Examples and exercises on Nash equilibrium of Cournot's model

To find a Nash equilibrium of Cournot's model for a specific cost function and demand function we follow the general procedure for finding a Nash equilibrium of a game using best response functions.

Example

Each of two firms has the cost function TC(y) = 30y; the inverse demand function for the firms' output is p = 120  Q, where Q is the total output. What are the firms' outputs in a Nash equilibrium of Cournot's model?

We conclude that there is a unique Nash equilibrium, in which the output of each firm is 30. Each firm's profit is (30)(120  30  30)  (30)(30) = 900.

Example

Each of two firms has the cost function TC(y) = y2. As in the previous example, the inverse demand function for the firms' output is p = 120  Q, where Q is the total output. What are the firms' outputs in a Nash equilibrium of Cournot's model?

We conclude that there is a unique Nash equilibrium, in which the output of each firm is 24. Each firm's profit is (24)(120  24  24)  (24)2 = 1152.

Exercise

An industry contains two firms, one whose cost function is TC(y) = 30y and another whose cost function is TC(y) = y2. The inverse demand function for the firms' output is p = 120  Q, where Q is the total output. What are the firms' outputs in a Nash equilibrium of Cournot's model?

[Solution]


Copyright © 1997 by Martin J. Osborne