You have a utility function given by U = 2I + 10√I. You are considering two job opportunities. The first pays a salary of $40,000 for sure. The other pays a base salary of $20,000, but offers the possibility of a $40,000 bonus on top of your base salary. You believe that there is a 0.50 probability that you will earn the bonus.
a) What is the expected salary under each offer?
b) Which offer gives you the higher expected utility?
c) Based on your answer to (a) and (b), are you risk averse?