Question

A firm is considering two projects, A and B, with the probability distributions of profits presented in the first three columns of Table 1. Denote the profit of project A as random variable X, and its distribution functions as F(x). Denote the profit of Project B, as random variable Y, distribution function G(y).

       Table 1.

Column 1	Column 2 X	Column 3 Y
Profits ($1,000s)	Project A Probability (%)	Project B Probability (%)
$ 20	10	10
40	15	15
60	50	25
80	15	40
100	10	10

1. Use the mean – variance approach to compare prospects X and Y. Comment and explain which project dominates according to this criterion.
2. Use the probability criteria to compare prospects X and Y. Comment and explain which project dominates according to this criterion.
3. Assume the utility function of the decision – maker is u(w) = ln w, where w is wealth and ln is natural log. Use the expected utility approach to tell which project dominate according to this criterion.

2. Consider three risky prospects that is uniformly distributed: X ~ U(0, 10); Y ~ U(2, 8); and Z ~ U(2,15)

1. Use the mean – variance approach to compare prospects X, Y, and Z. Comment and explain which project dominates according to this criterion.
2. Use the probability criteria to compare prospects X, Y, and Z. Comment and explain which project dominates according to this criterion.
3. Assume the utility function of the decision – maker is u(w) = (w)^1/2, where w is wealth and ln is natural log. Use the expected utility approach to tell which project dominate according to this criterion.

Answer 1