A nonlinear duopoly with efficient production-capacity levels

In this paper, we propose an oligopoly model where each firm can produce with linear costs up to its “maximum efficient scale” level and then it incurs quadratic costs for the production exceeding that level. As a consequence, the discrete dynamic model of firms’ choices over time is expressed by a piecewise-smooth map. For this model, we show how border collision bifurcations are responsible of the main qualitative changes in the dynamic of the system. In particular, employing specific numerical examples, we explain the basic mechanism of creation/destruction of periodic points and limit cycles through border crossings as the parameters of the model are changed.