Cournot Duopoly with Capacity Limit Plants
This article considers a Cournot duopoly under an isoelastic demand function and cost functions with built-in capacity limits. The special feature is that each firm is assumed to operate multiple plants, which can be run alone or in combination. Each firm has two plants with different capacity limits, so it has three cost options, the third being to run both plants, dividing the load according to the principle of equal marginal costs. As a consequence, the marginal cost functions come in three disjoint pieces, so the reaction functions, derived on basis of global profit maximization, as well can consist of disjoint pieces. We first analyze the case in which the firms are taken as identical, and then the generic case. It is shown that stable Cournot equilibria may coexist with several other stable cycles. Then we compare the coexistent periodic attractors in terms of the resulting profits. The main property is the non-existence of unstable cycles. This is reflected in a particular bifurcation structure, due to border collision bifurcations, and to particular basin frontiers, related to the discontinuities.
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- Zhusubaliyev, Zhanybai T. & Soukhoterin, Evgeniy & Mosekilde, Erik, 2007. "Quasiperiodicity and torus breakdown in a power electronic dc/dc converter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 364-377.