Insurance Contracting with Adverse Selection and Moral Hazard

Most of the previous research in the asymmetric information problem treats adverse selection and moral hazard separately, though they may coexist and interact with each other. We build a principal-agent model to examine optimal contracts in a competitive insurance market facing adverse selection and moral hazard simultaneously. We apply the change-of-variable method and the Kuhn-Tucker conditions to solve the optimization programs. Our model yields richer separating Nash equilibria than pure moral hazard and pure adverse selection models, although separating Nash equilibria may not exist in some cases. It also retains some properties, for example, no full insurance and the positive correlation between insurance coverage and risk type, in those benchmark models. Our study on comparative statics indicates that, under some conditions and with some exceptions, the optimal indemnity and premium decrease with disutility from effort, increase with potential loss, and decrease with the initial wealth of the insured