Cournot Duopoly with Capacity Limit Plants

Fabio Tramontana, Laura Gardini () and Puu Tonu
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Puu Tonu: CERUM, Umea University, Sweden

No 314, Working Papers from Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali

Abstract: 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.

Keywords: Border Collision Bifurcations; Capacity Limits; Cournot; Discontinuous Reaction Functions; Duopoly; Nonlinear Dynamics (search for similar items in EconPapers)
JEL-codes: C61 C62 C72 C73 D21 D24 L13 (search for similar items in EconPapers)
Pages: 29
Date: 2008-02
New Economics Papers: this item is included in nep-bec, nep-com, nep-ind and nep-mic
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:anc:wpaper:314

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