A median voter model of health insurance with ex post moral hazard

One of the main features of health insurance is moral hazard, as defined by Pauly [Pauly, M.V., 1968. The economics of moral hazard: comment. American Economic Review 58, 531-537), people face incentives for excess utilization of medical care since they do not pay the full marginal cost for provision. To mitigate the moral hazard problem, a coinsurance can be included in the insurance contract. But health insurance is often publicly provided. Having a uniform coinsurance rate determined in a political process is quite different from having different rates varying in accordance with one's preferences, as is possible with private insurance. We construct a political economy model in order to characterize the political equilibrium and answer questions like: "Under what conditions is there a conflict in society on what coinsurance rate should be set?" and "Which groups of individuals will vote for a higher and lower than equilibrium coinsurance rate, respectively?". We also extend our basic model and allow people to supplement the coverage provided by the government with private insurance. Then, we answer two questions: "Who will buy the additional coverage?" and "How do the coinsurance rates people are now faced with compare with the rates chosen with pure private provision?".