Adverse selection, moral hazard and propitious selection

We propose a simple model with preference-based adverse selection and moral hazard that formalizes the cherry picking/propitious selection argument. This argument assumes that individuals differ in risk aversion, potentially resulting in more risk averse agents buying more insurance while being less risky. The propitious selection argument is summarized by two properties: regularity (more risk averse agents exert more caution) and single-crossing (more risk averse agents have a higher willingness to pay for insurance). We show that these assumptions are incompatible with a pooling equilibrium, and that they do not imply a negative correlation between risk and insurance coverage at equilibrium.