Consider two lotteries, A and B. With lottery A, there is a 0.90 chance that you receive a payoff of $0 and a 0.10 chance that you receive a payoff of $400. With lottery B, there is a 0.50 chance that you receive a payoff of $30 and a 0.50 chance that you receive a payoff of $50.
a) Verify that these two lotteries have the same expected value but that lottery A has a bigger variance than lottery B.
b) Suppose that your utility function is U = √I + 500. Compute the expected utility of each lottery. Which lottery has the higher expected utility? Why?
c) Suppose that your utility function is U = I √ 500. Compute the expected utility of each lottery. If you have this utility function, are you risk averse, risk neutral, or risk loving?
d) Suppose that your utility function is U = (I √ 500)2. Compute the expected utility of each lottery. If you have this utility function, are you risk averse, risk neutral, or risk loving?