9781118041581

Quantity Competition 363

firm is to anticipate the supply response of the competitive fringe of firms. For

instance, suppose the dominant firm anticipates that any increase in price will

induce a significant increase in supply by the other firms and, therefore, a sharp

reduction in the dominant firm’s own net demand. In other words, the more

price elastic is the supply response of rivals, then the more elastic is the domi-

nant firm’s net demand. Under such circumstances, the dominant firm does

best to refrain from raising the market price.

Competition among Symmetric Firms

Now let’s modify the previous setting by considering an oligopoly consisting of

a small number of equally positionedcompetitors. As before, a small number of

firms produce a standardized, undifferentiated product. Thus, all firms are

locked into the same price. The totalquantity of output supplied by the firms

determines the prevailing market price according to an industry demand

curve. Via its quantity choice, an individual firm can affect total output and

therefore influence market price.

A simple but important model of quantity competition between duopolists

(i.e., two firms) was first developed by Augustin Cournot, a nineteenth-century

French economist. To this day, the principal models of quantity competition

bear his name. Knowing the industry demand curve, each firm must deter-

mine the quantity of output to produce—with these decisions made inde-

pendently. As a profit maximizer, what quantity should each firm choose? To

answer this question, let’s consider the following example.

DUELING SUPPLIERS A pair of firms compete by selling quantities of identi-

cal goods in a market. Each firm’s average cost is constant at $6 per unit. Mar-

ket demand is given by P  30 (Q 1 Q 2 ), where Q 1 and Q 2 denote the

firms’ respective outputs (in thousands of units). In short, the going market

price is determined by the totalamount of output produced and sold by the

firms. Notice that each firm’s profit depends on both firms’ quantities. For

instance, if Q 1 5 thousand and Q 2 8 thousand, the market price is $17.

The firms’ profits are  1 (17 6)(5) $55 thousand and  2 (17 6)(8)

$88 thousand, respectively.

To determine each firm’s profit-maximizing output, we begin by observing

the effect on demand of the competitor’s output. For instance, firm 1 faces the

demand curve

[9.1]

The demand curve (as a function of the firm’s own quantity) is downward slop-

ing in the usual way. In addition, the demand curve’s price intercept, the term

P(30Q 2 )Q 1.

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