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Braess paradox

One of the pretty results of road supply theory is that if you add extra links to a road network you can make everyone on the network worse off.  Equivalently closing down links can improve all traffic flows.  JB pointed me to this nice exposition.  It is called the Braess paradox and its a well known result in other types of network problems in fields such as computer science. Steinberg and Zangwill (1983) prove that under reasonable conditions this paradox is about as likely to arise as not – it is not a particularly weird outcome.  One circumstance where I believe this will never occur is if all roads are congestion priced at instantaneous marginal cost.  I have seen a claim made that this last view is unequivocally true in a 1994 paper by two of the best urban economists about the place – Richard Arnott and Kenneth Small.  Note that it was claimed here though not proven.  Still I believe the claim is true – it is a bit like the Bhagwati ‘immiserising growth’ literature in international economics – the paradox requires a distortion to operate – but I have never seen a proof.

Its a lovely result since it confirms – in a relatively minor way – the role of efficient pricing in limiting such paradoxes facilitates good road supply expansion decisions.  A simpler version of a similar insight is that, with efficient congestion pricing and with roads displaying constant returns, you know when to expand a road. Do so when with these efficient tolls the road makes a profit. In another lifetime I might spend my time studying the intriguing nature of road demands and supplies.  Beauty is in the eye of the beholder and, to me, this is aesthetic stuff.

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