# Suppose your company is considering three health insurance policies. The first policy requires no tests and covers all preexisting illnesses.

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 actually “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 .005. Calclulate the annual premium of the first policy. (hint: adverse selection.)b. If you don’t have insurance that covers HIV-related illness, the probability of getting HIV is 1%. If you have insurance that covers HIV-related illness, suppose tha the probability of getting HIV is 2%. Calculate the premium of the second policy. Show your calculations. (Hint: Moral Hazard.)c. In part b, suppose that 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?d. Calculate the premium of the third policy. Show your calculations
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