Summary 703b. Suppose, instead, that the government sets a fixed-price contract, and
the firms submit total cost bids. Which firm will be selected? Why
might firms insist on a higher required profit under a fixed-price
contract than under a cost-plus contract?
c. Finally, suppose the government uses an incentive contract and sets
the firm’s sharing rate at b .25 and the cost target at cT100.
Which firm can be expected to submit the lower required-profit bid?
Will the efficient firm be selected?- Firm S plans to sell an office building via an English auction. The firm
expects two buyers to bid, each with a value uniformly distributed
between $300,000 and $360,000. In addition, firm S knows it can sell the
building to a third outside buyer for $300,000 if the auction does not
produce a better price.
a. Suppose firm S sets the auction reserve price at Pmin$300,000.
Show that the expected price in the English auction is $320,000.
b. Suppose instead that firm S sets Pmin$330,000. What is the chance
that neither buyer will meet this price? What is the chance that exactly
one buyer will meet this price? What is the chance that both buyer
values exceed this price? Conditional on both values being above
$330,000, what will be the expected price in the English auction?
c. Averaging over the three possibilities in part (b) by the appropriate
probabilities, compute the seller’s expected revenue. Confirm that it
is to the seller’s advantage to set the higher reserve price.
Discussion Question New issues of U.S. Treasury bills are sold at auction. The
government decides on the total quantity of bills to be sold and seeks to pay the
lowest possible interest rates on these bills. Private parties submit sealed bids
specifying the quantity of bills sought and the interest rate they require. A pur-
chaser is allowed to submit multiple bids for different quantities at different
interest rates. (A purchaser also can place a “noncompetitive” or “market” bid
that is filled at the averageinterest rate as determined by the auction.) After
observing all bids, the government determines the cutoff interest rate at which
the volume of bids matched the volume of securities to be sold. The govern-
ment accepts all bids at interest rates below this cutoff.
a. Until the 1990s, winning bidders received the interest rates they bid.
(i) Consider a bidder just willing to accept a 4.2 percent return (her
reservation price). Will she bid 4.2 percent? Or a higher (or lower)
interest rate?
(ii) Explain why the ability to submit multiple bids is valuable to buyers.
(iii) Are small investors (with little expertise in discerning likely interest
rates) at a bidding disadvantage relative to sophisticated financial
experts?
b. Current auction rules call for all winning bidders to receive the same
interest rate—a rate equal to the highest accepted interest rate bid. If the
cutoff interest rate turned out to be 4.5 percent, a buyer submitting 4.2c16AuctionsandCompetitiveBidding.qxd 9/26/11 1:09 PM Page 703