2. Consider a one period choice problem with four equally likely states of the world at the end of the period. The consumer maximizes expected utility of end-of-period wealth. The current wealth must be invested in a single financial asset today. The consumer has three assets to choose from. All three assets have a current price equal to the current wealth of the consumer. The assets have the following end-of-period values: 1 state 1 2 3 4 probability 0.25 0.25 0.25 0.25 asset 1 100 100 100 100 asset 2 81 100 100 144 asset 3 36 100 100 225 (a) What asset would a risk-neutral individual choose? (b) What asset would a power utility investor, u (W) = EW1- choose if y = 0.5? If y = 2? If y = 5? (C) Now assume a power utility with y = 0.5. Suppose the individ- ual could obtain a perfect signal about the future state before she makes her asset choice. There are thus four possible sig- nals, which we can represent by $1 = {1}, s2 = {2}, $3 = {3}, and s4 = {4}. What is the optimal asset choice for each sig- nal? What is her expected utility before she receives the signal, assuming that the signals have equal probability? (d) Now suppose that the individual can receive a less-than-perfect signal telling her whether the state is in si = {1,4} or in 52 {2,3}. The two possible signals are equally likely. What is the expected utility of the investor before she receives the signal? 2. Consider a one period choice problem with four equally likely states of the world at the end of the period. The consumer maximizes expected utility of end-of-period wealth. The current wealth must be invested in a single financial asset today. The consumer has three assets to choose from. All three assets have a current price equal to the current wealth of the consumer. The assets have the following end-of-period values: 1 state 1 2 3 4 probability 0.25 0.25 0.25 0.25 asset 1 100 100 100 100 asset 2 81 100 100 144 asset 3 36 100 100 225 (a) What asset would a risk-neutral individual choose? (b) What asset would a power utility investor, u (W) = EW1- choose if y = 0.5? If y = 2? If y = 5? (C) Now assume a power utility with y = 0.5. Suppose the individ- ual could obtain a perfect signal about the future state before she makes her asset choice. There are thus four possible sig- nals, which we can represent by $1 = {1}, s2 = {2}, $3 = {3}, and s4 = {4}. What is the optimal asset choice for each sig- nal? What is her expected utility before she receives the signal, assuming that the signals have equal probability? (d) Now suppose that the individual can receive a less-than-perfect signal telling her whether the state is in si = {1,4} or in 52 {2,3}. The two possible signals are equally likely. What is the expected utility of the investor before she receives the signal