help needed

2. (7 points) Risk Preferences Shortstop Hustles McGee and first baseman Strapping Q. Blastington are battling through the ranks of the minor league system of a Major League Baseball team. Faced with supplementing their diet and training regimen with steroids, the agents have expected utility functions over wealth, W, earned during their careers. McGee's expected utility function is U(W) = 15W - W2, and Blastington's expected utility function is U(W) = 15W + W2. There are two possible states of the world if they use steroids; W, = 8 is wealth in millions of USD if they get away with it, and W2 = 2 is wealth in millions of USD if they get caught. Assume there is a fifty percent chance of getting caught. DO YOU WANT TO KNOW THE TERRIFYING TRUTH OR DO YOU WANT TO SEE ME SOCK A FEW DINGERS? a. (1 point) Use calculus to clearly state the shape of McGee's VNM utility function. Also explain the economic intuition behind your results (e.g. the behavior explained by the first and second derivatives of McGee's VNM utility function with respect to wealth) b. (2 points) Calculate and compare McGee's utility of expected wealth against the expected utility of the weighted average of his possible wealth levels to determine whether McGee is risk averse or risk seeking. Fully graph and label this outcome, and comment on the economic intuition about the behavior you've calculated and modeled (hint: for your graph, utility is on the y-axis, and wealth is on the x-axis). c. (1 point) Use calculus to clearly state the shape of Blastington's VNM utility function. Also explain the economic intuition behind your results (e.g. the behavior explained by the first and second derivatives of McGee's VNM utility function with respect to wealth). d. (2 points) Calculate and compare Blastington's utility of expected wealth against the expected utility of the weighted average of his possible wealth levels to determine whether Blastington is risk averse or risk seeking. Fully graph and label this outcome, and comment on the economic intuition about the behavior you've calculated and modeled (hint: for your graph, utility is on the y-axis, and wealth is on the x-axis). e. (1 point) Calculate the Arrow-Pratt risk aversion coefficient for McGee and Blastington. Compare the two mathematically, and explain the difference between them with economic intuition concerning the behavior of each agent