Cournot oligopoly when the competitors operate under capital constraints. (July 2022) - Merlone, Ugo; Szidarovszky, Ferenc
Abstract: In this paper we extend and generalize the interesting duopoly model proposed by Tönu Puu (1991). An n -firm oligopoly is considered without product differentiation, when the price function is hyperbolic and the production cost function is linear. It is assumed that in addition the firms have limited budgets to cover production costs, so if they exceed their budgets, then they have to borrow extra capital with given unit costs. This additional cost makes the payoff functions of the firms only piece-wise differentiable and the best response functions are not unimodal making the equilibrium analysis more complex than in the classical case. In this paper the mathematical model is first introduced and then the best response functions of the firms are determined. A graphical approach is shown to prove the existence of positive equilibrium. The stability of the equilibrium is examined in the simulation study. Highlights: The paper extends and generalizes a classic duopoly model proposed by Puu in 1991. We introduce capital constraints and study how these constraints affect the dynamics. The map that we obtain is piecewise smooth. Stability and coexistence are studied by simulation. The results are compared to those in the original model.