Private efforts, public test policy and insurance against pandemic health risks

In a pandemic, testing and personal protection efforts (e.g., masking) can help reduce contagion and ultimate health costs. These options are costly, however, and so individuals and policymakers must weight their costs against the benefits they provide. Insurance can help smooth the expenses associated with contagion. In this paper, we incorporate testing and effort decisions in an expected utility model. We analyze the effects of government's test and individual's efforts on consumer welfare with and without insurance. We first find that test and efforts without insurance are not necessarily substitutes in the Edgeworth-Pareto sense, while those with insurance are substitutes. Second, insurance enhances consumer welfare by fully hedging health risks. Third, test and efforts with insurance can be higher or lower than those without insurance, as the effects of insurance on the efficiencies of test and efforts are mixed. Fourth, we derive necessary and sufficient conditions for test and efforts with insurance to increase with a change in parameter values such as baseline contagion rate, infection probability and health loss size.