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. First, the case with identical consumers is analyzed. It is shown that the optimal policies allow to implement the second-best allocation. Then, consumers’ heterogeneity is introduced: consumers differ in their wage rate and labour supply is endogenous. It is assumed that public coverage is uniform and health expenditures are financed by linear taxation. Results show that the optimal public coverage is negative and consumers are under-insured.