A simple expected-value analysis identifies the optimal offer as $70. With
this offer, the firm earns a profit of $130 million, $90 million, or $60 million,
depending on the market response. For instance, under strong demand, the
firm’s profit is (80 70)(13) $130 million. Since each market response is
equally likely, the firm’s expected profit is $93.3 million. It is easy to check that
both the $72 and $74 offers deliver lower expected profits.
Now suppose that instead of setting a buyback price, the firm uses a par-
ticular kind of auction to repurchase shares. In this system, each shareholder
tenders any number of shares at a price he or she names. After all tenders are
collected, the firm buys shares (as many or as few as it wishes) at a single com-
mon priceconsistent with the tenders submitted.^2 For example, if the response
proves to be strong, the firm has a number of options. By choosing a common
price of $70, it could buy back 13 million shares (from all shareholders who
named prices of $70 or below). It could name $72 as the common price and
repurchase 14 million shares, or it could name $74 and repurchase 18 mil-
lion shares.
By waiting for the shareholders’ response, as revealed by the “auction,” the
firm can select the best repurchase price, given current market conditions. It
is easy to check that the firm’s most profitable offer is contingent on demand.
If demand proves strong, the firm’s best price is $70 (yielding $130 million in
profit). If demand is medium, its best price increases to $72. Here, the firm’s
resulting profit is (80 72)(12) $96 million. If demand is weak, its best offer
is $74 (with $72 million in profit). Using the auction method, what is the firm’s
expected profit? Since each response is equally likely, the firm’s expected profit
is simply (1/3)(130) (1/3)(96) (1/3)(72) $99.3 million. The firm’s
expected profit has increased by $6 million relative to the profit under its best
posted price, $70, which is fixed regardless of the market response. Using the
auction method, the firm effectively has acquired perfect information about
demand. As noted in Chapter 13, the difference in expected profit—in this
case $6 million—measures the expected value of perfect information. To sum
up, in an uncertain environment, this auction method has a clear advantage
over posted pricing.BIDDING VERSUS BARGAINING In Chapter 15, we considered the classic
example of bilateral monopoly, where a single seller faced a single buyer with
the aim of negotiating a mutually beneficial price. The following example illus-
trates the potential benefit of competitive bidding versus bargaining in secur-
ing a better price.^3 With the aid of its investment banker, a firm is seeking to672 Chapter 16 Auctions and Competitive Bidding(^2) The financial community commonly refers to this procedure as a Dutch auction. However, this
label is misleading because the method is very different from the usual Dutch auction described
later in this chapter.
(^3) You encountered an earlier version of this example in Chapter 13’s discussion of optimal search.
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