Journal of Economics

, Volume 124, Issue 1, pp 75–92 | Cite as

Optimal size of a residential area within a municipality

  • Juan Carlos Bárcena-Ruiz
  • F. Javier Casado-Izaga


The purpose of this paper is to analyze the optimal size of a residential area within a municipality under different market structures. We find that under a private duopoly the optimal size of the residential area depends on the ratio between transportation costs and a negative externality due to congestion. The optimal size is the whole municipality when the ratio is low enough and a small area of the municipality when the ratio is high enough. The transition from a flat residential area to a more compact one is not continuous, so some large-enough residential areas are never optimal. Under a mixed duopoly the transition from a flat residential area to a more compact one is continuous as the ratio increases. By comparing the two cases we find that for intermediate values of this ratio a flat city is optimal for a private duopoly while compact cities emerge under a mixed duopoly.


Spatial competition Location choice Residential area Congestion 

JEL Classification

D43 L13 R14 R52 



Financial support from Ministerio de Ciencia y Tecnología (ECO2015-66803-P) is gratefully acknowledged.


  1. Bárcena-Ruiz JC, Casado-Izaga FJ (2014) Zoning under spatial price discrimination. Econ Inq 52(2):659–665CrossRefGoogle Scholar
  2. Bárcena-Ruiz JC, Casado-Izaga FJ (2016) Zoning a metropolitan area. Pap Reg Sci. doi: 10.1111/pirs.12227. (forthcoming)
  3. Bárcena-Ruiz JC, Casado-Izaga FJ (2017) Zoning a cross-border city. J Reg Sci 57(1):173–189CrossRefGoogle Scholar
  4. Bárcena-Ruiz JC, Garzón MB (2017) Privatization of state holding corporations. J Econ 120(2):171–188CrossRefGoogle Scholar
  5. Ben-Akiva M, de Palma A, Thisse J-F (1989) Spatial competition with differentiated products. Reg Sci Urban Econ 19(1):5–19CrossRefGoogle Scholar
  6. Borck R, Tabuchi T (2015) Pollution and city size: can cities be too small? Beiträge zur Jahrestagung des Vereins für Socialpolitik 2015: Ökonomische Entwicklung - Theorie und Politik - Session: Urban Economics I, No. A15-V1. Available at:
  7. Braid RM (2011) Bertrand-Nash mill pricing and the locations of two firms with partially overlapping product selections. Pap Reg Sci 90(1):197–211CrossRefGoogle Scholar
  8. Braid RM (2016) Efficiency-enhancing horizontal mergers in spatial competition. Pap Reg Sci. doi: 10.1111/pirs.12228. (forthcoming)
  9. Brueckner J (2001) Urban sprawl: lessons from urban economics. Brookings-Wharton Pap Urban Aff 65–97: doi: 10.1353/urb.2001.0003
  10. Chen C-S, Lai F-C (2008) Location choice and optimal zoning under Cournot competition. Reg Sci Urban Econ 38(2):119–126CrossRefGoogle Scholar
  11. Colombo S (2012) On optimal zoning in a linear town with Cournot competitors. Lett Spat Resour Sci 5(2):113–118CrossRefGoogle Scholar
  12. Cremer H, Marchand M, Thisse J-F (1991) Mixed oligopoly with differentiated products. Int J Ind Org 9(1):43–53CrossRefGoogle Scholar
  13. d’Aspremont C, Gabszewicz JJ, Thisse J-F (1979) On Hotelling’s stability in competition. Econometrica 47(5):1145–1150CrossRefGoogle Scholar
  14. Ebina T, Matsumura T, Shimizu D (2011) Spatial Cournot equilibria in a quasi-linear city. Pap Reg Sci 90(3):613–628CrossRefGoogle Scholar
  15. Galster G, Hanson R, Ratcliffe MR, Wolman H, Coleman S, Freihage J (2001) Wrestling sprawl to the ground: defining and measuring an elusive concept. Hous Policy Debate 12(4):681–717CrossRefGoogle Scholar
  16. Haraguchi J, Matsumura T (2016) Cournot-Bertrand comparison in a mixed oligopoly. J Econ 117(2):117–136CrossRefGoogle Scholar
  17. Hotelling H (1929) Stability in competition. Econ J 39:41–57Google Scholar
  18. Inoue T, Kamijo Y, Tomaru Y (2009) Interregional mixed duopoly. Reg Sci Urban Econ 39(2):233–242CrossRefGoogle Scholar
  19. Johnson MP (2001) Environmental impacts of urban sprawl: a survey of the literature and proposed research agenda. Environ Plan A 33(4):717–735CrossRefGoogle Scholar
  20. Kasanko M, Barredo JI, Lavalle C, McCormick N, Demicheli L, Sagris V, Brezger A (2006) Are European cities becoming dispersed? A comparative analysis of 15 European urban areas. Landsc Urban Plan 77(1–2):111–130CrossRefGoogle Scholar
  21. Kitahara M, Matsumura T (2013) Mixed duopoly, product differentiation and competition. Manch Sch 81(5):730–744CrossRefGoogle Scholar
  22. Lai F-C, Tsai J-F (2004) Duopoly locations and optimal zoning in a small open city. J Urban Econ 55(3):614–626CrossRefGoogle Scholar
  23. Lambertini L (1994) Equilibrium locations in the unconstrained Hotelling game. Econ Notes 23:438–446Google Scholar
  24. Lambertini L (1997) Unicity of the equilibrium in the unconstrained Hotelling model. Reg Sci Urban Econ 27(6):785–798CrossRefGoogle Scholar
  25. Lopez R, Hynes HP (2003) Sprawl in the 1990s: measurement, distribution, and trends. Urban Aff Rev 38(3):325–355CrossRefGoogle Scholar
  26. Matsumura T (1998) Partial privatization in mixed duopoly. J Pubic Econ 70(3):473–483CrossRefGoogle Scholar
  27. Matsumura T, Matsushima N (2012a) Locating outside a linear city can benefit consumers. J Reg Sci 52(3):420–432CrossRefGoogle Scholar
  28. Matsumura T, Matsushima N (2012b) Airport privatization and international competition. Jpn Econ Rev 63(4):431–450CrossRefGoogle Scholar
  29. Matsumura T, Matsushima N (2012c) Welfare properties of strategic R&D investments in Hotelling models. Econ Lett 115(3):465–468CrossRefGoogle Scholar
  30. Matsumura T, Shimizu D (2005) Spatial Cournot competition and economic welfare: a note. Reg Sci Urban Econ 35(6):658–670CrossRefGoogle Scholar
  31. Matsushima N, Matsumura T (2003) Mixed oligopoly and spatial agglomeration. Can J Econ 36(1):62–87CrossRefGoogle Scholar
  32. Matsushima N, Matsumura T (2006) Mixed oligopoly, foreign firms, and location choice. Reg Sci Urban Econ 36(6):753–772CrossRefGoogle Scholar
  33. Tabuchi T, Thisse J-F (1995) Asymmetric equilibria in spatial competition. Int J Ind Org 13(2):213–227CrossRefGoogle Scholar
  34. Tsai Y-H (2005) Quantifying urban form: compactness versus ‘Sprawl’. Urban Stud 42(1):141–161CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  1. 1.Departamento de Fundamentos del Análisis Económico I, Facultad de Ciencias Económicas y EmpresarialesUniversidad del País VascoBilbaoSpain

Personalised recommendations