• Tönu Puu


Interesting complex dynamics in oligopoly arises whenever the reaction functions have discontinuity points, as we saw in, for instance, the Cournot/Stackelberg case. There are many possibilities for this in more standard cases, arising either from the demand or from the cost function. A long article by Tord Palander from 1939 (unfortunately in Swedish) provides an entire inventory of such models. One of the simplest deals with competition between duopolists who have several production plants, maybe some originally suited for small scale production, easy to set in operation, but with steeply rising marginal costs, and some more modern suitable whenever demand calls for a larger load of production. Actually, such a firm has three alternatives, as it can also operate both plants dividing production load using the principle of equal marginal costs. As there are also fixed costs in any real situation, the three alternatives provide for a cost function with three segments and two jumps. It is easy to understand that combining two such reaction functions provide for interesting dynamic scenarios. Palander used linear functions, which involve more constraints for eliminating negativity of variables, so in this stub we propose to replace them with smooth demand and cost functions.


  1. Palander TF (1939) Konkurrens och marknadsjämvikt vid duopol och oligopol. Ekonomisk Tidskrift 41:23–145, 222–250CrossRefGoogle Scholar
  2. Tramontana F, Gardini L, Puu T (2009) Cournot duopoly when the competitors operate multiple production plants. J Econ Dyn Control 33:250–265CrossRefGoogle Scholar

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Authors and Affiliations

  • Tönu Puu
    • 1
  1. 1.Centre for Regional Science (CERUM)Umeå UniversityUmeåSweden

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