One method for deciding among various investments involves the concept of expected utility. Economists describe the importance of various levels of wealth by using utility functions. For instance, in most cases, a single dollar is more important (has greater utility) for someone with little wealth than for someone with great wealth. Consider two investments, say, Investment A and Investment B. Measured in thousands of dollars, suppose that Investment A yields 0, 1, and 4 with probabilities 0.1, 0.5, and 0.4, respectively, and that Investment B yields 0, 1, and 16 with probabilities 0.5, 0.3, and 0.2, respectively. Let Y denote the yield of an investment. For the two investments, determine and compare
a. The mean of Y, the expected yield.
b. The mean of √Y, the expected utility, using the utility function u(y) =√y. Interpret the utility function u.
c. The mean of Y3/2, the expected utility, using the utility function v(y) = y3/2. Interpret the utility function v.