[OPE-L:7208] [OPE-L:732] Re: Re: Thought experiment on exchange

Gil Skillman (gskillman@mail.wesleyan.edu)
Tue, 23 Mar 1999 19:08:29 -0500

In response to the following passage from me,
>>3) For any given set of exchanges, can we infer the existence of an
>>element "common" to the three goods? No, I could define them in such a way
>>that they have *nothing in common other than being exchangeable*, and doing
>>so would contradict none of the foregoing conditions. Much less, then, can
>>it be inferred that exchangeable bundles have a common element "of
>>identical magnitude".

Rakesh writes:

>Gil, if they had nothing in common, then chance would determine their
>exchange ratios, correct?

No, not necessarily correct. To take just one example, one can define a
Walrasian equilibrium for goods which have nothing in common, in the manner
described earlier. In this case, exchange ratios would be determined by
excess demand functions, which can be defined deterministically--i.e., no
probabilistic elements need enter the determination of prices.

> But over time exchange ratios become stable.

Well, this large thread began with Alan's denial of this very claim,
specifically as it applied to the scenario of exchange being considered by
Marx in Chapter 1. Alan said that for Marx, markets were in *continual
disequilibrium*, which sounds like a contradiction of the claim that
exchange ratios become constant over time.

For what it's worth, I doubt that as an empirical matter "exchange ratios
become stable" over time. This suggests that the variability of a given
exchange ratio tends toward zero, at least for commodities. I don't see
much evidence for this.

But perhaps it could be said at least that prices gyrate around a fixed
center of gravity? Well, maybe, but that center of gravity *could* be
determined by demand conditions, as above. Or, to relate my answer here to
the previous thought experiment: replace the characterizations of
*deterministic* price ratios in the previous post with *distributions* of
price ratios, perhaps with given means equal to the previously
deterministic ones, and given variances, and the arguments presented
earlier go through as before. I think.

The converse problem also arises: "stable" exchange ratios, understood in
a statistical average sense, may not plausibly tell us *anything* about
values in Marx's sense. Take the case of persistent average profit
differentials between nominally competitive industries. Mainstream
economists explain these differences via reference to risk premia, and
"risk" is not a product of labor.

> As
>Carchedi points out: "It is this relative stability wich compels us to
>presuppose a common thing (abstract labor) whose relative stability (labour
>socially necessary) explains the relative stability of the exchange ratios,
>of the proportions in which products are exchanged."

I've suggested above that while such stability might be suggestive, it
doesn't "compel" us to presuppose the commonality of abstract labor.
But conversely, if, in fact, exchange ratios are not typically stable (as I
believe to be the case), can we conclude that there is *no* common element?

> I find myself unable
>to devote real attention to these threads because of how much difficulty I
>am having with other things I must finish. So just a quick challenge so I
>can stay in the game.

I'm in the same boat. After today, le deluge. Gil