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Continuous Approximations in the Study of Hierarchies


  • Timothy Van Zandt


Large organizations are typically modelled as hierarchies. Hierarchies are discrete structures (trees), but researchers frequently use continuous aproximations. The purpose of this article is to study the validity of these approximations. I show that modelling 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 approximations.

Suggested Citation

  • Timothy Van Zandt, 1995. "Continuous Approximations in the Study of Hierarchies," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 575-590, Winter.
  • Handle: RePEc:rje:randje:v:26:y:1995:i:winter:p:575-590

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    References listed on IDEAS

    1. Rey, Patrick & Stiglitz, Joseph, 1988. "Vertical restraints and producers' competition," European Economic Review, Elsevier, vol. 32(2-3), pages 561-568, March.
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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.

    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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