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# Fair Insurance Premium Under Different Circumstances

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AIDS INSURANCE

Suppose your company is considering three health insurance policies. The first policy requires no tests and covers all preexisting illnesses. The second policy requires that all covered employees test 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 risk averse. An individual with the HIV virus requires, on average, \$100,000 worth of medical care each year. An individual without the virus requires, on average, \$500 worth of medical care each year.

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 not 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 you calculations. (hint: moral hazard)
c. In question (b), suppose the insurance company wants to encourage low-risk behavior by individuals who have insurance. On average, it "costs" individuals \$100 to engage in low-risk behavior. Assume that if people get HIV, they pay the deductible; and if they do not get HIV, they do not pay the deductible. How high must the deductible be to encourage low-risk behavior?