2006) “Supplementary Insurance with Ex-Post Moral Hazard: Ef…ciency and Redistribution,” Annales d’Economie et de Statistique, 83-84 (July-December

This paper investigates the topping-up scheme in health insurance when both public and private firms use linear contracts. First, the case with identical consumers is analyzed. The optimal public coverage is derived both when the firms play simultaneously and when they play se-quentially. In the former case consumers are over-insured, whereas, in the latter case, the second-best allocation is obtained. Then, consumers ’ het-erogeneity 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, in the sequential game, the optimal public coverage is negative and con-sumers are under-insured