Abstract
It is by now well-known that there exists a system of prices at which decentralized, utility-maximizing behavior by a finite number of agents, each with convex preferences, leads to outcomes which ‘mesh’ in the aggregate. Technically, a competitive equilibrium is said to exist. The question arises as to what happens with non-convex preferences. Using Non-standard Analysis, we show that, provided the economy is ‘large’ enough, there exist various formulations of approximate competitive equilibria. We also relate our results to other work in this area.
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