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20-3 AIDS Insurance

20-3 AIDS InsuranceSuppose your company is considering three health insurance policies. The first policy requires notests and covers all preexisting illnesses. The second policy requires that all covered employeestest negative for the HIV virus. The third policy does not cover HIV- or AIDS-related illnesses.All insurance policies are priced at their actuarially “fair” value. All individuals are slightly riskaverse. An individual with the HIV virus requires, on average, $100,000 worth of medical careeach year. An individual without the virus requires, on average, $500 worth of medical care eachyear. a. Suppose that the incidence of HIV in the population is 0.005. Calculate the annual premium of the first policy. (Hint: Adverse selection.) b. If you don’t have insurance that covers HIV-related illnesses, the probability of getting HIV is 1%. If you have insurance that covers HIV-related illness, suppose that the probability of getting HIV is 2%. Calculate the premium of the second policy. Show your calculations.(Hint: Moral hazard.)

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