Smolin on theThe Landscape

Of economics, that is.

Earlier I mentioned Lee Smolin's recent paper on economics and gauge theory: http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.4274v1.pdf At that time I was pretty skeptical, but having now read much of it, I have a different view.

For one thing, he gives a nice introduction to General Equilbrium Theory in economics written in a fashion to be understandable to physicists. He also succinctly explains the underlying assumptions, the strengths of the model, and its weaknesses.

The biggest strength is that it says that there is a locally Pareto efficient equilibrium. [Pareto efficient meaning no other nearby states are better for all participants in the market]. This is sometimes [mistakenly] cited to claim that classical economics shows that the market cannot be improved upon. Unfortunately, it is not clear that these equilibria are either unique or stable, and quite likely, they are neither. There could well be an entire landscape of unstable equilibria with little to prefer one over another - moreover, local Pareto efficiency doesn't imply anything globally.

Even more unfortunate from the physicist's standpoint is the fact that the model has no time or dynamics. There is nothing to indicate how the economic systems approach equilibria or how they evolve in time - this is "block time" economics - minus any hint of geometry or metric in the block.

Smolin and some other physicists, mathematicians, and economists hope to exploit certain gauge like freedoms in the model to attempt to introduce a dynamics. I have no idea how likely this is to succeed or how useful it might be if it did.

Given that classical economists seem to be pretty wack, somebody ought to try something, and something mathematical enough to get their attention seems like a good place to start.