Aggregation, Determinacy, and Informational Efficiency for a Class of Economies with Asymmetric Information

We identify and analyze a class of economies with asymmetric information that we call quasi-complete. For quasi-complete economies we determine equilibrium trades, show that the set of fully informative equilibria is a singleton, and give necessary and sufficient conditions for the existence of partially informative equilibria. Besides unifying some familiar settings, such as those of Grossman (1976) and Milgrom and Stokey (1982), the following new results are proved: (a) The same restrictions that deliver Gorman aggregation under symmetric information are sufficient for Gorman aggregation under asymmetric information, even under partially informative prices; (b) the traditional assumptions of quadratic utilities and endowment spanning that result in the CAPM under symmetric information deliver a conditional CAPM under asymmetric information with prices that need not be fully informative; (c) the linear equilibrium in Grossman’s (1976) model is the only equilibrium (linear or not), while minor changes in the normality assumptions result in indeterminacy and partially informative equilibria; and (d) if there is no aggregate endowment risk, asymmetrically informed agents with common priors sell the risky part of their endowment in every equilibrium. Journal of Economic Literature Classification Numbers: D82; G14; C62.