1. (a) Solve the decision tree shown below.

(b) Create risk profiles and cumulative risk profiles for all possible strategies. Is one strategy stochastically dominant? Explain.

2. For the decision tree shown below:

(a) Determine the EVPI for chance event E only.

(b) Determine the EVPI for chance event F only.

(c) Determine the EVPI for both chance events E and F: that is, perfect information for both E and F is available before the decision is made.

(d) Do a sensitivity analysis on the probabilities for chance event F and explain/interpret your result.

3. A decision maker faces a risky gamble in which he/she may obtain one of five outcomes. The outcomes are labeled A, B, C, D, and E. Outcome A is the most preferred, and E is the least preferred. He/she has made the following three assessments:

(a) He/she is indifferent between having C for sure or a lottery in which he/she wins A with probability 0.5 or E with probability 0.5.

(b) He/she is indifferent between having B for sure or a lottery in which he/she wins A with probability 0.4 or C with probability 0.6.

(c) He/she is indifferent between these two lotteries:

1. A 50% chance at B and a 50% chance at D.

2. A 50% chance at A and a 50% chance at E.

What are U(A), U(B), U(C), U(D), U(E)?

4. Consider the following gamble:

Win $10 with probability 0.5

Win $40 with probability 0.5

(a) Using the above gamble, show that the logarithmic utility function, U(x) = ln (x), demonstrates decreasing risk aversion.

(b) Using the same reference gamble and a risk tolerance of $35, show that the exponential utility function, U(x) 1 - exp (-x/R), demonstrates constant risk aversion.