Tuesday, August 27, 2013

Keen on Collusion

I'm reading Steve Keen's Debunking Economics for the second time, and I'm stuck in the chapter where he debunks the notion that — compared to a monopoly — under perfect competition you get higher quantities at lower prices. I've checked various texts on the subject on the Internet, and this appears to be the gospel taught to countless students of economics. I'm a bit set back after several people (Paul Anglin, Minseong Louis Kim, Christopher Auld, among them) had found errors in the math and thus appear to have debunked Keen on this matter. While I can (just about) follow the math and their arguments in favour of the Holy Gospel, there remains a significant problem: Keen wrote a computer simulation of the "mechanics" of competition, and he found that even with thousands of firms output and price appear to converge to monopoly levels. Not that economists (of all people...) are incapable of committing rather stupid and embarrassing programming mistakes, but the rules of competition are simple enough that a simple program can be written in about an hour or so (I did).

What I found interesting is that I had to search for several hours until I found an explanation of competition that didn't appear to offer separate rules for a monopolist and for perfect competition. Of course, you can win any argument if you get to massage the rules such that one of them says "I'm right, whatever I say". I wanted a smooth function of N (the number of firms) that yields a monopoly situation if N=1, and perfect competition if N→∞. The function exists and is the one that Prof. Auld uses to debunk Keen. It's the Cournot-Nash solution of the equilibrium output under perfect competition. Except, it isn't: when simulated in software the so called equilibrium output is the same for any N > 0, with quantity and price being at monopoly-level.

The problem with this solution and also the Marshallian equilibrium (or whatever it's called) is the claim that firms have total knowledge about the quantities produced by all firms (and consequently the price they can expect when selling their warez):
Each firm takes the quantity set by its competitors as a given, evaluates its residual demand, and then behaves as a monopoly. [Wikipedia page on Cournot competition]
Keen states that this assumption is unrealistic (and his computer simulation doesn't rely on it), and, indeed, this is a strange requirement. Where would this information come from? The firms certainly don't tell one another — this would constitute collusion, wouldn't it, and the whole point of perfect competition is  the absence of collusion after all. Indeed so much so that a situation with monopoly-level prices under competition is routinely called "collusion" (see the title of Keen's paper: Emergent Effective Collusion in an Economy of Perfectly Rational Competitors [PDF]). But expecting them to share this private information about their production quota is even more absurd, when you consider that firms are profit maximizers, and by not-telling they can achieve higher i.e. monopoly-level profit margins as shown by Keen's computer simulation.

So it appears that to rationalize a certain desired result, namely that perfect competition is preferable to a monopoly, economic theory assumes a condition which is not only absurd on the surface (firms telling each other about their production plans) but also inconsistent with their being profit-maximizers (because sharing this information actually reduces profits in the simulation). That such simulations can lead to the "collusive" rather than the Cournot-Nash equilibrium happens to be a known fact (see this comment on the Worthwhile Canadian Initiative post on Keen), but I doubt that students of economics will ever get to hear of it. Incidentally, calling the undesired outcome with the loaded term "collusive", when its cause is actually the opposite: the removal the collusive assumption in the simulation, is rather brazen. But then, "Hitler-pricing" would presumably be over the top even for economists.

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