Rescale the utility function for Director A in Problem 14.15 so that it ranges between 0 and 1. That is, find constants a and b so that when you multiply the utility function by a and then add b, the utility for $10.30 billion is 1 and the utility for $0 is 0. Graph the rescaled utility function and compare it to the graph of the original utility function. Use the rescaled utility function to solve the Texaco-Pennzoil decision tree. Is the optimal choice consistent with the one you found in Problem 14.15?
Problem 14.15
Of course, Liedtke is not operating by himself in the Texaco-Pennzoil case; he must report to a board of directors. Table 14.6 gives utility functions for three different directors. Draw graphs of these. How would you classify each director in terms of his or her attitude toward risk? What would be the strategies of each? (That is, what would each one do with respect to Texaco€™s current offer, and how would each react to a Texaco counteroffer of $3 billion? To answer this question, you must solve the decision tree €” calculate EUs €” for each director.)
Table 14.6

Utility Payoff (Billions) $10.3 $5.0 S3.0 $2.0 Director A Director B Director C 42.05 23.50 16.50 13.00 6.00 2 100 30 15 2.9 1.0