An equilibrium contract for low-risk types must not be more attractive to high-risk types than aH; it must lie on the southeast side of UH, the high-risk indifference curve through aH. We leave it to the reader to demonstrate that of all such contracts, the one that low-risk types most prefer is aoL, the contract at the intersection of EL and UH in Figure III. This establishes that the set (aHH, aL) is the only possible equilibrium for a market with low- and high-risk customers. 6 How- ever, (aH, aL) may not be an equilibrium. Consider the contract y in Figure III. It lies above UL, the low-risk indifference curve through a L and also above UH. If y is offered, both low- and high-risk types
6. This largely heuristic argument can be made completely rigorous. See Wilson (1976).