IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v101y1999i1d10.1023_a1021762809393.html
   My bibliography  Save this article

Metric Distance Function and Profit: Some Duality Results

Author

Listed:
  • W. Briec

    (Université de Rennes 1)

  • J. B. Lesourd

    (Groupement de Recherche en Economis Quantitative d'Aix-Marseille II)

Abstract

In this paper, we intend to establish relations between the way efficiency is measured in the literature on efficiency analysis and the notion of distance in topology. To this effect, we are interested particularly in the Hölder norm concept, providing a duality result based upon the profit function. Along this line, we prove that the Luenberger shortage function and the directional distance function of Chambers, Chung, and Färe appear as special cases of some l p distance (also called Hölder distance), under the assumption that the production set is convex. Under a weaker assumption (convexity of the input correspondence), we derive a duality result based on the cost function, providing several examples in which the functional form of the production set is specified.

Suggested Citation

  • W. Briec & J. B. Lesourd, 1999. "Metric Distance Function and Profit: Some Duality Results," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 15-33, April.
    • Handle: RePEc:spr:joptap:v:101:y:1999:i:1:d:10.1023_a:1021762809393
    DOI: 10.1023/A:1021762809393
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1021762809393
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1021762809393?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    2. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
    3. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    4. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    5. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    6. Robert Russell, R., 1990. "Continuity of measures of technical efficiency," Journal of Economic Theory, Elsevier, vol. 51(2), pages 255-267, August.
    7. W. Briec, 1997. "Minimum Distance to the Complement of a Convex Set: Duality Result," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 301-319, May.
    8. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. W. Briec & K. Kerstens, 2009. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 55-73, April.
    2. Briec, Walter & Dumas, Audrey & Kerstens, Kristiaan & Stenger, Agathe, 2022. "Generalised commensurability properties of efficiency measures: Implications for productivity indicators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1481-1492.
    3. A. Abad & P. Ravelojaona, 2017. "Exponential environmental productivity index and indicators," Journal of Productivity Analysis, Springer, vol. 48(2), pages 147-166, December.
    4. Briec, Walter & Comes, Christine & Kerstens, Kristiaan, 2006. "Temporal technical and profit efficiency measurement: Definitions, duality and aggregation results," International Journal of Production Economics, Elsevier, vol. 103(1), pages 48-63, September.
    5. Arnaud Abad, 2020. "Environmental Efficiency and Productivity Analysis," Working Papers hal-03032038, HAL.
    6. Briec, Walter & Kerstens, Kristiaan & Prior, Diego & Van de Woestyne, Ignace, 2010. "Tangency capacity notions based upon the profit and cost functions: A non-parametric approach and a general comparison," Economic Modelling, Elsevier, vol. 27(5), pages 1156-1166, September.
    7. Yaryna Kolomiytseva, 2018. "Revisiting Transformation and Directional Technology Distance Functions," Papers 1812.10108, arXiv.org.
    8. Juan Aparicio & José L. Zofío & Jesús T. Pastor, 2023. "Decomposing Economic Efficiency into Technical and Allocative Components: An Essential Property," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 98-129, April.
    9. Deng, Zhongqi & Jiang, Nan & Pang, Ruizhi, 2021. "Factor-analysis-based directional distance function: The case of New Zealand hospitals," Omega, Elsevier, vol. 98(C).
    10. Mauricio Benegas & Emerson Marinho, 2008. "Duality, Net Supply, and The Directional Distance Function," Anais do XXXVI Encontro Nacional de Economia [Proceedings of the 36th Brazilian Economics Meeting] 200807211656140, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    11. Walter Briec & Kristiaan Kerstens & Diego Prior, 2009. "Tangency Capacity Notions Based upon the Pro?t and Cost Functions: A Non-Parametric Approach and a Comparison," Working Papers 2009-ECO-05, IESEG School of Management.
    12. Ravelojaona, Paola, 2019. "On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions," European Journal of Operational Research, Elsevier, vol. 272(2), pages 780-791.
    13. Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    14. Subhash C. Ray & Linge Yang, 2024. "Measurement and decomposition of profit efficiency under alternative definitions in nonparametric models," Journal of Productivity Analysis, Springer, vol. 62(3), pages 267-290, December.
    15. Fukuyama, Hirofumi & Weber, William L., 2009. "A directional slacks-based measure of technical inefficiency," Socio-Economic Planning Sciences, Elsevier, vol. 43(4), pages 274-287, December.
    16. Tsionas, Mike & Parmeter, Christopher F. & Zelenyuk, Valentin, 2023. "Bayesian Artificial Neural Networks for frontier efficiency analysis," Journal of Econometrics, Elsevier, vol. 236(2).
    17. Briec, Walter & Fukuyama, Hirofumi & Ravelojaona, Paola, 2021. "Exponential distance function and duality theory," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1002-1014.
    18. Jesus Pastor & C. Lovell & Juan Aparicio, 2012. "Families of linear efficiency programs based on Debreu’s loss function," Journal of Productivity Analysis, Springer, vol. 38(2), pages 109-120, October.
    19. Pestana Barros, Carlos & Peypoch, Nicolas, 2010. "Productivity changes in Portuguese bus companies," Transport Policy, Elsevier, vol. 17(5), pages 295-302, September.
    20. Valentin Zelenyuk, 2023. "Productivity analysis: roots, foundations, trends and perspectives," Journal of Productivity Analysis, Springer, vol. 60(3), pages 229-247, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:101:y:1999:i:1:d:10.1023_a:1021762809393. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.