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Shadow Profit Maximization and a Generalized Measure of Inefficiency

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  • Subhash C. Ray

    (University of Connecticut)

Abstract

Determining the profit maximizing input-output bundle of a firm requires data on prices. This paper shows how endogenously determined shadow prices can be used in place of actual prices to obtain the optimal input-output bundle where the firm.s shadow profit is maximized. This approach amounts to an application of the Weak Axiom of Profit Maximization (WAPM) formulated by Varian (1984) based on shadow prices rather than actual prices. At these prices the shadow profit of a firm is zero. Thus, the maximum profit that could have been attained at some other input-output bundle is a measure of the inefficiency of the firm. Because the benchmark input-output bundle is always an observed bundle from the data, it can be determined without having to solve any elaborate programming problem. An empirical application to U.S. airlines data illustrates the proposed methodology.

Suggested Citation

  • Subhash C. Ray, 2005. "Shadow Profit Maximization and a Generalized Measure of Inefficiency," Working papers 2005-14, University of Connecticut, Department of Economics.
  • Handle: RePEc:uct:uconnp:2005-14
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    File URL: http://web2.uconn.edu/economics/working/2005-14.pdf
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    References listed on IDEAS

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    1. Athanassopoulos, Antreas D. & Lambroukos, Nikos & Seiford, Lawrence, 1999. "Data envelopment scenario analysis for setting targets to electricity generating plants," European Journal of Operational Research, Elsevier, vol. 115(3), pages 413-428, June.
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    3. Walter Briec & Hervé Leleu, 2003. "Dual Representations of Non-Parametric Technologies and Measurement of Technical Efficiency," Journal of Productivity Analysis, Springer, vol. 20(1), pages 71-96, July.
    4. Ray, Subhash C & Mukherjee, Kankana, 1996. "Decomposition of the Fisher Ideal Index of Productivity: A Non-parametric Dual Analysis of US Airlines Data," Economic Journal, Royal Economic Society, vol. 106(439), pages 1659-1678, November.
    5. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    6. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-597, May.
    7. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    8. Douglas W. Caves & Laurits R. Christensen & Michael W. Tretheway, 1984. "Economies of Density versus Economies of Scale: Why Trunk and Local Service Airline Costs Differ," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 471-489, Winter.
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    More about this item

    Keywords

    DEA; Shadow Prices; Non-radial Efficiency;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory

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