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 illness. All insurance policies are priced at their actuerially "fair" value. All individuals are slightly risk averse. An individual with the HIV virus requires $100,000 worth of medical care each year. An individual wihtout the virus on average $500 worth of medical care each year.
If you don't have insurace that covers HIV related illnesses, the probability of getting HIV is 1%. If you have insurance that covers HIV related illness, suppose the the probability of getting HIV is 2%. Calculate the premium of the second policy.