Mathematical Complexity of Simple Economics

lesson learned from modern dynamics is that natural systems can be surprisingly complex. No longer are we astonished to discover that systems from, say, biology (e.g., [GOI, Ma1, Ma2]) or the Newtonian n-body problem (e.g., [MM, Mo, Mk, SX, X]) admit all sorts of previously unexpected dynamical behavior. This seeming randomness, however, sharply contrasts with what we have been conditioned to expect from economics. On the evening news and talk shows, in the newspapers, and during political debate we hear about the powerful moderating force of the market which, if just left alone, would steadily drives prices toward an equilibrium with the desired balance between demand and supply. The way this story is invoked to influence government and even health policies highlights its important, critical role. But, is it true? I have no idea whether Adam Smith’s invisible hand holds for the “real world,” but, then, no one else does either. This is because, even though Mathematical Complexity of Simple Economics