A town wants to build a new bridge. Construction firms will submit sealed bids. The town will award the contract to the firm that submits the lowest bid and will pay the firm the amount of the second lowest bid (that is, the town will conduct a second-price procurement auction). So, for example, if Firm A bids $8 million, Firm B bids $9 million, and Firm C bids $10 million then the city will award the contract to Firm A (it submitted the lowest bid) and pay Firm A $9 million (the amount of the second lowest bid). Suppose your firm is willing to build the bridge for a minimum of $9 million.
a. Show that bidding $9 million is a better strategy than bidding some amount below $9 million— say, $7 million.
b. Show that bidding $9 million is a better strategy than bidding some amount above $9 million—say, $11 million.