After rigorous field survey, the insurance company finds that the probability to have cancer is 10% on average. The company offers a fixed rate policy where the premium is $1,000. Reimbursement is $9,000, which is the amount of medical expense you must pay if you get cancer. Suppose there are two types of customers: heavy smoker, who has a probability of 15% of getting cancer. Nonsmoker, who has a probability of 5% of getting cancer.

A) Assuming utility function is ?? = ?? , where x is the amount of money. Calculate utilities for both heavy smoker and nonsmoker. Who will be buying the insurance?

B) What is the expected profit for the insurance company?