You have developed a new app that has a 30% chance of succeeding and earning $1,000,000, and a 70% chance of earning nothing. Your utility is the cube root of income (Utility = Y1/3); you have $1,000,0001/3 happiness if your app succeeds but 01/3 happiness if it fails.
a)  What is the expected value of your app? What is your utility at that income?
Note that in EXCEL, the cube root function is "=X^.3333" for the number X


b What is your expected utility from your app? (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 app and the insurance company would break even but make no profit?
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) Define moral hazard and adverse selection. How do these affect health insurance markets? Would you expect markets with moral hazard and adverse selection to provide the optimal amount of long-term care insurance at an efficient price?