Ray is planning to go to a 1-year graduate school program, but is worried he may fail out. He'd like to buy insurance to cover his tuition debt if he doesn't complete the program. His current wealth is $280,900. His utility over wealth is: U(w) = sqrt(w). Tuition costs $30,900. a) Give Ray's payoff matrix. b) Graph Ray's utility over wealth, indicating the possible wealth and utility outcomes under each state of the world. Plot the set of bundles corresponding to this gamble at different likelihoods of a loss. c) Ray believes that there is a 20% likelihood that he will not complete the program. What is his expected value of and expected utility in this scenario (i.e., absent insurance). Show your work, and label these values on your figure above. d) Find Ray's certainty equivalent, and label it on your figure above. Show e) A firm offers Ray actuarially fair insurance covering his tuition if he fails out at a premium of $5000. i. If Ray is correct about his own likelihood of failing, is he more or less likely to fail than the average person who purchases this insurance? Explain. ii. Will Ray buy this insurance? Explain why or why not. your work. Ray is planning to go to a 1-year graduate school program, but is worried he may fail out. He'd like to buy insurance to cover his tuition debt if he doesn't complete the program. His current wealth is $280,900. His utility over wealth is: U(w) = sqrt(w). Tuition costs $30,900. a) Give Ray's payoff matrix. b) Graph Ray's utility over wealth, indicating the possible wealth and utility outcomes under each state of the world. Plot the set of bundles corresponding to this gamble at different likelihoods of a loss. c) Ray believes that there is a 20% likelihood that he will not complete the program. What is his expected value of and expected utility in this scenario (i.e., absent insurance). Show your work, and label these values on your figure above. d) Find Ray's certainty equivalent, and label it on your figure above. Show e) A firm offers Ray actuarially fair insurance covering his tuition if he fails out at a premium of $5000. i. If Ray is correct about his own likelihood of failing, is he more or less likely to fail than the average person who purchases this insurance? Explain. ii. Will Ray buy this insurance? Explain why or why not. your work