Efficiency in trading markets with multi-dimensional signals

There is a continuum of agents, each of whom trades a divisible asset via demand function competition. Individual valuations are determined by payoff shocks that are correlated across agents. Agents observe multi-dimensional signals about the payoff shocks; it is only assumed that the signals are normally and symmetrically distributed. We give three results about this economy. First, an equilibrium exists. Second, the equilibrium is constrained inefficient; a higher total surplus could be attained if agents submitted different demands. Third, a constrained-efficient outcome can be implemented by setting an appropriate capital-gains tax. The second result identifies a new type of inefficiency that only arises when agents observe multi-dimensional signals; the third result identifies the taxation policy that allows correcting this inefficiency.