Markets with Multidimensional Private Information

This paper explores price formation when sellers are privately informed both about their preferences and the quality of their asset. In equilibrium, sellers recognize that it will be harder to sell their asset at higher prices, while buyers recognize that they will get higher quality assets on average at higher prices. There are many equilibria of this model, including one in which all trade takes place at one price. Under a behavioral restriction, we find a unique semi-separating equilibrium in which trade takes place over an interval of prices. We characterize necessary and sufficient conditions for this equilibrium to be Pareto optimal. Even though the semi-separating equilibrium allows for more trading opportunities, it may be Pareto dominated and may have less trade than the one-price equilibrium.