Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has a 40% chance of wealth of $100,000 and a 60% chance of wealth of $2,000,000 as summarized by P(0.40, $100,000, $2,000,000).
a. What is the expected value of wealth?
b. Construct a graph of this utility function (recall your excel?).
c. Is this person risk averse, risk neutral, or a risk seeker?
d. What is this person's certainty equivalent for the prospect?
3. Consider two prospects.
Problem 1: Choose between
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Prospect A:
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$2,500 with probability
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0.33
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$2,400 with probability
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0.66
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Zero with probability
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0.01
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Prospect B:
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$2,400 with probability
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1.00
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Problem 2: Choose between
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Prospect C:
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$2,500 with probability
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0.33
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Zero with probability
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0.67
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Prospect D:
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$2,400 with probability
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0.34
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Zero with probability
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0.66
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It has been shown by Daniel Kahneman and Amos Tversky (1979, "Prospect theory: An analysis of decision under risk," Econometrica 47(2), 263-291) that more people choose B when presented with problem 1 and when presented with problem 2, most people choose C. These choices violate expected utility theory. Why?