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La convergence d’équilibres stratégiques en prix-quantités vers l’équilibre concurrentiel

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  • Boyer, Marcel

    (Département de Sciences économiques, Université de Montréal)

  • Moreaux, Michel

    (GREMAQ)

Abstract

In this article, we study the convergence of a sequence of strategic equilibria in a model with a hierarchy of leaders and followers and where firms express their strategy in terms of both prices and quantity. In the duopoly case with an homogenous product, such a strategy set leads to equilibria with two prices and endogenous rationing; moreover, followership is the preferred position. We generalize here the model to an arbitrary number of firms organized in a hierarchy. We show that, as the number of firms increases, the sequence of equilibria converges to a "quasi-competitive" equilibrium: total production converges to the competitive production, the price chosen by any firm of a given rank goes to the competitive price and the relative production of the firms whose selling price is ε-above the competitive price goes to zero for all positive ε. However the distributions of both production and profits (total profits going to zero) remains strongly unequal. Dans le présent article, nous étudions la convergence d’une suite d’équilibres stratégiques dans un modèle avec hiérarchie de meneurs et de suiveurs dans lequel l’ensemble des stratégies de chaque agent correspond aux couples prix-quantités. Dans le cas d’un duopole, un tel ensemble de stratégies mène à des équilibres à prix multiples même lorsque le bien vendu par les duopoleurs est un bien homogène, la firme agissant comme meneur rationnant sa demande. De plus, et ce contrairement au cas du modèle de Stackelberg stricto sensu, l’avantage appartient au suiveur et non au meneur. Nous généralisons ici ce modèle à une hiérarchie comprenant un nombre quelconque de firmes. Nous montrons qu’avec l’augmentation du nombre de firmes, la configuration d’équilibre de l’industrie tend vers une configuration « quasi-concurrentielle » : la production totale tend vers la production concurrentielle, le prix de vente de toute firme d’un rang donné tend vers le prix d’équilibre concurrentiel, et enfin la production relative des firmes dont le prix de vente est supérieur d’un certain montant au prix d’équilibre concurrentiel tend vers zéro également quel que soit ce montant. Par ailleurs, les distributions de la production et des profits (les profits globaux tendent vers zéro) restent fortement inégalitaires.

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Bibliographic Info

Article provided by Société Canadienne de Science Economique in its journal L'Actualité économique.

Volume (Year): 61 (1985)
Issue (Month): 4 (décembre)
Pages: 411-427

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Handle: RePEc:ris:actuec:v:61:y:1985:i:4:p:411-427

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  1. Boyer, M. & Moreaux, M., 1985. "L'equilibre Concurrentiel Comme Limite de Suites D'equilibres Strategiques de Stackelberg," Cahiers de recherche 8527, Universite de Montreal, Departement de sciences economiques.
  2. Boyer, Marcel & Moreaux, Michel, 1987. "On Stackelberg Equilibria with Differentiated Products: The Critical Role of the Strategy Space," Journal of Industrial Economics, Wiley Blackwell, vol. 36(2), pages 217-30, December.
  3. Boyer, M. & Moreaux, M., 1985. "Rational Rationing with Differentiated Products," Cahiers de recherche 8523, Universite de Montreal, Departement de sciences economiques.
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