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Continuous Approximations in the Study of Hierarchies


  • Timothy Van Zandt

    (Princeton University)


Large organizations are typically modeled as hierarchies. Hierarchies are discrete structures (trees), but researchers frequently use continuous approximations. The purpose of this paper is to study the validity of these approximations. I show that modeling hierarchies with a continuum of tiers is not a good approximation. I also show, for a particular model of balanced hierarchies, that ignoring rounding operators and integer constraints in formulae derived from the discrete model can be a valid approximation, when hierarchies are suitably large. This is made precise by bounds on the relative errors of the approximations.

Suggested Citation

  • Timothy Van Zandt, 1995. "Continuous Approximations in the Study of Hierarchies," Microeconomics 9503001, University Library of Munich, Germany, revised 16 Dec 1997.
  • Handle: RePEc:wpa:wuwpmi:9503001
    Note: Published in Rand Journal of Economics, 26:575-590, 1995. (Contact author for a hard copy.)

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    Cited by:

    1. Meagher, Kieron J., 2003. "Generalizing incentives and loss of control in an optimal hierarchy: the role of information technology," Economics Letters, Elsevier, vol. 78(2), pages 273-280, February.
    2. Andrea Patacconi, 2009. "Coordination and delay in hierarchies," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 190-208, March.

    More about this item

    JEL classification:

    • D1 - Microeconomics - - Household Behavior
    • D2 - Microeconomics - - Production and Organizations
    • D3 - Microeconomics - - Distribution
    • D4 - Microeconomics - - Market Structure, Pricing, and Design


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