Microeconomics question. Expected utility

Consider an investor with utility of wealth v (w) = . She can purchase a stock that pays 1 in state 1 and 9 in state 2 at date 1. a. (1 mark) Is the investor in question risk-averse, risk-neutral or risk-loving? Your answer should be based on the information about '0 (w) = Jr}. b. (2 marks) Calculate the absolute risk aversion coefcient (ARA) for this in- vestor. Your answer should be the function of w. Is this investor DARA, CARA or IARA? c. (1 mark) Suppose the investor believes that states 1 and 2 are equally likely and think of the above asset as a lottery. What is the certainty equivalent of such lottery for this investor? d. Now suppose the investor has wealth to and she can purchase any quantity of the above stock at 3 dollars apiece and hold the rest of her wealth in cash. (Cash holding is equivalent to buying a bond that costs 1 and pays 1 in either state). (1 mark) Denoting the wealth levels in states 1 and 2 with 3/1 and :92, what is the investor's expected utility? (1 mark) Denoting the amount of stock with a and the amount of cash with (I, what is the investor's budget constraint? 6. (1 mark) If the investor holds a of stock, what wealth yl can she reach in state 1? Your answer should express yl in terms of a and w. (1 mark) If the investor holds a of stock, what wealth 3,2 can she reach in state 2? Your answer should express 312 in terms of the same a and w. (1 mark) Derive the connection between yl and y2 expressing away a. f. (5 marks) What is the investor's demand for the stock as a function of his wealth as? Your answer should be the function that connects a to w. Approach this formally via the Lagrange method using as objective the expected utility from d. and as a constraint the connection between yl and '92 from c. g. (1 mark) Is your a(w) increasing or decreasing in to? Explain this given your answer in b