On the foundation of monopoly in bilateral exchange

Abstract

We address the problem of monopoly in general equilibrium in a mixed version of a monopolistic two-commodity exchange economy where the monopolist, represented as an atom, is endowed with one commodity and “small traders,” represented by an atomless part, are endowed only with the other. First we provide an economic theoretical foundation of the monopoly solution in this bilateral framework through a formalization of an explicit trading process inspired by Pareto (Cours d’économie politique. F. Rouge Editeur, Lausanne, 1896) for an exchange economy with a finite number of commodities, and we give the conditions under which our monopoly solution has the geometric characterization proposed by Schydlowsky and Siamwalla (Q J Econ 80:147–153, 1966). Then, we provide a game theoretical foundation of our monopoly solution through a two-stage reformulation of our model. This allows us to prove that the set of the allocations corresponding to a monopoly equilibrium and the set of the allocations corresponding to a subgame perfect equilibrium of the two-stage game coincide. Finally, we compare our model of monopoly with a bilateral exchange version of a pioneering model proposed by Forchheimer (Jahrbuch für Gesetzgebung, Verwaltung und Volkswirschafts im Deutschen Reich 32:1–12, 1908), known as a model of “partial monopoly” since there a monopolist shares a market with a“competitive fringe.” Journal of Economic Literature Classification Numbers: D42, D51.