Tuesday, September 22, 2015

Noncooperative Oligopoly in Markets with a Cobb-Douglas Continuum of Traders

Giulio CODOGNATO (Universita degli Studi di Udine) and Ludovic A. JULIEN (Universite de Dijon LEG) explore Noncooperative Oligopoly in Markets with a Cobb-Douglas Continuum of Traders.

ABSTRACT: In this paper, we revisit two models of noncooperative oligopoly in general equilibrium proposed by Busetto et al. (2008, 2011), a version of Shapley’s “window†model for mixed exchange economies following Shitovitz and its reformulation following Cournot-Walras. We introduce the assumption that the preferences of traders belonging to the atomless portion are represented by Cobb-Douglas utility functions. This assumption permits us to prove the existence of a Cournot-Nash equilibrium in Shapley’s window model, known as the Cobb-Douglas-Cournot-Nash equilibrium, without introducing further assumptions of atom endowments and preferences previously used by Busetto et al. (2011). We then show that the set of Cobb-Douglas-Cournot-Nash equilibrium allocations coincides with that of Cournot-Walras equilibrium.

https://lawprofessors.typepad.com/antitrustprof_blog/2015/09/noncooperative-oligopoly-in-markets-with-a-cobb-douglas-continuum-of-traders.html

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