Scottie is a professional basketball player who plans to play for three more years. During the summer, he has been offered two different contracts by his current team. The first is a three-year guaranteed contract (meaning he gets paid even if he is injured or cut from the team) that would pay him $5 million per year. The second contract is a one-year guaranteed contract that would pay him $3 million, after which he could become a "free agent" and negotiate his next contract with any team in the league. Scottie, being a good business person, has commissioned a detailed statistical study of past basketball performances by similar players, and concluded that, if he accepts the one-year contract:
i. There is a 25% chance that he will be injured during the upcoming season and will never play again; and
ii. There is a 75% chance that he will play well enough this upcoming year to receive a two-year guaranteed contract for $7 million per year.
Scottie decides to accept the one-year contract.
a. What do you know about his risk preferences, given the choice that he has made? Explain how you know this both in words and by using a utility of wealth graph similar to the one used in class.
b. What can you say for sure about the relative magnitude of Scottie's certainty equivalent?