In Cournot competition, firms compete over the quantity of a good they produce. The inverse demand curve P(Q) = 50−2Q, where Q = q1 + q2 defines the market demand, and the cost function for each of the two firms in the industry is C(qi) = 2qi.

## Best Response Function of a Firm

The best response function of a firm is the output level at which the firm maximizes its profits given the output level of its competitors. The best response for firm 1 is given by the equation BR1(q2) = (50 – 2q2 – 2C1) / 2, while the best response for firm 2 is given by the equation BR2(q1) = (50 – 2q1 – 2C2) / 2.

## Cournot Equilibrium Firm Output and Firm Profits

The Cournot equilibrium occurs when both firms are producing at the level where their best response functions intersect. This occurs when q1 = q2 = 24. At this output level, firm 1 has a profit of 336 and firm 2 has a profit of 336. The price that clears the market is P = 2Q = 2(q1 + q2) = 48. This outcome is not efficient, as the optimal quantity of production is 36, which would result in higher profits for both firms than the Cournot equilibrium.

## Related Questions

• What is Cournot competition?
• What is an inverse demand curve?
• What is a cost function?
• What is a best response function?
• What is the Cournot equilibrium?
• What is market clearing price?
• What is an efficient outcome?
• What is q1 and q2?
• What is the optimal quantity of production?
• What is the profit for each firm at the Cournot equilibrium?