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Loss Distance Functions and Profit Function: General Duality Results

Author

Listed:
  • Aparicio, Juan

    () (Center of Operations Research (CIO), Universidad Miguel Hernandez de Elche)

  • Borras, Fernando

    () (Department of Statistics, Mathematics and Computer Science, University Miguel Hernandez of Elche.)

  • Pastor, Jesús T.

    () (Center of Operations Research (CIO), Universidad Miguel Hernandez de Elche)

  • Zofio, Jose Luis

    () (Departamento de Análisis Económico (Teoría e Historia Económica). Universidad Autónoma de Madrid.)

Abstract

The concept of loss distance functions is introduced and compared with other functional representations of the technology including the Hölder metric distance functions (Briec and Lesourd (1999)), the directional distance functions due to Chambers et al. (1996, 1998), and the Shephard’s input and output distance functions as particular cases of the directional distance functions. Specifically, it is shown that, under appropriate normalization conditions defined over the (intrinsic) input and output prices, the loss distance functions encompass a wide class of well-known and much less known distance functions. Additionally, a dual correspondence is developed between the loss distance functions and the profit function, and it is shown that all previous dual connections appeared in the literature are special cases of this general correspondence. Finally, we obtain several interesting results assuming differentiability.

Suggested Citation

  • 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).
  • Handle: RePEc:uam:wpaper:201506
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    File URL: http://www.uam.es/departamentos/economicas/analecon/especifica/mimeo/wp20156.pdf
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    References listed on IDEAS

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    1. Jean-Marc Bonnisseau & Bertrand Crettez, 2007. "On the Characterization of Efficient Production Vectors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 213-223, May.
    2. 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.
    3. Paul A. Samuelson, 1953. "Prices of Factors and Goods in General Equilibrium," Review of Economic Studies, Oxford University Press, vol. 21(1), pages 1-20.
    4. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
    5. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    6. Diewert, W. E., 1973. "Functional forms for profit and transformation functions," Journal of Economic Theory, Elsevier, vol. 6(3), pages 284-316, June.
    7. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    8. Aparicio, Juan & Borras, Fernando & Pastor, Jesus T. & Vidal, Fernando, 2015. "Measuring and decomposing firm׳s revenue and cost efficiency: The Russell measures revisited," International Journal of Production Economics, Elsevier, vol. 165(C), pages 19-28.
    9. Cooper, W.W. & Pastor, Jesus T. & Aparicio, Juan & Borras, Fernando, 2011. "Decomposing profit inefficiency in DEA through the weighted additive model," European Journal of Operational Research, Elsevier, vol. 212(2), pages 411-416, July.
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    11. repec:spr:compst:v:60:y:2004:i:1:p:101-123 is not listed on IDEAS
    12. 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.
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    Cited by:

    1. Orea, Luis & Zofío, José L., 2017. "A primer on the theory and practice of efficiency and productivity analysis," Efficiency Series Papers 2017/05, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).

    More about this item

    Keywords

    Loss distance functions; directional distance functions; Hölder distance functions; duality; profit function.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance

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