FINC645 graded homework 1

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?