Suppose that you have a utility function given by the equation U = √50I. Consider a lottery that provides a payoff of $0 with probability 0.75 and $200 with probability 0.25.
a) Sketch a graph of this utility function, letting I vary over the range 0 to 200.
b) Verify that the expected value of this lottery is $50.
c) What is the expected utility of this lottery?
d) What is your utility if you receive a sure payoff of $50? Is it bigger or smaller than your expected utility from the lottery? Based on your answers to these questions, are you risk averse?