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’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.)
264 SECTION V UNCERTAINTY
c. In Question 20-3b, 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?
d. Calculate the premium of the third policy. Show your calculations.
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