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Consider the example we discussed in class. In particular, assume there are two states of the world: state 1 (healthy, no medical spending) and state 2 (sick, medical spending). Also, let p-probability of being sick; assume p=1/2. Let Jay's utility function over income (I) be defined as U (1) = log (0.051 + 1). If state 1 occurs, Jay's income is 1 = $500. If state 2 occurs, Jay's income is Iz = $0. a. What is Jay's expected income? b. What is Jay's utility from his expected income? What about his utilities in states 1 and 2, respectively? c. 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 scenario graphically using the numbers from (a) - (c). (Hint: plot utility on the y-axis, and income on the x-axis). e. Is Jay risk-averse? Why or why not? f. Propose an insurance contract that is full and actuarially fair. Should Jay buy it? Why