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A couple of comments on Julian's OPE-L 2028.
Julian seems to be using "paradox" to mean "antinomy."
I suspect that antinomies, strictly speaking, do not occur in
economics because economists do not interrogate their core
concepts -- they use conventional definitions and/or primitives.
As to whether a dialectical theory (which I take to mean, inter
alia, one that does interrogate its concepts) can contain
antinomies, my guess is that it can't if it is successful -- if,
that is, mediation does in fact lead to results that contain the
opposites within themselves. Hegel's dialectic was in large part
a response to Kant's antinomies.
While I don't think there are antinomies in economics, there is
something very close. In theories that use a numeraire or money
commodity as a substitute for value (e.g., neoclassical, Sraffian,
simultaneist-Marxist), it is possible to deduce self-contradictory
conclusions from the same set of premises, varying only the
numeraire or money commodity. For instance:
* the level of the *uniform* rate of profit is arbitrary, even in
the long run; it can depend upon which commodity is the numeraire
* given that the price of a good changes in response to excess
demand, the direction of relative price movements is arbitary; it
can depend upon which commodity is the numeraire
* movements in the level of the average rate of profit are
arbitrary; they always depend upon which commodity is the
* the sizes of profit rate differentials across firms or
industries are arbitrary; they always depend upon which commodity
is the numeraire
* thus, if capital flows in response to profit rate differentials,
one and the same economy can either converge to equilibrium or
explode, depending upon which commodity is the numeraire.
In short, yield arbitrary measures and arbitrary behavior
dependent of those arbitrary measures. The reason this is so is
that physical goods are heterogeneous, so "value" magnitudes based
on them are heterogeneous. Since there is no objective reason for
"choosing" one good over another as the substance of value,
theories that substitute numeraires or money commodities for value
are internally incoherent and indeterminate.
I should also mention another "antinomy-like" paradox. Orthodox
"Marxian economics" holds that the value of a commodity as an
input must equal the value of that commodity as output. It
follows from this that *one and the same* commodity, at *one and
the same* time, has two different values! -- one as the output of
one period, and another as the input of the next! In their
"Conservation of Value" paper, Dumenil and Levy have acknowledged
this. Yet although they recognize that a commodity can't have two
different prices at one and the same time, they attempt to resolve
the inconsistency by saying that values are not prices! This
solves nothing. If the rate of exploitation were zero or
compositions of capital were equal, then production prices *would*
equal values. So simultaneism does indeed imply that commodities
can have two different prices at one and the same time.
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