Price Rigidity and Kinked Demand

and approaches 24 thousand as the number of firms becomes large (say, 19 or more). In turn, the equilibrium market price approaches 30 24 6; that is, price steadily declines and approaches average cost. It can be shown that this result is very general. (It holds for any symmetric equilibrium, not only in the case of linear demand.) The general result is as follows:

As the number of firms increases, the quantity equilibrium played by identical oligopolists approaches the purely competitive (zero-profit) outcome.

In short, quantity equilibrium has the attractive feature of being able to account for prices ranging from pure monopoly (n 1) to pure competition (n very large), with intermediate oligopoly cases in between.

PRICE COMPETITION

In this section, we consider two basic models of price competition. The first is a model of stable prices based on kinked demand. The second is a model of price wars based on the paradigm of the prisoner’s dilemma.

Price Rigidity and Kinked Demand

Competition within an oligopoly is complicated by the fact that each firm’s actions (with respect to output, pricing, advertising, and so on) affect the profitability of its rivals. Thus, actions by one or more firms typically will trigger competitive reactions by others; indeed, these actions may trigger “secondround” actions by the original firms. Where does this jockeying for competitive position settle down? (Or does it settle down?) We begin our discussion of pricing behavior by focusing on a model of stable prices and output. Many oligopolies—steel, automobiles, and cigarettes, to name a few—have enjoyed relatively stable prices over extended periods of time. (Of course, prices adjust over time to reflect general inflation.) Even when a firm’s cost or demand fluctuates, it may be reluctant to change prices.

Price rigidity can be explained by the existence of kinked demand curves for competing firms. Consider a typical oligopolist that currently is charging price P*. Why might there be a kink in its estimated demand curve, as in Figure 9.3? Suppose the firm lowers its price. If price competition among firms is fierce, such a price cut is likely to be matched by rival firms staunchly defending their market shares. The upshot is that the firm’s price reduction will generate only a small increase in its sales. (The firm will not succeed in gaining market share from its rivals, although it could garner a portion of the increase in industry sales owing

Dollars per Unit of Output

P *

Demand

FIGURE 9.3

Optimal Output with Kinked Demand

If the demand curve is kinked, the firm’s marginal revenue curve has a gap at quantity Q*.

MC

MC ′

Q MR

Output

to lower marketwide prices.) In other words, when it comes to price reductions, demand is relatively inelastic. Conversely, suppose the firm raises its price above P*. By holding to their present prices, rival firms can acquire market share from the price raiser. If the other firms do not follow, the firm will find its sales falling precipitously for even small price increases. In short, demand is elastic for price increases. This explains the demand curve’s kink at the firm’s current price.

In view of kinked demand, the firm’s profit-maximizing price and quantity are simply P* and Q*. This is confirmed by noting that the firm’s marginal revenue curve in Figure 9.3 is discontinuous. The left part of the MR curve corresponds to the demand curve to the left of the kink. But MR drops discontinuously if price falls slightly below P*. The presence of the vertical discontinuity in MR means that P* and Q* are optimal as long as the firm’s marginal cost curve crosses MR within the gap. The dotted MC curve in the figure shows that marginal