Esperanza has been an expected utility maximize ever since she was five years old. As a result of the strict education she received at an obscure British boarding school, her utility function over returns on assets u(R) is strictly increasing and strictly concave u(R) = R1/2. Now at the age of thirty something, Esperanza is evaluating an asset whose return (R) is a random variable that takes on one of two possible outcomes: good (G), or poor (P). The returns for each of the two outcomes are as follows: RG = $4900, RP = 2500. The probability of each outcome is: Pr(G) = .475, Pr(P) = .525.

1. What is the expected return of this asset? What is Esperanza's expected utility? What is her certainty equivalent?

2. Provide an extremely well-labelled graph of Esperanza's utility function that includes your results from part (a). (Hint: You may wish to graph a modification of the utility function given in part (a) that does not change the representation of Esperanza's preferences. If you utilize this hint make clear the modification that you are choosing.)

3. Suppose that Esperanza can purchase insurance that guarantees her a return of $4900 regardless of the return on the asset. How much would this full insurance cost if its price is actuarially fair? How much of a premium over the price of actuarially fair insurance would Esperanza be willing to pay for this full insurance?