Abstract
We study conjectured variations equilibrium (CVE) in a model of mixed oligopoly with not necessarily continuous demand functions. The agents’ conjectures concern the price variations depending upon their production output increase or decrease. We establish the existence and uniqueness results for the CVE (called exterior equilibrium) for any set of feasible conjectures. To introduce the notion of interior equilibrium, we develop a consistency criterion for the conjectures (referred to as influence coefficients) and prove the existence theorem for the interior equilibrium (understood as CVE with consistent conjectures, or CCVE). In addition, we also examine the behavior of the consistent conjectures as functions of a parameter representing the demand’s derivative with respect to the market price. The latter results allow one to predict the behavior of groups of consumers with different consumption abilities. The proposed techniques permit one to develop a qualitative description of the dependence of the market price on the active demand component, too. It should be noticed that due to the non-smoothness of the demand function, there is possibly a path dependency and indeterminacy of equilibria in certain cases. This is, on the one hand, a theoretically inconvenient result (multiple equilibria), but on the other hand, it may happen to be extremely useful for applications. Indeed, the latter multiplicity of equilibria might serve as a rationale for the regulatory intervention to induce a change of equilibrium whenever the total welfare could be improved (cf., for example, the Keynesian stimulus).
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Acknowledgments
The research activity of the first and the fourth authors was financially supported by the R&D Department (Cátedra de Investigación) CAT-174 of the Tecnológico de Monterrey (ITESM), Campus Monterrey, and by the SEP-CONACYT project CB-2008-01-106664, Mexico. Also, the work of the third author was supported the National Council of Science and Technology (CONACyT) of Mexico as part of the project CB-2011-01-169765; PROMEP 103.5/11/4330, and PAICYT 464-10. The authors also acknowledge their profound gratitude to the anonymous referee whose valuable comments and suggestions have helped greatly to improve the presentation.
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Kalashnikov, V.V., Bulavsky, V.A., Kalashnikov, V.V. et al. Structure of demand and consistent conjectural variations equilibrium (CCVE) in a mixed oligopoly model. Ann Oper Res 217, 281–297 (2014). https://doi.org/10.1007/s10479-014-1558-x
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DOI: https://doi.org/10.1007/s10479-014-1558-x