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The Hierarchical Structure of the Firm: A Geometric Perspective

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Abstract

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 span of control. A perfectly competitive firm chooses height and width, as well as capital, in order to maximize profit. We analyze 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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Paper provided by School of Economics, University of Queensland, Australia in its series Discussion Papers Series with number 362.

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Date of creation: 2008
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Handle: RePEc:qld:uq2004:362

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Keywords: Theory of the firm; Hierarchical structure; Economies of scale; Input substitutability; Inequality;

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  1. repec:ebl:ecbull:v:12:y:2005:i:13:p:1-7 is not listed on IDEAS
  2. Oliver E. Williamson, 1967. "Hierarchical Control and Optimum Firm Size," Journal of Political Economy, University of Chicago Press, vol. 75, pages 123.
  3. Raghuram G. Rajan & Luigi Zingales, 2001. "The Firm As A Dedicated Hierarchy: A Theory Of The Origins And Growth Of Firms," The Quarterly Journal of Economics, MIT Press, vol. 116(3), pages 805-851, August.
  4. Kam Ki Tang & Leopoldo Yanes, 2009. "The hierarchical structure of the firm: a geometric perspective," Prague Economic Papers, University of Economics, Prague, vol. 2009(2), pages 156-175.
  5. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: controls," Games and Economic Behavior, Elsevier, vol. 45(1), pages 153-170, October.
  6. 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.
  7. 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.
  8. Hart, Oliver D. & Moore, John, 2005. "On the Design of Hierarchies: Coordination Versus Specialization," Scholarly Articles 3448676, Harvard University Department of Economics.
  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. 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.
  11. 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.
  12. Edward P. Lazear & Sherwin Rosen, 1979. "Rank-Order Tournaments as Optimum Labor Contracts," NBER Working Papers 0401, National Bureau of Economic Research, Inc.
  13. Dubey, Pradeep & Haimanko, Ori, 2003. "Optimal scrutiny in multi-period promotion tournaments," Games and Economic Behavior, Elsevier, vol. 42(1), pages 1-24, January.
  14. 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.
  15. 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.
  16. Hu, Xingwei & Shapley, Lloyd S., 2003. "On authority distributions in organizations: equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 132-152, October.
  17. Lloyd S. Shapley & Jorge R. Palamara, 2000. "Simple Games and Authority Structure," UCLA Economics Working Papers 796, UCLA Department of Economics.
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Cited by:
  1. Kam Ki Tang & Leopoldo Yanes, 2009. "The hierarchical structure of the firm: a geometric perspective," Prague Economic Papers, University of Economics, Prague, vol. 2009(2), pages 156-175.
  2. Luis Otávio Façanha & Marcelo Resende, 2006. "Hierarchical Structure in Brazilian Industrial Firms: an Econometric Study," Economics Working Papers ECO2006/1, European University Institute.
  3. Luis Façanha & Marcelo Resende, 2010. "Determinants of hierarchical structure in industrial firms: an empirical study," Economics of Governance, Springer, vol. 11(3), pages 295-308, June.

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