Standard insurance models predict that people with high (health) risks have high insurance coverage. It is empirically documented that people with high income have lower health risks and are better insured. We show that income differences between risk types lead to a violation of single crossing...

We study optimal risk adjustment in imperfectly competitive health insurance markets when high-risk consumers are less likely to switch insurer than low-risk consumers. First, we find that insurers still have an incentive to select even if risk adjustment perfectly corrects for cost differences...