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Shadow profit maximization and a measure of overall inefficiency

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  • Subhash Ray

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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) The Non-parametric approach to production analysis. Econometrica 52:3 (May) 579–597] based on shadow prices rather than actual prices. At these shadow prices, the shadow profit of a firm is zero. The maximum shadow profit that could have been attained at some other input–output bundle is shown to be 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. Copyright Springer Science+Business Media, LLC 2007

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File URL: http://hdl.handle.net/10.1007/s11123-007-0036-8
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Bibliographic Info

Article provided by Springer in its journal Journal of Productivity Analysis.

Volume (Year): 27 (2007)
Issue (Month): 3 (June)
Pages: 231-236

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Handle: RePEc:kap:jproda:v:27:y:2007:i:3:p:231-236

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Web page: http://www.springerlink.com/link.asp?id=100296

Related research

Keywords: Shadow prices; Weak Axiom of Profit Maximization; Data envelopment analysis; C61; D20;

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  1. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
  2. Pastor, J. T. & Ruiz, J. L. & Sirvent, I., 1999. "An enhanced DEA Russell graph efficiency measure," European Journal of Operational Research, Elsevier, vol. 115(3), pages 596-607, June.
  3. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
  4. 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.
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Cited by:
  1. Jesús T. Pastora & C.A. Knox Lovell & Juan Aparicioc, 2009. "Families of Linear Efficiency Programs based on Debreu's Loss Function," CEPA Working Papers Series WP042009, School of Economics, University of Queensland, Australia.
  2. Zofío, José Luis & Pastor, Jesús & Aparicio, Juan, 2010. "The Directional Profit Efficiency Measure: On Why Profit Inefficiency is either Technical or Allocative," Working Papers in Economic Theory 2010/09, Universidad Autónoma de Madrid (Spain), Department of Economic Analysis (Economic Theory and Economic History).
  3. Hervé Leleu, 2012. "Inner and Outer Approximations of Technology: A Shadow Profit Approach," Working Papers 2012-ECO-06, IESEG School of Management.
  4. Aparicio, Juan & Pastor, Jesus T. & Ray, Subhash C., 2013. "An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’," European Journal of Operational Research, Elsevier, vol. 226(1), pages 154-162.

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