Eur. Phys. J. B (2016) 89: 270
https://doi.org/10.1140/epjb/e2016-70148-9

Regular Article

Spatial firm competition in two dimensions with linear transportation costs: simulations and analytical results

Department of Physics, Chemin du Musée 3, 1700 Fribourg, Switzerland

^a e-mail: matus.medo@unifr.ch

Received: 7 March 2016
Received in final form: 16 September 2016
Published online: 12 December 2016

Abstract

Models of spatial firm competition assume that customers are distributed in space and transportation costs are associated with their purchases of products from a small number of firms that are also placed at definite locations. It has been long known that the competition equilibrium is not guaranteed to exist if the most straightforward linear transportation costs are assumed. We show by simulations and also analytically that if periodic boundary conditions in a plane are assumed, the equilibrium exists for a pair of firms at any distance. When a larger number of firms is considered, we find that their total equilibrium profit is inversely proportional to the square root of the number of firms. We end with a numerical investigation of the system’s behavior for a general transportation cost exponent.