3 minute read
Infinitely repeated games
Figure 11-5:
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Price leadership.
The aggregate marginal cost for the following firms is represented by
where ΣMCf is the horizontal summation of marginal cost for the following firms and qf is the aggregate quantity produced by the following firms.
The dominant firm’s marginal cost curve is
where MCd is the dominant firm’s marginal cost in dollars and qd is the quantity produced by the dominant firm.
In order to determine the good’s market price and the quantity of the good produced by the dominant firm and the following firms, you take the following steps:
1. Derive the dominant firm’s demand curve.
Note that the market quantity demanded Q equals:
2. Rearrange the following firms’ aggregate marginal cost curve to get
Chapter 11: Oligopoly: I Need You
3. Substitute P for MCf in the equation from Step 2.
This substitution is allowed because following firms produce where price equals marginal cost in order to maximize profit.
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4. In the Step 1 equation, substitute the market demand equation for Q and the equation for qf from Step 3.
This step generates the equation for the dominant firm’s demand curve.
5. Rearrange the equation in Step 4 to solve for P as a function of qd.
This form is converted to the total revenue equation in the next step.
6. Determine the dominant firm’s total revenue equation.
Remember, total revenue equals price multiplied by quantity.
7. Determine the dominant firm’s marginal revenue equation.
Take the derivative of total revenue with respect to qd.
8. Determine the dominant firm’s profit-maximizing quantity of output.
Set the dominant firm’s marginal revenue equal to the dominant firm’s marginal cost and solve for qd.
9. Substitute qd equals 800 into the dominant firm’s demand curve in order to determine the price established by the dominant firm.
10. Determine the following firms aggregate quantity of output.
Following firms are price takers, so the dominant firm’s price is the following firms’ marginal revenue.
11. Determine the market quantity demanded.
Substitute 14 for price P in the market demand equation.
So the dominant firm produces 800 units of output at a price of $14. The following firms produce an aggregate of 1,500 units. The market quantity demanded given a price of $14 is 2,300 units — the same as qd plus qf.
In the price leadership model, only the dominant firm has monopoly power — only the dominant firm can set price.
Working together by using cartels and collusion
Recognizing that mutual interdependence can lead to undesirable outcomes, firms have an incentive to cooperate by colluding or forming cartels that limit competition. With collusion, rival firms cooperate for their mutual benefit. Although such behavior is generally illegal in the United States, in other parts of the world, collusion is permitted. Airbus, one of the two biggest civilian aircraft manufacturers in the world, arose from a consortium of European companies and, until recent years, collusion among Japanese firms manufacturing auto parts was widespread. A cartel is the result of an open, formal, and legal collusive agreement. Today, the Organization of Petroleum Exporting Countries (OPEC) is the most widely recognized cartel “success” story.
Through collusion, firms act together so their behavior mirrors a monopoly’s behavior. In essence, the firms try to gain monopoly profits by eliminating competition among them. If the cartel’s goal is to maximize the cartel’s total profit, the cartel takes the actions represented in Figure 11-6.
The cartel’s marginal cost is the horizontal summation of the individual firm marginal cost curves. In Figure 11-6, firms A and B have the marginal cost curves MCA and MCB. A marginal cost of $2 is associated with 6 units of output for firm A and 8 units of output for firm B. The horizontal summation of marginal cost means that, for the cartel, a marginal cost of $2 is associated with 14 units of output — 8 plus 6. The cartel’s marginal cost curve is represented by ΣMC.
