Consider an investor with an initial wealth of $5 with the following utility function: for x 5 (a) Draw a sketch of the utility function U(x) labelling the main features. (b) Classify an investor with the utility function U(x) as risk-averse, risk-neutral or risk-loving. Justify your answer. (c) Suppose the investor is now offered the risky game X such that X= +$10 with probability 0.5 -$15 with probability 0.5 Compute the certainty equivalent and risk premium for the risky game X. (d) The investor is now offered another risky game Y such that Y = { +$20 with probability 0.5 -$30 with probability 0.5 Compute the certainty equivalent and risk premium for the risky game Y . For an investor with utility function U(x) which risky game X or Y is preferred? Justify your answer. (e) Compute the Absolute Risk Aversion coefficient and Relative Risk Aversion coefficient for this investor. If the investor's initial wealth were decreased from $5 to $1 would their appetite for risk increase or decrease? Justify your answer. Consider an investor with an initial wealth of $5 with the following utility function: for x 5 (a) Draw a sketch of the utility function U(x) labelling the main features. (b) Classify an investor with the utility function U(x) as risk-averse, risk-neutral or risk-loving. Justify your answer. (c) Suppose the investor is now offered the risky game X such that X= +$10 with probability 0.5 -$15 with probability 0.5 Compute the certainty equivalent and risk premium for the risky game X. (d) The investor is now offered another risky game Y such that Y = { +$20 with probability 0.5 -$30 with probability 0.5 Compute the certainty equivalent and risk premium for the risky game Y . For an investor with utility function U(x) which risky game X or Y is preferred? Justify your answer. (e) Compute the Absolute Risk Aversion coefficient and Relative Risk Aversion coefficient for this investor. If the investor's initial wealth were decreased from $5 to $1 would their appetite for risk increase or decrease? Justify your