Bertrand Competition with Linear or Quadratic Costs

This Demonstration offers a quick way of analyzing Bertrand (i.e. price) competition among firms, assuming they are identical and have costs that are linear (no capacity constraints) or quadratic (capacity constraints). You can choose the number of firms, the type of costs involved, and the parameters governing a linear demand.

The graph shows, for a hypothetical firm 1:
• Profits earned when the firm acts as a monopolist (brown),
• Profits earned when the firm charges the same price as the competitors (green),
• Profits that the firm can earn for any price it charges, given that the competitors are all charging a certain price (blue).

The behavioral assumption is that, when firm 1 charges less than , the firm sells to the entire demand; when firm 1 charges , each of the firms sells of the entire demand (the consumer buys equally from all the firms); when firm 1 charges more than , the firm sells nothing (consumers buy from the other firms because they are cheaper). The dynamics of price competition involve each firm acting in its best interest given the prices set by the other firms (). As the model is symmetric, the Nash equilibrium of the game is symmetric and involves all the firms charging the same price. You can discover the Nash equilibria of this game by varying and observing how firm 1's profits (blue) change according to the choice of . The red dots indicate the range of prices that generate a symmetric Nash equilibrium of the game. To facilitate comprehension, shown in the gray box turns red when it reaches a Nash equilibrium price.