Response to the following problem:
Two oil brokerage firms, Murphy Company and Sardon Brothers, supply heating oil to 10 oil delivery companies in northern New Jersey. Each day the two brokerage firms fax their offering prices to these delivery companies, and the delivery companies purchase their daily needs from the firm that has the cheapest offering price. (If both brokerage firms have the same offering price, Murphy Company tends to get 40% of the business, while Sardon Brothers gets 60%.) The two oil brokers' offering price is pegged at $0.01, $0.02, or $0.03 above the New York spot price of Number 2 fuel oil. The management science analyst working for Sardon Brothers believes that the following payoff table holds regarding the expected daily profit earned by Sardon Brothers based on its and Murphy Company's offering price.
The management scientist also believes that Murphy Company will use an offering price of Spot + $.0.01 with probability 30% and an offering price of Spot + $0.02 with probability 50%.
a. If the company's objective is to maximize its expected daily profit, what should Sardon Brothers use as an offering price?
b. What is the most that Sardon Brothers should pay for information that would improve its probability estimates for Murphy Company's pricing strategy?
c. Suppose Sardon Brothers uses the following utility function: U(x) = 2(x+600)/,60° - 1. (For example, the utility of a $200 profit to the company equals 2(200+600)/1600 -1 = 2(1/2) = 1.41 - 1= .41.) Would you characterize Sardon Brothers as risk averse, risk neutral, or risk loving?
d. Using the utility function given in part (c), what offering price should Sardon Brothers use for the oil if its objective is to maximize its expected utility?