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.
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References
H.R. Varian, J. Repcheck, in Intermediate microeconomics: A modern approach (WW Norton New York, 2010), Vol. 7
J. Bertrand, Journal des Savants 67, 499 (1883)
F. Edgeworth, Giornale degli Economisti 40, 13 (1897)
A. Shaked, J. Sutton, Rev. Econom. Stud. 49, 3 (1982)
K. Clay, R. Krishnan, E. Wolff, D. Fernandes, J. Indus. Econom. 50, 351 (2002)
D.M. Kreps, J.A. Scheinkman, Bell J. Econom. 14, 326 (1983)
S.P. Anderson, R. Renault, The RAND Journal of Economics 30, 719 (1999)
H. Hotelling, Economic Journal 39, 41 (1929)
H.A. Eiselt, G. Laporte, Eur. J. Oper. Res. 39, 231 (1989)
R. Biscaia, I. Mota, Papers in Regional Science 92, 851 (2013)
C. d’Aspremont, J.J. Gabszewicz, J.F. Thisse, Econometrica 47, 1145 (1979)
P. Champsaur, J.C. Rochet, Existence of a price equilibrium in a differentiated industry, INSEE Discussion Paper No. 8801 (1988)
T. Tabuchi, Regional Science and Urban Economics 24, 207 (1994)
K.E. Boulding, in Economic analysis (Harper & Row, 1966), Vol. 1
D.A. Hay, in Sequential entry and entry-deterring strategies in spatial competition (Oxford Economic Papers, 1976), pp. 240–257
S. Brenner, Determinants of product differentiation: A survey (Humboldt University, 2001)
A. Irmen, J.F. Thisse, J. Economic Theory 78, 76 (1998)
A. Smithies, J. Political Economy 49, 423 (1941)
B.C. Eaton, R.G. Lipsey, Rev. Econom. Stud. 42, 27 (1975)
A. Egli, Australian Economic Papers 46, 39 (2007)
S.C. Salop, The Bell Journal of Economics 10, 141 (1979)
A. Kats, Int. J. Indus. Organ. 13, 89 (1995)
M. Newman, Networks: An introduction (OUP, Oxford, 2010)
J.J. Gabszewicz, J.F. Thisse, Fundamentals of Pure and Applied Economics 5, 1 (1986)
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Roncoroni, A., Medo, M. Spatial firm competition in two dimensions with linear transportation costs: simulations and analytical results. Eur. Phys. J. B 89, 270 (2016). https://doi.org/10.1140/epjb/e2016-70148-9
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DOI: https://doi.org/10.1140/epjb/e2016-70148-9