Deductible or co-insurance: Which is the better insurance contract under adverse selection?

The standard solution to adverse selection is the separating equilibrium introduced by Rothschild and Stiglitz. Usually, the Rothschild-Stiglitz argument is developed in a model that allows for two states of the world only. In this paper adverse selection is dis-cussed for continuous loss distributions. This gives rise to the new problem of finding the proper form of an insurance contract to impose partial insurance of the low risks. This paper contributes to the discussion on optimal insurance. It analyzes two basic forms of insurance contracts: A contract with a deductible and a contract imposing a positive co-insurance rate. Since high risks can always self-reveal themselves as high risks and buy the optimal insurance contract at high risks' premiums the Pareto-superior insurance contract is the one that leaves the low risks with higher expected utility while deterring high risks from joining the contract that is designed for low risks. The deductible contract turns out to be superior if premiums contain a sufficiently high loading.