Insurer testing for HIV provides a good example of how the cost of gathering information about mortality risk can sometimes cause insurers not to gather information. Insurers commonly use blood tests to identify HIV (if permitted by law). 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 Table 15.3.
a. What are the expected claim costs for a 30 -year-old male applying for $$\$ 100,000$$ of one-year term insurance if he is HIV negative? HIV positive?
b. Suppose that 1,00030 -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?