ACIFIC insurer is offering a new term life insurance product covering premature death including AIDS. Assume that by law PACIFIC can use blood tests to identify preexisting condition of customers for AIDS. PACIFIC can decline life insurance coverage for all customers with HIV positive results (indicates a high possibility of AIDS). However, since blood tests are not free, insurers only use blood tests if the expected costs of misclassification exceed the cost of the test. Suppose that the cost of the blood test is $100 and the probabilities of death for HIV-infected males is 20 times the probability listed in 2001 CSO Mortality Table. Discount rate is 5 percent. (50 points)

1. What are the expected claim costs for a 30-year-old male applying for $ 1 00,000 of two- year term insurance if he is HIV negative? What are the costs if he is HIV positive?
2. Suppose that 10,000 30-year-old males apply for insurance. The insurer knows that 2 percent of them are HIV positive but needs the blood test to identify those specific applicants. Should the insurer give all applicants a blood test?

** The probabilities of dying for ages 1 to 84 are computed as follows:

q(x)=[2mg(x)] / [2 + mg (x)]