Question 5: (30 points) Suppose that Jeffrey has initial wealth $10,000, but, before he consumes it, he is subject to the following health risk (these events are mutually exclusive): Required Medical Payment Probability $1000 10% $500 20% An insurance agent offers J eifrey the option to buy partial insurance, wherein he can pay a premium 0:2 to insure against proportion a of any medical payment that he needs to make (e.g., if he needs to make the $1000 payment, the insurance company would pay $1000a). Jeffrey is restricted to choosing a E [0, 1]. (a) Suppose Jeffrey is an expected utility maximizer with initial wealth is and utility function u(a:). Provide an equation that reects his utility as a function of a and z. (b) Suppose further that Jeffrey has utility function u(:v) = 3:. Which a will he choose? Explain your answer. Note: Your answer might depend on 2:. (c) Suppose instead that Jeffrey has initial wealth to but he evaluates gambles according to prospect theory with probabilityweighting function 77(1)) and value function v(:.-:). Provide an equation that reects his prospective utility as a function of a and 2. (d) Suppose further that Jeffrey has probability-weighting function is 7r(p) = p and value function _ as ifac20 \"(3') Am ifzSD. Which a will he choose? Explain your answer. Note: Your answer might depend on 2