Loss reduction and implicit deductibles in medical insurance

This note presents a modest extension of the very useful "theorem of the deductible" (Arrow, American Economic Review, 1963). The extension concerns ex post moral hazard in medical insurance. Under full insurance above a deductible, the marginal cost of treatment to the insured is zero, resulting in over-consumption. Co-insurance is the standard approach to mitigate that problem. Assuming that resources and consumption preferences are independent of health (to separate medical insurance from disability insurance), the optimal co-insurance contract results in the same indemnities as a contract with 100% coverageabove a variable deductible, related positively to the elasticity of medical expenditures withresp ect to the coverage rate.