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?