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Bipartite producer–consumer networks and the size distribution of firms

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

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    2. 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).
    3. 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.
    4. 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.
    5. 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).
    6. 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.
    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.

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