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The hierarchical structure of the firm: a geometric perspective

  • Kam Ki Tang
  • Leopoldo Yanes

This paper incorporates hierarchical structure into the neoclassical theory of the firm. Firms are hierarchical in two respects: the organization of workers in production and the wage structure. The firm's hierarchy is represented as a sector of a circle, where the radius represents the hierarchy's height, the width of the sector represents the breadth of the hierarchy at a given height, and the angle of the sector represents the span of control. A perfectly competitive firm chooses height and width, as well as capital, in order to maxi-mize profit. We analyse the short-run and long-run impact of changes in scale economies, input substitutability, and input and output prices on the firm's hierarchical structure. We find that the firm grows as the specialization of its workers increases or as its output price increases relative to input prices. The effect of changes in scale economies is contingent on the price of output. The model also brings forth an analysis of wage inequality within the firm, which is found to be independent of the firm's hierarchical organization of workers, and only depends on the firm's wage schedule.

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Article provided by University of Economics, Prague in its journal Prague Economic Papers.

Volume (Year): 2009 (2009)
Issue (Month): 2 ()
Pages: 156-175

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Handle: RePEc:prg:jnlpep:v:2009:y:2009:i:2:id:347:p:156-175
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  1. Kam Ki Tang & Leopoldo Yanes, 2008. "The Hierarchical Structure of the Firm: A Geometric Perspective," Discussion Papers Series 362, School of Economics, University of Queensland, Australia.
  2. Grossman, Sanford J & Hart, Oliver D, 1986. "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 691-719, August.
  3. Oliver Hart & John Moore, 1999. "On the Design of Hierarchies: Coordination Versus Specialization," NBER Working Papers 7388, National Bureau of Economic Research, Inc.
  4. Luis Garicano, 2000. "Hierarchies and the Organization of Knowledge in Production," Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 874-904, October.
  5. Raghuram G. Rajan & Luigi Zingales, 2000. "The Firm as a Dedicated Hierarchy: A Theory of the Origin and Growth of Firms," NBER Working Papers 7546, National Bureau of Economic Research, Inc.
  6. Edward P. Lazear & Sherwin Rosen, 1979. "Rank-Order Tournaments as Optimum Labor Contracts," NBER Working Papers 0401, National Bureau of Economic Research, Inc.
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  8. Pradeep Dubey & Ori Haimanko, 2000. "Optimal Scrutiny in Multi-Period Promotion Tournaments," Cowles Foundation Discussion Papers 1254, Cowles Foundation for Research in Economics, Yale University.
  9. Teece, David J., 1980. "Economies of scope and the scope of the enterprise," Journal of Economic Behavior & Organization, Elsevier, vol. 1(3), pages 223-247, September.
  10. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  11. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
  12. Lloyd S. Shapley & Jorge R. Palamara, 2000. "Simple Games and Authority Structure," UCLA Economics Working Papers 796, UCLA Department of Economics.
  13. Qian, Yingyi, 1994. "Incentives and Loss of Control in an Optimal Hierarchy," Review of Economic Studies, Wiley Blackwell, vol. 61(3), pages 527-44, July.
  14. Oliver E. Williamson, 1967. "Hierarchical Control and Optimum Firm Size," Journal of Political Economy, University of Chicago Press, vol. 75, pages 123.
  15. Kam Ki Tang & Rodney Beard & Evelyn Ng & Leopoldo Yanes, 2005. "The hierarchical structure of a firm: a geometric approach," Economics Bulletin, AccessEcon, vol. 12(13), pages 1-7.
  16. Garrouste, Pierre & Saussier, Stephane, 2005. "Looking for a theory of the firm: Future challenges," Journal of Economic Behavior & Organization, Elsevier, vol. 58(2), pages 178-199, October.
  17. Wernerfelt, Birger, 1997. "On the Nature and Scope of the Firm: An Adjustment-Cost Theory," The Journal of Business, University of Chicago Press, vol. 70(4), pages 489-514, October.
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