When Adam's annual income is $5,000, $5,500, $6,000, $6,500, $7,000, $7,500, $8,000,his corresponding utility would be 495, 655, 795, 905, 995, 1065, 1110, respectively.

(36 points)

(a)SketchAdam's utility function (money on the x-axis and utility on the y-axis). Is Adam risk-averse, risk-neutral, or risk-loving? (5 points)

(b)Adam's current income is $8,000. However, Adam knows that there is a 1/3 chance that his hours will be cut on his job and he will make only $5,000 rather than $8,000. What is Adam's expected income? (6 points)

(c)Suppose that there is an insurance contract that pays Adam $3000 if his hours are cut. The premium is P. What is the Adam's expected utility when paying for the insurance? What is his expected utility when not paying for the insurance? (12 points)

(d)Calculate the maximum premium that Adam is willing to pay for this insurance. [Hint: The maximum Adam is willing to pay would make him indifferent between having the insurance and not. Adam will also equalize the marginal value of a dollar across the various possible outcomes.] (13 points)