11.10: Equilibrium in a Cournot Oligopoly

In the Cournot model, businesses compete based on the assumption that each firm chooses its production quantity by presuming its rivals’ output levels. No firm has an incentive to change its production quantity given the rivals’ output levels, resulting in a stable market price where all firms maximize their individual profits.

Consider two companies that produce identical goods, such as two automobile manufacturers. Initially, Company A decides to produce 50 cars as a profit-maximizing output level. Company B responds by producing 25 cars, assuming that Company A will not change its production quantity. However, based on its reaction function, Company A adjusts its output to 40 cars. In turn, Company B increases its production to 30 cars. This adjustment continues until both companies reach an equilibrium with zero marginal profit. Over time, both firms reach a point where they each produce 35 cars. At this stage, neither firm has an incentive to change its production because each has maximized its profit given the rival’s output levels. Since neither firm can improve its profit by unilaterally adjusting its output, this stable outcome is known as the Cournot equilibrium, which satisfies the Nash equilibrium condition.

Reaction curves help explain this balance. Given what the competitor is producing, these curves show the best (i.e., profit-maximizing) production level for each company. The point where the curves meet is the equilibrium, where both companies make the best possible decisions. Once they reach this point, any change by one company would reduce its profit, preventing further adjustments. The Cournot model helps explain how businesses in competitive markets make strategic decisions and gradually find a balance that benefits them both.

The Cournot model provides a fundamental framework for understanding how firms in oligopolistic markets strategically adjust their production and gradually converge to a stable competitive balance.

In a Cournot model, firms compete by simultaneously choosing quantities of a homogeneous product, anticipating the amount their competitor chooses to produce as fixed.

Consider two firms, Firm A and Firm B.

Firm A is the first to start producing.

It produces 50 units, half the quantity of the total market at price P, where profits are maximized, assuming marginal cost equals marginal revenue, without any competition. 

Now, firm B assumes that firm A will keep its output fixed and produce half the remaining market demand.

Given this expectation, Firm B decided to produce 25 units, taking a smaller portion because it expected Firm A to take a larger share.

In the next period, Firm A decides to adjust its output and produce 37.5 units, which is half the remaining demand of 75 units.

Further, B continues and produces 31.25, which is half the remaining demand of 62.5 units.

Eventually, they reach a point where both firms produce 33.33 units each; this is the Cournot equilibrium.

This equilibrium is plotted on the reaction curve of both firms.

The intersection of the two reaction curves at 33 units each is the Cournot equilibrium, in which both firms are satisfied with their output choices.