A number of Marxian economists (Mark Glick, Dumenil and Levy and others)
have conducted convincing empirical studies demonstrating that over the
long term average profit rates equalize throughout the economy between
industries which over the long term had persistent differing degrees of
market concentration (i.e. over the long term profit rates in
oligopolistic and monopolistic industries were equal to those with many
sellers).

This is all well and good, but I think some of these authors may go over
bounds in attributing implications to this.

In the Elgar Companion to Radical Political Economy, Glick asserts
something along the lines of "this evidence refutes the Monopoly Capital
dogma."

Howard Botwinick, in Persistent Inequalities, contrasts the Marxian with
the Neoclassical theory of competition. He calls the neoclassical spectrum
of perfect-imperfect competition a quantity theory of competition. How
competitive the market is is determined by the size of the market relative
to the number of sellers. Monopolisitc Competition can also be thought of
this way, but with a more complex determination of what the market is and
its size. Botwinick seems to hold that the fact that more concentrated
markets don't earn greater long run (defined basically as a greater period
of study than most other studies which found differential profit rates)
profits refutes neoclassical economics, and he explains how Marxian
economics actually predicts this fact.

Botwiick also points out the contrast between the neoclassical theory of
competition, and the colloquial notion of the term. The latter refers to
conscious rivalry, and most people would think that Pepsi and Coke or BK
and MacDonalds are ultra-competitive, whereas NC economics would hold them
as monopolistically competitive or oligopolistic markets.

But here is the rub. Couldn't the "conscious rivalry" theory of
competition be grafted onto neoclassical economics? Does NC economics
really require that more concentrated industries earn higher profits
(barring the intervention of the state or unions etc...)?

As for Glick's comment, I have heard monopoly capital theorists state they
don't rely on the quantity theory of competition. Same with other
heterodox economists whose theories monopoly occupies a central role in.

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