A Model of Three Cities

Abstract

We develop a spatial model representing three cities of different size and connected by a road. We study two versions of a two-stage game where firms first decide where to locate and then set quantities or prices. We show that, in the case of quantity competition, maximal dispersion or agglomeration arises. Also, multiple equilibria are possible. In the case of price competition, maximal dispersion or partial dispersion arises. An asymmetric spatial equilibrium is possible even if the model is completely symmetric ex ante. A number of results are also derived when comparing the Cournot and the Bertrand locational equilibria in terms of profits, consumer surplus, and total welfare, and with respect to the welfare-maximizing locations.

Zoning a metropolitan area*

“…With more than two firms, Gupta et al (2004) obtain that agglomeration and dispersion or a combination of both may be obtained in equilibrium, and Matsushima and Matsumura (2006) obtain multiple equilibria in a mixed market depending on the number of foreign firms. Multiple equilibria are also obtained depending on the consumers' reservation price (Chamorro-Rivas 2000) and on the transportation cost parameter (Benassi et al 2007) or in a model of three connected cities with different size (Colombo 2016a). When firms do not face Cournot competition multiplicity of equilibria is shown to arise when consumers live in a discrete number of towns and firms adopt fixed mill prices.…”