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 $2000 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 the logarithmic utility of wealth functions and current wealth of $10,000 each, will these individuals buy watch insurance at the premium calculated in part (a)? c) Given your results from part (b), is the insurance premium 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 maximum premiums for blue-eyed and brown-eyed people. What would be the premiums? How would these individuals maximum utilities compare to those in parts (b) and (c)?