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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, EconWPA, 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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    References listed on IDEAS

    1. Charles Blackorby & Daniel Primont & R. Russell, 2007. "The Morishima gross elasticity of substitution," Journal of Productivity Analysis, Springer, vol. 28(3), pages 203-208, December.
    2. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    3. Chambers,Robert G., 1988. "Applied Production Analysis," Cambridge Books, Cambridge University Press, number 9780521314275, March.
    4. Kohli, Ulrich, 1993. "A Symmetric Normalized Quadratic GNP Function and the U.S. Demand for Imports and Supply of Exports," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(1), pages 243-255, February.
    5. repec:mes:challe:v:31:y:1988:i:4:p:56-58 is not listed on IDEAS
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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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