Prices and Allocations in a Trading Market with Multi-Dimensional Signals

Abstract

There is a continuum of agents, each of whom trades a divisible asset via demand function competition. Individual valuations are determined by multiple idiosyncratic and common shocks, regarding which the agent observes multi-dimensional signals. The only assumptions are that the signals are normally and symmetrically distributed. We introduce two measures to quantify the distance between an outcome of the demand function competition game and the first-best outcome: the allocative distortion and the price distortion. We say that an equilibrium is “price-quantity efficient” if no outcome of the demand function competition game generates lower allocative and price distortions. We give three results about this economy. First, an equilibrium exists. Second, we give “lax” sufficient conditions (that is, an agent learns about different payoff shocks from different signals) so that every Nash equilibrium is price-quantity efficient. Third, every price-quantity efficient outcome can be implemented by setting an appropriate capital gains tax; because this tax reduces agents’ incentives to speculate on the asset’s price, it decreases the allocative distortion but increases the price distortion.