A game show contestant has the following power utility function: u(w) = 173 Y WY where y = 0.5 and w is the contestant's wealth in 000s. a) Test whether the utility function satisfies the properties of non-satiation and diminishing marginal utility of wealth. Prize () 100,000 10,000 1,000 b) Derive the contestant's coefficients of absolute and relative risk aversion. For which kinds of investment problems is this type of utility function most suitable? Explain your answer. c) The contestant has initial wealth of 10,000 and is faced with two alternatives: accept a fixed cash sum of 20,000 with certainty or enter the following lottery: Probability 0.1 0.5 0.4 Using the utility function provided at the start of the question, determine which option the contestant should choose. d) Using the same information as in part c), calculate the maximum risk premium that the contestant is willing to pay in order to receive a fixed cash sum with certainty.