3. Suppose Alice has recently opened a bakery. She is concerned that the machines she has bought will break. If they break, her revenue for the next year will drop to WLoss = 250 (in hundreds of dollars). If they don't break, her revenue will be WNo loss = 750. The probability that the machines will break is p = 0.10. Alice's Bernoulli utility function is: v(W) = W1/2 a) What is the expected value of Alice's revenues? What is Alice's expected utility if she does not purchase insurance? What is Alice's utility for the expected value of her revenues? b) Is Alice risk-averse, risk-loving, or risk-neutral? Why? c) Draw a graph showing Alice's risk attituded) What money would Alice need to receive, with certainty, to be as well-off as she is simply facing the risk that her machines might break? What is this amount called? e) Suppose that an insurance company is willing to charge q = 0.15 dollars for each dollar of coverage in case of machine failure for local businesses. If Alice decides to buy Z hundreds of dollars worth of coverage, her expected utility would be given by: EUinsurance = (1 - p)v(WNO Loss) + pv(WLoss) Since Alice is purchasing insurance, her final wealth in the two states of nature will be: WNOLOSS = 750 - 0.15 * Z and WLoss = 250 - 0.15 * Z + Z Find Alice's optimal amount of coverage, Z*. How does this amount compare to the size of her potential loss? Will Alice overinsure, underinsure, or fully insurance (without going above)? Is the insurance actuarially fair, unfair, or overfair?f) Suppose the firm decides to lower its price to q = 0.10. What is Alice's new optimal amount of coverage? Does Alice under, over, or fully insure (without going over)? Is the insurance actuarially fair, unfair, or overfair? g) Would actuarially fair insurance ever happen in real life? What are the conditions necessary for actuarially fair insurance to be charged