10. Assume there are two states of the world: one healthy, in which there is no medical spending, and one sick, in which there is medical spending. Let p be the probability of being sick; assume p = 1/2. Let Jay's utility function over income (I) be dened as follows: U(I) = log (0.051 + 1). If Jay is healthy, Jay's income is In = $500. If Jay is sick, Jay's income is 15= $0. a. What is Jay's expected income? b. What is Jay's utility from his expected income? What about his utilities in the healthy and sick states, respectively? c. Now, calculate Jay's expected utility from the uncertainty he faces due to sickness (Hint: This is just the expected utility of a lottery that pays $500 with probability 1/2 and $0 with probability 1/2). d. Represent Jay's situation graphically using the numbers from parts (a) (c). (Hint: plot utility on the y-axis, and income on the x-axis). e. Is Jay risk-averse? Explain. f. Propose an insurance contract that is both full and actuarially fair in Jay's situation. Should Jay buy it? Why