3. Risk and Insurance Suppose a local soccer team signs a player for their upcoming season. However the player is currently undergoing surgery and there is 40 % chance that the player will not be able to compete in the next season. If the player recovers and is able to compete the team will make a profit of $ 100. However, if the player does not recover the team will end up making only $ 60 in profit.

(a) Find the expected profit for the team.

(b) Lets assume that the team is risk averse and has a utility function U() = ln(). Find the expected utility for the team.

(c) Find the certainty equivalence (CE), a certain profit level that will give the same utility as the uncertain case.

(d) Now suppose there is an insurance available to the team that will pay the difference in profit i.e. $ 40 if the player is not able to compete for a premium of $ 25. In other words the team will earn a profit of $ 75 regardless of whether or not the player is injured. Should the team buy the insurance?