On behalf of your company, you are preparing a price bid to supply a fixed quantity of a good to a potential buyer. You are aware that a number of competitors also are eager to obtain the contract. The buyer will select the lowest bid. Your cost is $100,000. If yours is the winning bid, your profit is the difference between your bid and your cost. If not, your profit is zero. You are considering three possible bids:
Bid $110,000; the probability of winning is .9. Bid $130,000; the probability of winning is .5. Bid $160,000; the probability of winning is .2.
a. Assuming your company's aim is to maximize its expected profit, which bid should you submit?
b. In part (a), your cost is $100,000 for certain. Now suppose it is uncertain: either $80,000 or $120,000, with each cost equally likely. Will this fact change your bidding behavior in part (a)? Explain briefly.
c. Suppose it is possible to gain information about the cost so that you will know exactly what the cost will be ($80,000 or $120,000) before submitting a bid. Use a decision tree to find the value of this information.