I.6 Imperfect Information: Equilibrium with Two Classes of Customers
Suppose that the market consists of two kinds of customers: low-risk individuals with accident probability pL, and high-risk in- dividuals with accident probability pH > p L. The fraction of high-ris'k customers is X, so the average accident probability is p = XpH + (1 - X)pL. This market can have only two kinds of equilibria: pooling equilibria in which both groups buy the same contract, and separating equilibria in which different types purchase different contracts. A simple argument establishes that there cannot be a pooling equilibrium. The point E in Figure II is again the initial endowment of all customers. Suppose that a is a pooling equilibrium and consider 7r(p, a). If ir(p, a) < 0, then firms offering a lose money, contradicting