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Bipartite producer–consumer networks and the size distribution of firms

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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
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    References listed on IDEAS

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    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.
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    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. 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.

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