IDEAS home Printed from https://ideas.repec.org/a/wly/jnlmpe/v2023y2023i1n6910016.html

Investigations to the Dynamics of City‐Size Distribution Containing Birth and Death Factors

Author

Listed:
  • Xue Xia
  • Wenyi Huang

Abstract

A kinetic model, which involves emigration, immigration, birth, death, and fluctuation terms, is utilized to investigate the evolution of city‐size distribution. The Boltzmann‐type equation and the corresponding Fokker–Planck equation are obtained to analyze the urban size distribution. Three different population variable functions, containing both birth and death rates, are considered. For each population variable function, the closed form of its stationary solution is derived. It is found that the size of urban population distribution follows a power law. Numerical simulation illustrates the correctness of the results.

Suggested Citation

  • Xue Xia & Wenyi Huang, 2023. "Investigations to the Dynamics of City‐Size Distribution Containing Birth and Death Factors," Mathematical Problems in Engineering, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:6910016
    DOI: 10.1155/2023/6910016
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2023/6910016
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2023/6910016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    2. Garmestani, Ahjond S. & Allen, Craig R. & Gallagher, Colin M., 2008. "Power laws, discontinuities and regional city size distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 68(1), pages 209-216, October.
    3. Lorenzo Pareschi & Giuseppe Toscani, 2014. "Wealth distribution and collective knowledge. A Boltzmann approach," Papers 1401.4550, arXiv.org.
    4. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
    5. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    6. Wenbiao Zhang & Degang Yang & Jinwei Huo, 2016. "Studies of the Relationship between City Size and Urban Benefits in China Based on a Panel Data Model," Sustainability, MDPI, vol. 8(6), pages 1-18, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Valente J. Matlaba & Mark J. Holmes & Philip McCann & Jacques Poot, 2013. "A Century Of The Evolution Of The Urban System In Brazil," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 25(3), pages 129-151, November.
    2. Rafael González-Val, 2019. "US city-size distribution and space," Spatial Economic Analysis, Taylor & Francis Journals, vol. 14(3), pages 283-300, July.
    3. Gualandi, Stefano & Toscani, Giuseppe, 2019. "Size distribution of cities: A kinetic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 221-234.
    4. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, vol. 71(C), pages 193-208.
    5. González-Val, Rafael, 2018. "The spatial distribution of US cities," MPRA Paper 89586, University Library of Munich, Germany.
    6. Arturo, Ramos, 2019. "Have the log-population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century," MPRA Paper 93562, University Library of Munich, Germany.
    7. Kristian Giesen & Jens Suedekum, 2012. "The Size Distribution Across All 'Cities': A Unifying Approach," SERC Discussion Papers 0122, Centre for Economic Performance, LSE.
    8. Marco Bee, 2020. "On discriminating between lognormal and Pareto tail: A mixture-based approach," DEM Working Papers 2020/9, Department of Economics and Management.
    9. Giorgio Fazio & Marco Modica, 2015. "Pareto Or Log-Normal? Best Fit And Truncation In The Distribution Of All Cities," Journal of Regional Science, Wiley Blackwell, vol. 55(5), pages 736-756, November.
    10. Nigai, Sergey, 2017. "A tale of two tails: Productivity distribution and the gains from trade," Journal of International Economics, Elsevier, vol. 104(C), pages 44-62.
    11. Aurélie Lalanne, 2014. "Zipf’s Law and Canadian Urban Growth," Urban Studies, Urban Studies Journal Limited, vol. 51(8), pages 1725-1740, June.
    12. Aurélie Lalanne & Shana Sundstrom & Ahjond Garmestani, 2023. "Discontinuous structure of regional and subregional urban systems: Nouvelle-Aquitaine, France (1800–2015)," Urban Studies, Urban Studies Journal Limited, vol. 60(5), pages 869-884, April.
    13. Kristian Giesen & Jens Suedekum, 2012. "The Size Distribution across all "Cities": A Unifying Approach," CESifo Working Paper Series 3730, CESifo Group Munich.
    14. Rafael Gonz�lez-Val & Arturo Ramos & Fernando Sanz-Gracia, 2013. "The accuracy of graphs to describe size distributions," Applied Economics Letters, Taylor & Francis Journals, vol. 20(17), pages 1580-1585, November.
    15. Ramos, Arturo & Sanz-Gracia, Fernando, 2015. "US city size distribution revisited: Theory and empirical evidence," MPRA Paper 64051, University Library of Munich, Germany.
    16. Jakub Growiec & Fabio Pammolli & Massimo Riccaboni, 2020. "Innovation and Corporate Dynamics: A Theoretical Framework," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(1), pages 1-45, March.
    17. Su, Hsuan-Li, 2020. "On the city size distribution: A finite mixture interpretation," Journal of Urban Economics, Elsevier, vol. 116(C).
    18. Rafael González-Val, 2011. "Deviations from Zipf’s Law for American Cities," Urban Studies, Urban Studies Journal Limited, vol. 48(5), pages 1017-1035, April.
    19. Ruben Dewitte & Michel Dumont & Glenn Rayp & Peter Willemé, 2022. "Unobserved heterogeneity in the productivity distribution and gains from trade," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(3), pages 1566-1597, August.
    20. Anna Kaźmierczak & Alexander Shapoval & Shlomo Weber, 2025. "Unified Zipf-Gibrat Framework for City Formation and Growth: A Theory and Empirics behind the Core-Periphery Tiebout-Weibull Model," Networks and Spatial Economics, Springer, vol. 25(4), pages 1163-1185, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlmpe:v:2023:y:2023:i:1:n:6910016. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/2629 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.