Robert F. Graboyes
When the value of a medical treatment differs across individuals, it may be socially beneficial to treat some, but not all, patients. If individuals are ignorant of their health status ex ante, they should be willing to purchase insurance fully covering treatments for high-benefit patients (Hs) and denying treatment for low-benefit patients (Ls). But if prognoses are observable but not verifiable, insurers may have trouble denying care to Ls. Deductibles force Ls to reveal their status by imposing a marginal cost on treatment, but at a price of incomplete risk-sharing. Lump-sum indemnities can similarly induce Ls to forgo treatment but are rare in health insurance markets. They were once more common and remain so in non-health markets. This paper reviews the potential for health insurance indemnities. We model an insurance market for a single illness and derive conditions determining the relative efficiency of indemnities and deductibles.
We define a disease that strikes randomly, where there is no private information, and where benefits are measured as cure rates. These and other assumptions yield several rules of thumb: It is never socially or (ex ante) privately beneficial to offer an indemnity larger than the cost of treatment. The optimal indemnity is always larger than the optimal deductible. If Ls outnumber Hs, the best deductible contract always yields higher welfare than the best indemnity contract. As the Ls' cure rate approaches 0, the choice of indemnity or deductible depends entirely upon the relative numbers of Hs and Ls.