8) Michael, a farmer, has an initial wealth of 100. He can invest all his wealth in planting a new crop, which has a 50:50 chance of succeeding. If the crop succeeds, his final wealth will be 196, but if it fails, his final wealth will be 25. Michael's preferences over monetary outcomes, y, are summarised by the utility function: U(y) = 20y1/2 a. Find the certainty equivalent of Michael's risky opportunity and explain why Michael will prefer not to plant the new crop. [10 points] b. Peter, also a farmer, has the same preferences and initial wealth as Michael. Peter suggests to Michael that they each invest 50 in planting the new crop in Michael's farm and divide the yield equally. Should Michael accept Peter's offer? Illustrate and explain Michael's choice in a diagram. [10 points] c. Suppose instead Peter can use his wealth to plant the new crop in his own farm, and has the same chances of success and failure as Michael, though crop success or failure in each farm is independent. Now Peter suggests they each plant the new crop on their respective farms and divide total proceeds equally between them. Should Michael accept Peter's offer? Explain your answer. [10 points] d. Suppose Michael's initial wealth were 200. Show he is now willing to plant the new crop in his farm. Use the Arrow-Pratt coefficient of absolute risk aversion to explain why Michael displays less risk averse behaviour when he gets wealthier. [10 points]