9.4 Blue-eyed people are more likely to lose their expensive watches than are brown-eyed people. Specifically, there is an 80 percent probability that a blue-eyed individual will lose a

$1,000 watch during a year, but only a 20 percent probability that a brown-eyed person will.

Blue-eyed and brown-eyed people are equally represented in the population.

a. If an insurance company assumes blue-eyed and brown-eyed people are equally likely to buy watch-loss insurance, what will the actuarially fair insurance premium be?

b. If blue-eyed and brown-eyed people have logarithmic utility-of-wealth functions and current wealths of $10,000 each, will these individuals buy watch insurance at the premium calculated in part (a)?

c. Given your results from part (b), will the insurance premiums be correctly computed?

What should the premium be? What will the utility for each type of person be?

d. Suppose that an insurance company charged different premiums for blue-eyed and brown-eyed people. How would these individuals’ maximum utilities compare to those computed in parts

(b) and (c)? (This problem is an example of adverse selection in insurance.)