An individual with wealthwis deciding how much to invest in the stock market. Denote the investment byz.With probabilitythe price of this stock will go up byr100%, and with probability(1)the price of this stock will go down byr100%. The current price of the stock is$1.

(a) What is her total wealth when she makes a profit on her investment? What is her total wealth when she makes a loss on her investment?

Her Bernoulli utility function is given by

u(x) =x^, (0,1)

(b) What is her expected utility from the investment levelz? [Hint: Each lottery in this case is denoted by a different level ofzbecause nothing else varies across lotteries. So we can think of the expected utility as a function ofz.]

(c) What is her expected utility maximizing level of investment in terms of,wandr?

(d)If =0.5, how much does she invest? What if =1?

(e) Suppose the parameter values are= 0.5,=4andr= 1. How much does she invest?

(f) What is the certainty equivalent and risk premium for the lottery corresponding toz? What is the risk premium?

(g) What happens to the risk premium as1? Provide an intuition for this

result?