Question: Utility functions need not relate to dollar values. Here is a problem in which we know little about five abstract outcomes. What is important, however, is that a person who does know what \(A\) to \(E\) represent should be able to compare the outcomes using the lottery procedures we have studied.

A decision maker faces a risky gamble in which she may obtain one of five outcomes. Label the outcomes A, B, C, D, and E . A is the most preferred, and \(E\) is least preferred. She has made the following three assessments.

- She is indifferent between having \(C\) for sure or a lottery in which she wins \(A\) with probability 0.5 or \(E\) with probability 0.5.

- She is indifferent between having \(B\) for sure or a lottery in which she wins \(A\) with probability 0.4 or \(C\) with probability 0.6.

- She is indifferent between these two lotteries:

i: A 50% chance at \(B\) and a 50% chance at \(D\)

ii: A 50% chance at \(A\) and a 50% chance at \(E\)

What are \(\mathrm{U}(A), \mathrm{U}(B), \mathrm{U}(C), \mathrm{U}(D)\), and \(\mathrm{U}(E) ?\)

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