=9.40. You are given the following payoff table:

Outcome Probability Receive $10,000 0.3 Receive $30,000 0.7 State of Nature Alternative S1 S2 A1 25 36 A2 100 0 A3 0 49 Prior probability p 1 p Outcome Probabilities Receive Treatment No Treatment for Disease A Outcome A B A B Die 0.2 0.5 0 1.0 Survive with poor health 0.8 0.5 0.5 0 Return to good health 0 0 0.5 0

a. Assume that your utility function for the payoffs is U(x) = x. Plot the expected utility of each decision alternative versus the value of p on the same graph.

For each decision alternative, find the range of values of p over which this alternative maximizes the expected utility.

A

b. Now assume that your utility function is the exponential utility function with a risk tolerance of R 50. Use TreePlan to construct and solve the resulting decision tree in turn for p 0.25, p 0.5, and p 0.75.