The Post Office uses two freight carriers, Federal Parcel and Emery Express, to carry mail between New York and Boston. Federal Parcel has 30% of this business, and Emery Express has 70%. The Post...

The Post Office uses two freight carriers, Federal Parcel and Emery Express, to carry mail between New York and Boston. Federal Parcel has 30% of this business, and Emery Express has 70%. The Post Office is interested in signing an exclusive contract with one of the carriers to handle the mail between the cities. Federal Parcel is considering bidding either $0.02, $0.04, or $0.06 per ounce as the fee charged the Post Office. Emery Express is considering bidding either $0.02, $0.05, or $0.06 per ounce as the fee charged the Post Office. The carrier who submits the lower bid will get the contract; if both bids are the same, the Post Office will use the carriers to carry an equal amount of mail.

The following table describes the change in market share that Federal Parcel will experience as a function of the amount that the two carriers bid.

a. What is Federal Parcel’s optimal strategy if it wishes to maximize its expected change in market share?

 b. Suppose that Federal Parcel estimates that the total weight the Post Office will be sending between the two cities this year will be 1.5 million pounds. Federal Parcel estimates that serving this route will cost it a fixed amount of $20,000 plus $0.01 per ounce. If Emery Express is believed to be equally likely to bid $0.02, $0.05, or $0.06 per pound, what should Federal Parcel’s bid be in order to maximize its expected profit?