What is the calculation process for this question?

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 Worst Bad OK Good Great Probability 0.1 0.2 0.4 0.2 0.1 Cotton 200 300 400 500 600 Alfalfa 100 250 400 550 700 Durum 0 200 400 600 800 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 on the basis of this E[U] criterion? grow The expected utility of profit is the weighted average utility of profit from each possible state of the world. For cotton, the E[U] is $60.10, for alfalfa it is $59.26, and $56.96 for Durum wheat. Based on the expected utility criterion, therefore, he should grow cotton. (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? To find the utility of expected profit, just calculate the average profit level, then substitute this value into the utility function. In this way, we find that the utility of expected profit for each crop is the same ($60.69), because the average (expected) profit is the same. Comparing these values to the expected utility numbers in the table above verifies that the utility of expected profit is indeed greater than the expected utility of profit. Therefore, the utility function is concave. (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? The certainty equivalent value (CE) is found by inverting the expected utility calculation, that is, by substituting the E[U] value back into the original equation and solving for the value of profit that results. For cotton, the CE value is $393.66, for alfalfa it is $384.39 and for Durum is $359.12. Therefore, the higher value of CE confirms our conclusion in part (a) above, and suggests that the farmer would be willing to pay about $6.34 for a cotton- yield insurance policy that would indemnify him back to his $400 expected profit level. For the other crops, the likely insurance premiums are $15.61 and $40.88 for alfalfa and Durum wheat, respectively.