibrium (see above), which Marx nowhere invokes in Chapter
1. But even if this strong additional assumption were added, it would not
suffice to debar the central point of my (and Steve Cullenberg's, among
others) point that systemic exchange establishes a relation of equivalence,
not equality.

>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.

But the latter condition is precisely what *does not* follow unless one
invokes a strong form of equilibrium. For example, there is no linearity
in the exchange ratio if the producer of A offers volume
discounts--something which often goes on in the real world of commodity

But even if exchange relations were "not the same" as indifference
relations in the sense suggested here by Alan, it would not follow that
they establish relations of equality rather than equivalence.

Bottom line: to support his argument here, Alan must invoke exchange
conditions which are *only* plausible under *very strong* market
equilibrium conditions. It's hard to see how this position coheres with
his starting point, that markets "are never in equilibrium". But even
granting his interpretation, the inference necessary for Marx's Chapter 1
argument does not follow.