Consider an individual with the utility function () = ()1/3. In other words, her utility equals the cubed root of her income. When healthy, her income is $8,000. There is a 25% chance that she will become sick and suffer a financial loss that decreases her income to $1,000. a. Show or describe how to show that the utility function exhibits diminishing marginal utility in income. b. What is the expected value of her income? c. What is her expected utility without insurance? d. Suppose an insurer offers this individual an insurance policy that charges her a premium of $1,250, and pays her $5,000 if she gets sick but $0 otherwise. i. Is this policy full? Show your work. ii. Is this policy fair? Show your work. e. If she is able to purchase a full, actuarially fair insurance policy, what is her utility? Compare her utility here to the expected utility she would attain from the plan offered in part d. f. What is the certainty equivalent for the income she faces when uninsured?