Advantageous monopolies in general equilibrium: a noncooperative approach

Turchet, Damiano (2022) Advantageous monopolies in general equilibrium: a noncooperative approach. PhD thesis, University of Glasgow.

Abstract

The aim of this dissertation is to provide a comprehensive and novel approach to the study of monopoly in general equilibrium. First, a foundational paper is provided, in which we define a concept of monopoly equilibrium within a bilateral exchange market a la Shitovitz, in which an atomic monopolist, that owns the totality of one commodity, faces an ocean of small traders (also called the atomless part of the economy), that owns another commodity. A monopoly equilibrium is defined as a quantity offered by the monopolist that maximizes her utility, given a price selection induces by her offers. After defining the notion of equilibrium, we provide parallels with the standard notions in partial equilibrium, under further assumptions on the structure of the demand function of the atomless sector for the good owned by the monopolist, namely its invertibility and differentiability. In particular, under the differentiability assumptions, we show that an interior monopoly equilibrium lies at the tangency point between the monopolists’ indifference curve and the small traders’ offer curve.

Once the notion of a monopoly equilibrium is established, the first follow up for the analysis is a game theoretic foundation for such an equilibrium. Following the work of Busetto et al. (2011), and recognizing the two stage flavour of the definition of a monopoly equilibrium, we provide a theorem that states the equivalence between the set of monopoly equilibrium and set of subgame perfect equilibria.

Next, to show the concept of monopoly equilibrium holds non vacuously, I proceed to study the existence properties of such equilibrium. Non existence examples in which small traders have CES utility functions are provided and a link between the existence of an equilibrium and the degree of substitutability of the goods is explored. Therefore, the existence result is proved by introducing a sufficient assumption on the utilities of the small traders, stressing that they need to be locally equivalent to CES utility functions whose elasticity is larger than unity.

Finally, an analysis of the optimality of such equilibrium is explored. In particular, drawing from Aumann seminal’s paper on advantageous monopolies, we show how our model (under mild assumptions) is able to rule out the unintuitive situation of a monopolist being better off by being competitive. In particular, we show that a monopolist can be walrasian, i.e. the monoply equilibrium might coincide with a competitive equilibrium, and we characterize this equivalence proving that this only occurs whenever the monopolist optimal bid coincided with her endowment. However, whenever the set of monopoly equilibria and the set of competitive equilibria are disjoint, then the monopolist is always better off at a monopoly equilibrium and the small traders are exploited, i.e. their utility is always lower at a monopoly equilibrium with respect to a competitive equilibrium.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Subjects: H Social Sciences > HB Economic Theory
• Colleges/Schools: College of Social Sciences > Adam Smith Business School > Economics
• Funder's Name: Economic and Social Research Council (ESRC)
• Supervisor's Name: Ghosal, Professor Sayantan and Vailakis, Professor Yiannis
• Date of Award: 2022
• Depositing User: Theses Team
• Unique ID: glathesis:2022-82799
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 12 Apr 2022 09:53
• Last Modified: 12 Apr 2022 09:56
• Thesis DOI: 10.5525/gla.thesis.82799
• URI: https://theses.gla.ac.uk/id/eprint/82799