Quantity Competition
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 dominant 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 positioned competitors. As before, a small number of firms produce a standardized, undifferentiated product. Thus, all firms are locked into the same price. The total quantity 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 determine the quantity of output to produce—with these decisions made independently. As a profit maximizer, what quantity should each firm choose? To answer this question, let’s consider the following example. A pair of firms compete by selling quantities of identical goods in a market. Each firm’s average cost is constant at $6 per unit. Market 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 total amount 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 DUELING SUPPLIERS
P (30 Q 2) Q 1.
[9.1]
The demand curve (as a function of the firm’s own quantity) is downward sloping in the usual way. In addition, the demand curve’s price intercept, the term
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