An investor has $25,000 in assets and faces a difficult choice between two investments. If he invests in the first opportunity there is a 70% chance that he will increase his assets by $75,000 and a 30% chance that he will increase his assets by $20,000. If he invests in the second option there is a 40% chance that he will increase his assets by $150,000 and a 60% chance that he will increase his assets by $5,000.
Please show all calculations.
(A) Construct a decision tree to help the investor make his decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities.
(B) What is the best choice for the investor? Why?
(C) Suppose that investor has an exponential utility function for changes in wealth (x) with a risk tolerance parameter equal to $60,000. Which investment opportunity will he prefer in this case? What is his certainty equivalent?