On the existence of Cournot equilibrium. (English) Zbl 0547.90011

Novshek, William

Rev. Econ. Stud. 52, 85-98 (1985).

Summary: This paper examines the existence of n-firm Cournot equilibrium in a market for a single homogeneous commodity. It proves that if each firms’s marginal revenue declines as the aggregate output of other firms increases (which is implied by concave inverse demand) then a Cournot equilibrium exists, without assuming that firms have nondecreasing marginal cost or identical technologies. Also, if the marginal revenue condition fails at a ”potential optimal output”, there is a set of firms such that no Cournot equilibrium exists. The paper also contains an example of nonexistence with two nonidentical firms, each with constant returns to scale production.

MSC:

91B24	Microeconomic theory (price theory and economic markets)
91B50	General equilibrium theory

Keywords:

existence of Cournot equilibrium; single homogeneous commodity; marginal revenue; nonexistence