On the Informational Role of Prices with Rational Expectations

Traders' expected utilities in fully revealing rational expectations equilibrium (REE) are shown to decrease as the number of informed traders is increased for an asset market model with diverse information as in Grossman (1976). It follows that no trader has any incentive to acquire information even if no other traders do. Consequently, when information acquisition is endogenous, there exists unique overall equilibrium with no trader acquiring information that has the fully revealing REE as an integral part, so that prices would fully reveal private information were it to be acquired by traders. This result provides a strengthening of the fundamental conflict between the efficiency with which markets spread information through the prices and the incentive to acquire information. Both the existence and the no information acquisition feature of the overall equilibrium do not depend on whether traders are endowed with the risky asset or not.