Answers to Back-of-the-Chapter Problems
1. a. Each buyer should bid bi = vi. If the buyer bids above her value, it makes a
difference only when she outbids an opponent who bids bj > vi, in which case
she obtains the good for a price bj above her value. In short, bidding above
b. In the English auction, the bidding stops at (or just above) the second-highest
c. The absent buyer should report a bid equal to his true value, bi = vi. If he wins,
he pays only the price required to win the auction, which may be well below his
2. a. As outlined in the first section of the chapter, auctions have the advantage of
marshalling competition among bidders and discovering the best price that the
b. After the fact, it is evident that Paramount made a huge error in choosing the
negotiation route rather than an auction. The film in question was James
Cameron’s 1997 release Titanic, which after a modest opening week became
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Within a week, the howls of protest sounded. The ABC and CBS television
networks asked why they were denied the chance to bid. Paramount’s
production partner, Twentieth Century Fox, threatened to bring suit for
Paramount’s failure to auction the film and to include an escalator clause,
3. a. Against a single rival, the optimal bid is $2.4 million implying an expected
b. Each firm’s equilibrium bidding strategy is: bi = (1/3)(2) + (2/3)vi. Thus, the
4. a. Both buyers are mistakenly deviating from their equilibrium sealed bidding
strategies: b = .5v; buyer 1 is bidding too low, and buyer 2 is bidding too high.
b. In the English auction, buyer 1 wins the bowl at a price of $450. So the seller’s
payoff is $450, and buyer 1’s payoff is: 700 – 450 = $250, for a total payoff of
$700. The English auction is efficient and delivers a greater total “pie.” The
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c. If buyer 2 sells the bowl to buyer 1 for $600, the final payoffs are $300, $100
(700 – 600), and $300 (600 – 300) for the seller and the buyers, respectively.
5. a. A firm can only lose money by bidding above its value. Bidding below one’s
value risks getting neither position and can only help if moving down to
position two is more profitable than winning the top position. Firm 1’s profit
b. Now if Firm 1 bids just below 35¢ and wins the second position at 20¢, its
b. The outsider’s expected profit is: [v1 – b][(b – 200)/60]. Therefore, her optimal
c. The seller’s expected price is:
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7. a. Under blind bidding, each firm’s reservation price is simply the expected value
of the film. The common expected value for each bidder is (1/3)(10,000) +
(1/3)(6,000) + (1/3)(2,000) = $6,000, and this will be the equilibrium bid for
each in a sealed-bid auction. Thus, the distributor’s revenue from the auction
b. Selective screening works only if bidders are naive. Sophisticated bidders will
c. Against an astute bidder, the less well-informed theaters must bid cautiously to
avoid the winner’s curse, that is, winning films that the astute bidder knows are
poor box-office bets. This kind of bid deterrence allows the astute bidder to
8. a. In sequential bidding for identical items, a potential buyer must decide whether
or not to try to win the first item or try to get the second, third, … or last item
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b. When items can be bought as a lot, the high initial bidder may take one item,
some items, or all items at the bid price. Leftover items are reauctioned and
9. a. From Table A we can compute the expected profit for any bid by multiplying
the bid markup by the fraction of bids won. For example, the expected profit
b. Table B lists a total of 128 lowest competing bids. If Reliant Press were to use a
20 percent markup, it would lose to only 6 of these 128 LCBs (i.e., bids with
markups of 19 percent or below). Thus, the firm’s expected profit is (122/128)
(20) = 19.06. If it bids 50 percent, its expected profit is (84/128)(50) = 32.8. If
it bids 60 percent, its expected profit is (64/128)(60) = 30.0. If it bids 70
10. a.With 100 percent of production costs covered by the government, Firm J will
b. With a fixed-price contract, Firm K will submit the lower bid (based on a lower
c. Firm J’s expected profit is :T + .25(100 – 105). To clear its required $5 million
in profit, the Firm submits :T = $6.25 million. Firm K’s expected profit is :T + .
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11. a. At an English auction, the seller’s expected price is: [2/(n + 1)]300 +
b. The chance is .5 that an individual buyer’s value is less than $330 thousand.
The chance that both values are less than the reserve is (.5)(.5) = .25. The
c. With Pmin = $330 thousand, the seller’s expected revenue is (.25)(300) + (.5)
Discussion Question
a. Many bidders can be expected to have downward sloping demand curves; they
may wish to guarantee the purchase of a certain amount of securities (even at
b. The government should select the lowest interest rate bids first and then accept
c. In a uniform price auction, buyers should make bids equal to their true
reservation values. Here, it does not pay to mark up one’s interest rate bid
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Spreadsheet Problem
S1. a. and b. To find the firm’s optimal bid markup, use your spreadsheet’s
c. If the BCB distribution has a mean of 40 (instead of 60), the optimal markup
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