Local stability condition of the equilibrium of a constraint profit maximization duopoly model

A Cournot duopoly is a market dominated by two firms with profit maximization as their goal. An alternative to the profit maximization model is the constraint profit maximization model, where firms maximize their profits subject to minimum sales constraints. In this paper, a duopoly model with isoelastic demand function and homogeneous product is considered. The local stability condition of the Cournot equilibrium in the cases of sales constraint and no sales constraint were obtained. Initial results implied that it is easier for the duopoly model to be stable if firms impose some minimum constraints on their sales.A Cournot duopoly is a market dominated by two firms with profit maximization as their goal. An alternative to the profit maximization model is the constraint profit maximization model, where firms maximize their profits subject to minimum sales constraints. In this paper, a duopoly model with isoelastic demand function and homogeneous product is considered. The local stability condition of the Cournot equilibrium in the cases of sales constraint and no sales constraint were obtained. Initial results implied that it is easier for the duopoly model to be stable if firms impose some minimum constraints on their sales.