1. Why might some prefer a prix fixe (fixed price) dinner costing about the same as an à la carte one (where you pay individually for each item)? (Assume the food is identical.)
2. 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
| Prospect A: | $2,500 with probability | 0.33 |
| $2,400 with probability | 0.66 | |
| Zero with probability | 0.01 | |
| Prospect B: | $2,400 with probability | 1.00 |
Problem 2: Choose between
| Prospect C: | $2,500 with probability | 0.33 |
| Zero with probability | 0.67 | |
| Prospect D: | $2,400 with probability | 0.34 |
| Zero with probability | 0.66 |
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?