[OPE-L:7028] [OPE-L:523] Re: Equality and equivalence [OPE 491]

Steve Cullenberg (stephen.cullenberg@ucr.edu)
Thu, 25 Feb 1999 15:06:37 -0800

Alan writes:

>By and large I don't disagree with your central point in it, or at least I
haven't until now when you say that linearity isn't the issue, because I
think linearity is the issue.
>However before we get onto that, there's a prior point of clarity; it
seems abundantly clear from all your contributions that what you mean by
equality is exchange in proportion to magnitude of abstract labour. If you
mean something different, then perhaps we should get that clear before
proceeding onto linearity.
>Here's a list of citations from your post that suggest to me that when you
speak of equality, you mean exchange at values. I hope you'll enlighten me
if your own meaning is different from that which I attribute to you.

Gil has already responded to this point and I agree with him. The equality
of "abstract labor" per se is not what I am concerned about. It is the
issue of the special structure of thinking about exchange in terms of an
equality operator. My question again is why do that? If rejecting the
assumption of exchange as an equality takes us outside the realm of
Marxism, that is not much different than a version of the question I've
been pressing. Do we then lose a cogent theory of surplus value if we drop
the assumption of exchange as an equality? If so that is serious. But
even more serious, I would suggest, is if it is the case that our theory of
surplus value depends on a not very robust assumption about exchange.
Should we have a discussion about what's in the hard core of marxian

I would imagine you would agree that there can be consistent theories of
exchange where no assumption of exchange as an equality is imposed. Arrow,
Debreu, Sraffa all come to mind.....(btw, I have not commented on the law
of one price/linearity debate -- one can insist on linearity in exchange
and not presume equality, no? -- and I haven't taken a position on this).

Let me pose the question as I see it this way:

1. I see no prima facie reason to assume that exchange must necessarily be
presumed to take the form of an equality. Indeed, I see many presumptive
reasons not to do so, namely one being that the vast majority of economists
who think about exchange do not.

Therefore, I see exchange as an equality as a special assumption which is
presumed because either:

(a) there are strong theoretical reasons to do so. If so, I am asking
what are they?

(b) there are strong emprical regulative tendencies that enforces such a
condition? If so, what are they? I actually think in fact that this is a
category mistake because we are talking about a theoretical structure here
that no empirical evidence could confirm or falsify.

(c) one sets the exchange ratios between commodities so as to find
expression of the desired equality. This is of course always possible to
do, but my question then is why do so? If doing marxian economics hinges
on this move then it seems an awfully thin read to build so much on.


Stephen Cullenberg Office: 909-787-5037, ext. 1573
Department of Economics Fax: 909-787-5685
University of California Email: stephen.cullenberg@ucr.edu
Riverside, CA 92521 www.ucr.edu/CHSS/depts/econ/sc.htm