Networks of Firms and the Ridge in the Production Space

  • Wataru Souma
Part of the New Economic Windows book series (NEW)


We develop complex networks that represent activities in the economy. The network in this study is constructed from firms and the relationships between firms, i.e., shareholding, interlocking directors, transactions, and joint applications for patents. Thus, the network is regarded as a multigraph, and it is also regarded as a weighted network. By calculating various network indices, we clarify the characteristics of the network. We also consider the dynamics of firms in the production space that are characterized by capital stock, employment, and profit. Each firm moves within this space to maximize their profit by using controlling of capital stock and employment. We show that the dynamics of rational firms can be described using a ridge equation. We analytically solve this equation by assuming the extensive Cobb-Douglas production function, and thereby obtain a solution. By comparing the distribution of firms and this solution, we find that almost all of the 1,100 firms listed on the first section of the Tokyo stock exchange and belonging to the manufacturing sector are managed efficiently.


Production Function Capital Stock Production Space Manufacturing Sector Betweenness Centrality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aoyama H, et al. (2007) The production function and the ridge theory of firms. in preparationGoogle Scholar
  2. 2.
    Aoyama H, Kikuchi H (1992) A new valley method for instanton deformation. Nuclear Physics B 369: 219–234CrossRefADSGoogle Scholar
  3. 3.
    Battiston S, Bonabeau E, Weisbuch G (2003) Decision making dynamics in corporate boards. Physica A 322: 567–582MATHCrossRefADSGoogle Scholar
  4. 4.
    Cobb CW, Douglas PH (1928) A theory of production. American Economic Review 18: 139–165Google Scholar
  5. 5.
    Davis G, Yoo M, Baker WE (2003) The small world of the American corporate elite, 1982–2001. Strategic Organization 3: 301–326CrossRefGoogle Scholar
  6. 6.
    Garlaschelli D, et al. (2003) The scale-free topology of market investments. Physica A 350: 491–499CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Li X, Jin YY, Chen G (2003) Complexity and synchronization of the World trade Web. Physica A 328: 287–296MATHCrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Li X, Jin YY, Chen G (2004) On the topology of the world exchange arrangements web. Physica A 343: 573–582CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Souma W, Fujiwara Y, Aoyama H (2003) Complex networks and economics. Physica A 324: 396–401MATHCrossRefADSMathSciNetGoogle Scholar
  10. 10.
    Souma W, Fujiwara Y, Aoyama H (2004) Random matrix approach to shareholding networks. Physica A 344: 73–76CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Souma W, Fujiwara Y, Aoyama H (2005) Heterogeneous economic networks. In: Namatame A, et al. (Eds.) The Complex Networks of Economic Interactions: Essays in Agent-Based Economics and Econophysics (Lecture Notes in Economics and Mathematical Systems, Vol. 567), Springer-Verlag, Tokyo, pp. 79–92Google Scholar
  12. 12.
    Souma W, Fujiwara Y, Aoyama H (2005) Shareholding networks in Japan. In: Mendes JFF, et al. (Eds.) Science of Complex Networks: From Biology to the Internet And WWW CNET2004 (API Conference Proceedings, Vol. 776), Melville, New York, pp. 298–307.Google Scholar
  13. 13.
    Souma W, et al. (2006) Correlation in business networks. Physica A 370: 151–155CrossRefADSGoogle Scholar
  14. 14.
    Varian H.R (1992) Microeconomic Analysis-Third edition. W. W. Norton & Company, Inc.Google Scholar

Copyright information

© Springer-Verlag Italia 2007

Authors and Affiliations

  • Wataru Souma
    • 1
  1. 1.NiCT/ATR CIS Applied Network Science Lab.KyotoJapan

Personalised recommendations