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Evolutionary Model of the Growth and Size of Firms

  • Joachim Kaldasch

The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat's law of proportionate effects as the result of the competition between products. Applying a preferential attachment mechanism for firms the theory allows to establish the size distribution of products and firms. Also established are the growth rate and price distribution of consumer goods. Taking into account the characteristic property of human activities to occur in bursts, the model allows also an explanation of the size-variance relationship of the growth rate distribution of products and firms. Further the product life cycle, the learning (experience) curve and the market size in terms of the mean number of firms that can survive in a market are derived. The model also suggests the existence of an invariant of a market as the ratio of total profit to total revenue. The relationship between a neo-classic and an evolutionary view of a market is discussed. The comparison with empirical investigations suggests that the theory is able to describe the main stylized facts concerning the size and growth of firms.

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File URL: http://arxiv.org/pdf/1208.1123
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Paper provided by arXiv.org in its series Papers with number 1208.1123.

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Date of creation: Aug 2012
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Handle: RePEc:arx:papers:1208.1123
Contact details of provider: Web page: http://arxiv.org/

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  1. Kaushik Matia & Dongfeng Fu & Sergey V. Buldyrev & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2005. "Statistical Properties of Business Firms Structure and Growth," Papers physics/0502081, arXiv.org.
  2. De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003. "On Size and Growth of Business Firms," MPRA Paper 15866, University Library of Munich, Germany.
  3. Sergey V. Buldyrev & Jakub Growiec & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2007. "The Growth of Business Firms: Facts and Theory," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 574-584, 04-05.
  4. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
  5. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
  6. Jos\`e T. Lunardi & Salvatore Miccich\`e & Fabrizio Lillo & Rosario N. Mantegna & Mauro Gallegati, 2011. "Do firms share the same functional form of their growth rate distribution? A new statistical test," Papers 1103.2234, arXiv.org.
  7. Fu, Dongfeng & Pammolli, Fabio & Buldyrev, Sergey V. & Riccaboni, Massimo & Matia, Kaushik & Yamasaki, Kazuko & Stanley, H. Eugene, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," MPRA Paper 15905, University Library of Munich, Germany.
  8. Joachim Kaldasch, 2011. "Evolutionary Model of Non-Durable Markets," Papers 1109.5791, arXiv.org.
  9. Giulio Bottazzi & Sandro Sapio & Angelo Secchi, 2004. "Some Statistical Investigations on the Nature and Dynamics of Electricity Prices," LEM Papers Series 2004/13, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  10. Peter Richmond & Sorin Solomon, 2000. "Power Laws are Boltzmann Laws in Disguise," Papers cond-mat/0010222, arXiv.org.
  11. Banerjee, Anand & Yakovenko, Victor M. & Di Matteo, T., 2006. "A study of the personal income distribution in Australia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 54-59.
  12. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
  13. repec:cup:cbooks:9780521191494 is not listed on IDEAS
  14. Anand Banerjee & Victor M. Yakovenko & T. Di Matteo, 2006. "A study of the personal income distribution in Australia," Papers physics/0601176, arXiv.org.
  15. Kaldasch, Joachim, 2011. "Evolutionary model of an anonymous consumer durable market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2692-2715.
  16. Boris Podobnik & Davor Horvatic & Alexander M. Petersen & Branko Uro\v{s}evi\'c & H. Eugene Stanley, 2010. "Bankruptcy risk model and empirical tests," Papers 1011.2670, arXiv.org.
  17. Zhu Wang, 2008. "Income Distribution, Market Size and the Evolution of Industry," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 542-565, July.
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