Insurance and social policy
You are taking a job with a 70% chance of working for a year and earning $60,000 but a 30% chance of being unemployed after a few months and earning only $20,000. Your utility is the square root of income (Utility = Y.5).
a) What is the expected value of your income from the job? What is your utility at that income?
Note that in EXCEL, the root function is “=X^.5” for the number X
b) What is your expected utility from your job? (Note: this is the weighted average of utility when the app succeeds and when it fails where the weight is the probability of success.)
c) What would be the price, P, of a risk-neutral insurance plan where you have a guaranteed income of a successful job and the insurance company breaks even without make profit? What would your utility be at your income after paying break-even premiums?
d) What is the maximum price you would be willing to pay? (Hint: what is the expected utility with and without insurance? The premium is the maximum amount that you would sacrifice to be guaranteed as much utility as without insurance.)
e) Considering your answer to part A, in general, why do people buy insurance? How can insurance companies profit? What happens to expected utility when people can buy insurance at a fair market price?
f) How else can insurance companies make profits? What is moral hazard and what is adverse selection. How do these affect insurance markets? Give examples from the marketing of automobile insurance. Would you expect markets with moral hazard and adverse selection to provide the optimal amount of car insurance at an efficient price?