IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v363y2006i2p359-366.html
   My bibliography  Save this article

Bipartite producer–consumer networks and the size distribution of firms

Author

Listed:
  • Dahui, Wang
  • Li, Zhou
  • Zengru, Di

Abstract

A bipartite producer–consumer network is constructed to describe the industrial structure. The edges from consumer to producer represent the choices of the consumer for the final products and the degree of producer can represent its market share. So the size distribution of firms can be characterized by producer's degree distribution. The probability for a producer receiving a new consumption is determined by its competency described by initial attractiveness and the self-reinforcing mechanism in the competition described by preferential attachment. The cases with constant total consumption and with growing market are studied. The following results are obtained: (1) Without market growth and a uniform initial attractiveness a, the final distribution of firm sizes is Gamma distribution for a>1 and is exponential for a=1. If a<1, the distribution is power in small size and exponential in upper tail. (2) For a growing market, the size distribution of firms obeys the power-law. The exponent is affected by the market growth and the initial attractiveness of the firms.

Suggested Citation

  • Dahui, Wang & Li, Zhou & Zengru, Di, 2006. "Bipartite producer–consumer networks and the size distribution of firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 359-366.
    • Handle: RePEc:eee:phsmap:v:363:y:2006:i:2:p:359-366
    DOI: 10.1016/j.physa.2005.08.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437105008319
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2005.08.006?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Guilmi, Corrado Di & Gallegati, Mauro & Ormerod, Paul, 2004. "Scaling invariant distributions of firms’ exit in OECD countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 267-273.
    2. Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004. "Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 197-216.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Heinrich, Torsten, 2015. "A Discontinuity Model of Technological Change: Catastrophe Theory and Network Structure," MPRA Paper 68089, University Library of Munich, Germany.
    2. Heinrich, Torsten & Dai, Shuanping, 2016. "Diversity of firm sizes, complexity, and industry structure in the Chinese economy," Structural Change and Economic Dynamics, Elsevier, vol. 37(C), pages 90-106.
    3. Bill McKelvey & Benyamin B. Lichtenstein & Pierpaolo Andriani, 2012. "When organisations and ecosystems interact: toward a law of requisite fractality in firms," International Journal of Complexity in Leadership and Management, Inderscience Enterprises Ltd, vol. 2(1/2), pages 104-136.
    4. Yang, Shiju & Li, Chuandong & He, Xiping & Zhang, Wanli, 2022. "Variable-time impulsive control for bipartite synchronization of coupled complex networks with signed graphs," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    5. Sun, Mei & Zhang, Pei-Pei & Shan, Tian-Hua & Fang, Cui-Cui & Wang, Xiao-Fang & Tian, Li-Xin, 2012. "Research on the evolution model of an energy supply–demand network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4506-4516.
    6. Cao, GangCheng & Fang, Debin & Wang, Pengyu, 2021. "The impacts of social learning on a real-time pricing scheme in the electricity market," Applied Energy, Elsevier, vol. 291(C).
    7. Pierpaolo Andriani & Bill McKelvey, 2009. "Perspective ---From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations," Organization Science, INFORMS, vol. 20(6), pages 1053-1071, December.
    8. Wang, Pengyu & Fang, Debin & Cao, GangCheng, 2022. "How social learning affects customer behavior under the implementation of TOU in the electricity retailing market," Energy Economics, Elsevier, vol. 106(C).
    9. Torsten Heinrich, 2018. "A Discontinuity Model of Technological Change: Catastrophe Theory and Network Structure," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 407-425, March.

    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. Ma, Qi & Chen, Yongwang & Tong, Hui & Di, Zengru, 2008. "Production, depreciation and the size distribution of firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3209-3217.
    2. Gao, Baojun & Chan, Wai Kin (Victor) & Li, Hongyi, 2015. "On the increasing inequality in size distribution of China's listed companies," China Economic Review, Elsevier, vol. 36(C), pages 25-41.
    3. Wang Dahui & Zhou Li & Di Zengru, 2005. "Bipartite Producer-Consumer Networks and the Size Distribution of Firms," Papers physics/0507163, arXiv.org.
    4. Petra Štamfestová & Lukáš Sobíšek & Jiří Hnilica, 2023. "Firm Size Distribution in the Central European Context," Central European Business Review, Prague University of Economics and Business, vol. 2023(5), pages 151-175.
    5. Segarra, Agustí & Teruel, Mercedes, 2012. "An appraisal of firm size distribution: Does sample size matter?," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 314-328.
    6. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, January.
    7. Caiani, Alessandro & Godin, Antoine & Caverzasi, Eugenio & Gallegati, Mauro & Kinsella, Stephen & Stiglitz, Joseph E., 2016. "Agent based-stock flow consistent macroeconomics: Towards a benchmark model," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 375-408.
    8. Xavier Gabaix & Augustin Landier, 2008. "Why has CEO Pay Increased So Much?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 49-100.
    9. Atushi Ishikawa, 2007. "The log-normal distribution from Non-Gibrat's law in the middle scale region of profits," Papers 0705.1056, arXiv.org.
    10. Atushi Ishikawa & Shouji Fujimoto & Tsutomu Watanabe & Takayuki Mizuno, 2012. "The Emergence of Different Tail Exponents in the Distributions of Firm Size Variables," UTokyo Price Project Working Paper Series 003, University of Tokyo, Graduate School of Economics, revised Dec 2012.
    11. Dosi, Giovanni & Fagiolo, Giorgio & Napoletano, Mauro & Roventini, Andrea, 2013. "Income distribution, credit and fiscal policies in an agent-based Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1598-1625.
    12. Giovanni Dosi & Mauro Napoletano & Andrea Roventini & Joseph E. Stiglitz & Tania Treibich, 2020. "Rational Heuristics? Expectations And Behaviors In Evolving Economies With Heterogeneous Interacting Agents," Economic Inquiry, Western Economic Association International, vol. 58(3), pages 1487-1516, July.
    13. Gerrit de Wit, 2005. "Zipf's Law in Economics," Scales Research Reports N200503, EIM Business and Policy Research.
    14. Kiyoyasu Tanaka & Naomi Hatsukano, 2011. "The size distribution of all Cambodian establishments," Economics Bulletin, AccessEcon, vol. 31(3), pages 2128-2137.
    15. Ormerod, Paul, 2015. "The economics of radical uncertainty," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 9, pages 1-20.
    16. Andrew G. Haldane & Arthur E. Turrell, 2019. "Drawing on different disciplines: macroeconomic agent-based models," Journal of Evolutionary Economics, Springer, vol. 29(1), pages 39-66, March.
    17. Yue Xu & Zebin Wang & Yung-Ho Chiu & Fangrong Ren, 2020. "Research on energy-saving and emissions reduction efficiency in Chinese thermal power companies," Energy & Environment, , vol. 31(5), pages 903-919, August.
    18. Ishikawa, Atushi & Fujimoto, Shouji & Mizuno, Takayuki, 2011. "Shape of growth-rate distribution determines the type of Non-Gibrat’s Property," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4273-4285.
    19. Marko Peric & Vanja Vitezic, 2016. "Impact of global economic crisis on firm growth," Small Business Economics, Springer, vol. 46(1), pages 1-12, January.
    20. Faustino Prieto & José María Sarabia & Enrique Calderín-Ojeda, 2021. "The nonlinear distribution of employment across municipalities," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(2), pages 287-307, April.

    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:eee:phsmap:v:363:y:2006:i:2:p:359-366. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.