Supplementary Insurance with 'ex post' moral hazard: efficiency and redistribution

This paper investigates the topping-up scheme in health insurance when both public and private insurers use a linear contract. It is shown that, with identical consumers, the second-best allocation is obtained. Whereas, introducing consumers' heterogeneity with respect to the wage rate when labour supply is endogenous, public coverage is uniform, and health expenditures are financed by linear taxation, it is shown that the optimal public coverage is negative and consumers are under-insured.