Cournot Competition - Cournot Competition With Many Firms and The Cournot Theorem

Cournot Competition With Many Firms and The Cournot Theorem

For an arbitrary number of firms, N>1, the quantities and price can be derived in a manner analogous to that given above. With linear demand and identical, constant marginal cost the equilibrium values are as follows:

edit; we should specify the constants. Given the following results are these;

Market Demand;

Cost Function;, for all i

, which is each individual firm's output

, which is total industry output

, which is the market clearing price

and

, which is each individual firm's profit.

The Cournot Theorem then states that, in absence of fixed costs of production, as the number of firms in the market, N, goes to infinity, market output, Nq, goes to the competitive level and the price converges to marginal cost.

Hence with many firms a Cournot market approximates a perfectly competitive market. This result can be generalized to the case of firms with different cost structures (under appropriate restrictions) and non-linear demand.

When the market is characterized by fixed costs of production, however, we can endogenize the number of competitors imagining that firms enter in the market until their profits are zero. In our linear example with firms, when fixed costs for each firm are, we have the endogenous number of firms:

and a production for each firm equal to:

This equilibrium is usually known as Cournot equilibrium with endogenous entry, or Marshall equilibrium.