Examples and exercises on Cournot's oligopoly model and the competitive model

Example

Each of n 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?

The case in which n = 2 is considered in another example. We use the same procedure to find a Nash equilibrium as we did in that case.

The conclusion is that a Nash equilibrium when there are n firms has each firm producing 90/(n+1) units of output.

In this equilibrium, the total output of the firms is

n(90/(n+1)) = 90n/(n+1)
and the price is
120  90n/(n+1).
As n increases, the total output thus approaches 90 and the price approaches 30, the total output and price in the long run competitive equilibrium. That is, if there is a large number of firms then the outcome in a Nash equilibrium of Cournot's model is close to the long run competitive equilibrium.
Copyright © 1997 by Martin J. Osborne