Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 32

This problem will help you understand why Application 4.6: The Equity Premium Puzzle" really is a puzzle. Suppose that a person with $100,000 to invest believes that stocks will have a real return over the next year of 7 percent. He or she also believes that bonds will have a real return of 2 percent over the next year. This person believes (probably contrary to fact) that the real return on bonds is certain-an investment in bonds will definitely yield 2 percent. For stocks, however, he or she believes that there is a 50 percent chance that stocks will yield 16 percent, but also a 50 percent chance they will yield -2 percent. Hence stocks are viewed as being much riskier than bonds.
a. Calculate the certainty equivalent yield for stocks using the three utility functions in Problem 4.6. What do you conclude about whether this person will invest the $100,000 in stocks or bonds?
b. The most risk-averse utility function economists usually ever encounter is U(I) = -I -10. If your scientific calculator is up to the task, calculate the certainty equivalent yield for stocks with this utility function. What do you conclude?
(Hint: The calculations in this problem are most easily accomplished by using outcomes in dollars-that is, for example, those that have a 50-50 chance of producing a final wealth of $116,000 or $98,000. If this were to yield a certainty equivalent wealth of, say, $105,000, the certainty equivalent yield would be 5 percent.)