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On the Characterization of Efficient Production Vectors

Author

Listed:
  • Jean-Marc Bonnisseau

    () (CES - Centre d'économie de la Sorbonne - CNRS - Centre National de la Recherche Scientifique - UP1 - Université Panthéon-Sorbonne, PSE - Paris School of Economics)

  • Bertrand Crettez

    (LIBRE - Laboratoire interdisciplinaire bisontin de recherches économiques - M.E.N.E.S.R. - Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche - UFC - Université de Franche-Comté)

Abstract

In this paper we study the efficient points of a closed production set with free disposal. We first provide a condition on the boundary of the production set, which is equivalent to the fact that all boundary points are efficient. When the production set is convex, we also give an alternative characterization of efficiency around a given production vector in terms of the profit maximization rule. In the non-convex case, this condition expressed with the marginal pricing rule is sufficient for efficiency. Then we study the Luenberger's shortage function. We first provide basic properties on it. Then, we prove that the above necessary condition at a production vector implies that the shortage function is locally Lipschitz continuous and the efficient points in a neighborhood are the zeros of it and conversely.

Suggested Citation

  • Jean-Marc Bonnisseau & Bertrand Crettez, 2007. "On the Characterization of Efficient Production Vectors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00265699, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00265699
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00265699
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    References listed on IDEAS

    as
    1. Cornet, B., 1984. "Existence of equilibria in economies with increasing returns," CORE Discussion Papers 1984007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Khan, M Ali, 1999. " The Mordukhovich Normal Cone and the Foundations of Welfare Economics," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(3), pages 309-338.
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    Citations

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    Cited by:

    1. R. Russell & William Schworm, 2011. "Properties of inefficiency indexes on 〈input, output〉 space," Journal of Productivity Analysis, Springer, vol. 36(2), pages 143-156, October.
    2. repec:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0558-y is not listed on IDEAS
    3. repec:spr:joptap:v:174:y:2017:i:3:d:10.1007_s10957-017-1146-8 is not listed on IDEAS
    4. Aparicio, Juan & Borras, Fernando & Pastor, Jesús T. & Zofio, Jose Luis, 2015. "Loss Distance Functions and Profit Function: General Duality Results," Working Papers in Economic Theory 2015/06, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
    5. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    6. Fabián Flores-Bazán & Sigifredo Laengle & Gino Loyola, 2013. "Characterizing the efficient points without closedness or free-disposability," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(2), pages 401-410, March.

    More about this item

    Keywords

    Shortage function; Production efficiency;

    JEL classification:

    • D20 - Microeconomics - - Production and Organizations - - - General
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

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