Q3). Risk and Return. Perhaps not surprisingly, the owner of Coyote Cotton Co. is none other than Wile E. Coyote, genius. Having departed Acme Manufacturing with a generous severance package, he started Coyote Cotton as a retirement activity but has recently taken interest in it as a viable financial venture. As such, Wile E. is, of course, interested in maximizing the amount of profit he can earn from his Cotton venture. However, Wile E. recognizes that he is risk averse, so knows that he has to maximize the expected utility of profit, and not just profit from his cotton farm. Suppose Wile E. has three options to choose from: (1) grow cotton in Maricopa county, (2) grow alfalfa, and (3) grow Durum wheat and sell to a local pasta cooperative. Suppose further that there are five possible "states of the world" in terms of some combination of markets and weather that result in anywhere from a "worst" profit scenario (bad weather, bad market) to "best" (good weather, good market) with the associated probabilities in the table below. Table 1. Annual Returns to Cropping Alternatives ($ profit / acre) Outcome Probability Cotton Alfalfa Durum Worst 0.1 200 100 0 Bad 0.2 300 250 200 OK 0.4 400 400 400 Good 0.2 500 550 600 Great 0.1 600 700 800 Assume that Wile E. Coyote has a power utility function with a coefficient of risk aversion of 0.4, so he is only moderately risk averse. (a) Find the expected utility of profit under each alternative crop. Which should he grow on the basis of this E[U] criterion?

(b) For each crop, verify that his utility function is concave, that is, the utility of expected profit lies above the expected utility of profit. What does this mean in intuitive terms? (c) Find the certainty equivalent for each crop. What does this value mean in terms of any risk management activities ie. insurance, that Wile E. may be considering?