Sequential-move, one-shot games

194 Part III: Market Structures and the Decision-Making Environment

The Bertrand duopoly model indicates that firm A maximizes profit by charging $64, and firm B maximizes profit by charging $56. Figure 11-4 illustrates the Bertrand duopoly model. Note that both the horizontal and vertical axes on the figure measure price and not quantity (as in the Cournot and Stackelberg models).

Figure 11-4: A Bertrand duopoly.

In the Bertrand model, firms compete with price. Therefore, reaction functions are expressed in terms of price, not quantities.

Leading the pack: Another view of price leadership

The Stackelberg model of oligopoly illustrates one firm’s leadership in an oligopoly. In the Stackelberg model, the leader decides how much output to produce with other firms basing their decision on what the leader chooses. Another common form of leadership is for the leading firm to set price. Rival firms then use the same price for their products. However, as is always the case in oligopoly, the leading firm must take into account the behavior of its rivals.

The leading firm that initially sets price is called the dominant firm. The firms that use the price set by the dominant firm are typically smaller in size and

Chapter 11: Oligopoly: I Need You

called following firms. Markets for steel and agricultural implements have been observed to operate in this manner.

The theory of price leadership represents a combination of monopoly behavior on the dominant firm’s part and perfectly competitive behavior on the part of following firms.

Figure 11-5 illustrates price leadership. The market has a downward-sloping demand curve labeled D. A crucial point: The dominant firm must take into account that its following firms satisfy part of that market demand. Because the following firms act as price takers, their marginal revenue curve is the price set by the dominant firm. To maximize profits, the following firms produce where price/marginal revenue equals marginal cost. Therefore, each following firm’s supply curve corresponds to its marginal cost curve, and the aggregate supply curve for all following firms is the horizontal summation of the marginal cost curves. This horizontal summation of marginal cost is represented by the curve ΣMCf.

In Figure 11-5, the dominant firm’s demand curve, dd, is derived from the market demand and the aggregate supply curve for the following firms. The dominant firm simply subtracts the quantity provided by the following firms from the quantity demanded in the market to determine its quantity demanded. In other words, the dominant firm’s demand curve equals the market demand curve minus the sum of the following firm’s marginal cost curves, ΣMCf.

Given the linear relationships in Figure 11-5, the dominant firm’s marginal revenue curve, MRd, is twice as steep as its demand curve. The dominant firm maximizes profit by producing the quantity of output that corresponds to marginal revenue, MRd, equals marginal cost, MCd. This output level is qd. The dominant firm determines price by going from the quantity qd up to its demand curve, dd. Thus, the dominant firm sets the price at Pd.

As already noted, following firms are price takers. The dominant firm’s price Pd is the price that all following firms charge for every unit of the product they sell. For the following firms, the dominant firm’s price becomes their marginal revenue, Pd = MRf. The following firms then maximize profit by setting marginal revenue, MRf, equal to marginal cost, MCf. In aggregate, the following firms produce qf of output.

For the market, consumers pay a price of Pd quantity consumed Q equals qd plus qf. and consume the quantity Q. The

The market demand for an oligopoly characterized by price leadership is