Emma is an expected utility maximizer. Her utility function over an amount of money x is u(x) = x 1 3 . (a) Graph Emma's utility function. (b) Suppose Emma has a lottery ticket that pays $100 with probability 1 2 and $0 with probability 1 2 . What amount of money $x would make Emma indifferent between keeping the lottery ticket and the sure amount $x? You must show the reasoning behind your answer to get credit. (c) Suppose that Emma's utility function is instead u(x) = x 2 3 . What amount of money $x would make Emma indifferent between the lottery ticket in (b) and the sure amount $x? You must show the reasoning behind your answer to get credit. (d) Suppose that Emma's utility function is instead u(x) = x 3 2 . What amount of money $x would make Emma indifferent between the lottery ticket in (b) and the sure amount $x? You must show the reasoning behind your answer to get credit. (e) Compare the answers to questions (b), (c) and (d) with the expected value of the lottery. A person is said to be risk (averse, neutral, seeking) if the amount they are willing to receive for certain in exchange for a lottery is (smaller, equal, larger) than the expected value of the lottery. Which function(s) represents risk averse, neutral and seeking preferences, if any? You must show the reasoning behind your answer to get credit