Equilibrium in a Cournot Oligopoly

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.