Sunday, August 26, 2007

first principles

I was telling these two transvestites about Hotelling's spatial duopoly model. About how the problem isn't so much the discontinuities in the reciprocal reaction functions, as their failure to be quasi-concave.

Hotelling's innovations certainly contributed toward the development of useful models for understanding capitalist competition (e.g. Paul Sweezy's theory of monopoly); but his ideas are also interesting as a very pure form of the logic of economism. So, in Stability in Competition Hotelling criticises the mathematician Bertrand's presupposition (from his monograph on Cournot's book) that:

"one merchant can take away his rival's entire business by undercutting his price ever so slightly. Thus discontinuities appear, though a discontinuity, like a vacuum, is abhored by nature. More typical of real situations is the case in which the quantity sold by each merchant is a continuous function of two variables, his own price and his competitor's. Quite commonly a tiny increase in price by one seller will send only a few customers to the other."

In so far as Hotelling's system proved not to be internally consistant it invites consideration as ideology, i.e. as a product of the imagination under the circumstances in which it was formulated. Of course it's the logic of neoliberalism, something like:

"given the abstraction of the situation, and given the antithetical interests of participants involved, we must deduce or further presuppose the contiguity of their positions, hence equilibrium, a practically useful conjecture that cancels abstraction practically without cancelling it really."

Without going into the ruinous absurdities derived from, or related to this system of thought just yet, it's not irrelevant that this does recall previously existing figures of ideology, as discussed by Bachelard:

"The Grand Bénitier's strength is on a par with the height and bulk of its walls. Indeed, according to one observer, it would take two horses hitched to each valve to force the Grand Bénitier "to yawn, in spite of itself."

I should love to see an engraving that represented this exploit. I can imagine it, however, by recalling an old picture, which I have looked at long and often, of horses hitched to the two hemispheres, between which nothing existed but space. Here this image depicting the "Magdeburg experiment," which is legendary in elementary scientific culture, would have a biological illustration. Four horses to overcome fourteen pounds of limp flesh!"

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