9781118041581

Price Competition 369

TABLE 9.2

A Price War

Each firm’s optimal

strategy is to set

a low price.

Firm 2

High Price Low Price

High Price 10, 10 5, 12

Firm 1

Low Price 12, 5 7, 7

units. (The market-wide price reduction spurs total sales.) Finally, if one firm

sets a high price and the other a low price, the former sells 1.25 million units,

the latter 6 million units.

Table 9.2 presents a payoff table summarizing the profit implications of

the firms’ different pricing strategies. Firm 1’s two possible prices are listed in

the first and second rows. Firm 2’s options head the two columns. The upper-

left cell shows that if both firms charge high prices, each will earn a profit of

$10 million. (It is customary to list firm 1’s payoff or profit first and firm 2’s pay-

off second.) Each firm’s profit is computed as: (P AC)Q (8 4)(2.5)

$10 million. The other entries are computed in analogous fashion. (Check

these.) Notice that firm profits are lower when both charge lower prices. (The

price reduction increases the firms’ total sales, but not by enough to compen-

sate for lower margins. Demand is relatively inelastic.) Notice also that if one

firm undercuts the other’s price, it wins significant market share and, most

important, profit at the expense of the other.

Each firm must determine its pricing decision privately and independ-

ently of the other. Naturally, each seeks to maximize its profit. What pricing

policy should each firm adopt? The answer is that each should set a low

price. Indeed, this is each firm’s more profitable alternative, regardless of

what action its rival takes. To see this, let’s look at the payoffs in Table 9.2

from firm 1’s point of view. To find its best strategy, firm 1 asks a pair of

“what if” questions about its rival. What if firm 2 were to charge a high price?

Then, clearly, firm 1 does best by setting a low price, that is, undercutting.

(A profit of 12 is superior to a profit of 10.) Alternatively, if firm 2 sets a low

price, firm 1’s profit-maximizing response is to set a low price, that is, to

match. (Here, 7 is better than 5.) Because the firms face symmetric payoffs,

exactly the same logic applies to firm 2. In short, self-interest dictates that

each firm set a low price; this is the better strategy for each, regardless of the

action the other takes.

The upshot of both sides charging low prices is profits of 7 for each—lower

than the profits (10 each) if they both charged high prices. Both would prefer

the larger profits enjoyed under a high-price regime. Yet the play of self-interested

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