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Spatial-structure differences between urban and regional systems


The total population and the overall average density are derived for a single city, in which the spatial structure conforms approximately to the negative exponential function. It is then shown that across the cities of an urban system, the areal extent of a city is positively related to its average density and also to its population. Consideration is next given to a system of regions and again to the manner in which areal extent is related to average density and population across regions. In this setting, however, the relationships are usually different from those found within an urban system.

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  1. Alesina A, Spolaore E (1997) On the number and size of nations. Q J Econ 112: 1027–1056

  2. Alonso W (1964) Location and land use. Harvard University Press, Cambridge, MA

  3. Amson J (1972) The dependence of population distribution on location costs. Environ Plann 4: 163–181

  4. Ashenfelter O (1976) On the interpretation of urban density functions. J Urban Econ 3: 82–87

  5. Batty M, Kim S (1992) Form follows function: reformulating urban population density functions. Urban Stud 18: 1043–1070

  6. Berry B, Simmons J, Tennant R (1963) Urban population densities: structure and change. Geogr Rev 53: 389–405

  7. Bleicher H (1892) Statistische Beschreibung der Stadt Frankfurt am Main und ihrer Bevölkerung. J Sauerländer Verlag, Frankfurt am Main

  8. Bogue D (1950) The structure of the metropolitan community. Horace H. Rackham School of Graduate Studies, University of Michigan, Ann Arbor, MI

  9. Bussière R (1972) Static and dynamic characteristics of the negative exponential distribution. In: Wilson A (ed) Patterns and processes in urban and regional systems (London Papers in Regional Science, vol 3). Pion, London

  10. Bussière R, Stovall T (1977) Modèle générale de la région et de ses villes. Urbanism 157–158: 60

  11. Clark C (1951) Urban population densities. J R Stat Soc Ser A 114: 490–496

  12. Cliff A, Haggett P, Ord J, Bassett K, Davies R (1975) Elements of spatial structure: a quantitative approach. Cambridge University Press, Cambridge

  13. Edmonston B, Davies O (1978) Interpreting the negative exponential density gradient. J R Stat Soc Ser A 141: 235–241

  14. Lösch A (1944/1954) Die räumliche Ordnung der Wirtschaft (2nd edn). Gustav Fischer, Jena. Translated by William H. Woglom and Wolgang F. Stolper as The economics of location. Yale University Press, New Haven CT

  15. Meuriot P (1898) Des agglomérations urbaines dans l’Europe contemporaine: essai sur les causes, les conditions, les conséquences de leur développment. Belin Frères, Paris

  16. Meyer J (1963) Regional economics: a survey. Am Econ Rev 53: 19–54

  17. Mills E (1972) Studies in the structure of the urban economy. The Johns Hopkins Press, Baltimore MD

  18. Muth R (1969) Cities and housing. University of Chicago Press, Chicago IL

  19. Parr J (1985) The form of the regional density function. Reg Stud 19: 535–546

  20. Parr J (2007) On the spatial structure of administration. Environ Plann A 39: 1255–1268

  21. Rushton G (1972) Map transformations of point patterns: central place patterns in areas of variable population density. Pap Reg Sci Assoc 28: 111–129

  22. Skinner G (1964) Marketing and social structure in rural China. J Asian Stud 24: 3–43

  23. Stephan G (1972) International tests of the size-density hypothesis. Am Sociol Rev 37: 365–368

  24. Stephan G (1977) Territorial subdivision: the least-time constraint behind the forma-tion of subnational boundaries. Science 196: 523–524

  25. Stewart J, Warntz W (1958) Physics of population distribution. J Reg Sci 1: 99–123

  26. Vining D, Louw S (1978) A cautionary note on the use of the allometric function to estimate urban populations. Prof Geogr 30: 365–370

  27. Vining D, Yang C-H, Yeh S-T (1979) Political subdivision and population density. Science 205: 219

  28. Weiss H (1961) The distribution of urban population and an application to a servicing problem. Oper Res 9: 860–874

  29. Winsborough H (1961) A comparative study of urban population densities. Unpublished PhD Dissertation, University of Chicago, Chicago IL

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Author information

Correspondence to John B. Parr.

Additional information

The author wishes to thank C. Athorne, G. Wood, T. Gloyne, A Grimes, D. Holden and D. Vining for their suggestions and comments on earlier versions of this paper.

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Parr, J.B. Spatial-structure differences between urban and regional systems. Ann Reg Sci 49, 293–303 (2012). https://doi.org/10.1007/s00168-010-0421-5

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JEL Classification

  • R12
  • R23
  • R53