Measuring the Technical Efficiency of Multiple Output Production Technologies

  • Rolf Färe
  • C. A. Knox Lovell
  • Kimberly Zieschang


In this paper we consider a production unit employing many inputs to produce many outputs, subject to the constraints imposed by given technology. Our purpose is to present and analyze various measures of the effectiveness with which inputs are transformed into outputs. Early efforts in this direction were made by Koopmans [1951] and Debreu [1951]. Koopmans defined a feasible input-output vector to be efficient if it is technologically impossible to increase any output and/or to reduce any input without simultaneously reducing other outputs and/or increasing other inputs. Using this definition, he was able to prove that a vector is efficient if, and only if, it possesses a positive normal to the production possibilities set. While Koopmans offered a definition and a characterization of efficiency, Debreu provided a measure of efficiency with his “coefficient of resource utilization.” This coefficient is computed as one minus the maximum equiproportionate reduction in all inputs consistent with continued production of existing outputs, and from it Debreu obtained a measure of the cost of inefficiency. More recently Vincze [1960] and Eichhorn [1972, 1978a, 1978b] have considered a production process involving many variable inputs, one fixed input, many outputs and a time dimension. In this context he defined the price-dependent notions of technical and economic “effectiveness” in terms of families of functional equations, and derived closed-form parametric indexes of technical and economic effectiveness as solutions to the respective families of functional equations.


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  1. Al-Ayat, R., and R. Färe: On the Existence of Joint Production Functions. Naval Research Logistics Quarterly 26 (4), 1979, 627–630.CrossRefGoogle Scholar
  2. Debreu, G.: The Coefficient of Resource Utilization. Econometrica 19 (3), 1951, 273–292.CrossRefGoogle Scholar
  3. Diewert, W.E.: Functional Forms for Profit and Transformation Functions. Journal of Economic Theory 6 (3), 1973, 284–316.CrossRefGoogle Scholar
  4. Eichhorn, W.: Effektivität von Produktionsverfahren. Operations Research-Verfahren 12, 1972, 98–98, –115.Google Scholar
  5. Eichhorn, W.: What Is an Economic Index? An Attempt of an Answer. Theory and Applications of Economic Indexes. Ed. by W. Eichhorn et al. Würzburg-Wien 1978a.Google Scholar
  6. Eichhorn, W.: Functional Equations in Economics. Reading, Mass., 1978b.Google Scholar
  7. Färe, R.: Efficiency and the Production Function. Zeitschrift für Nationalökonomie 35, 1975, 317–324.Google Scholar
  8. Färe, R.: On Strictly Monotonic Production Correspondences. Quantitative Studies on Production and Prices. Ed. by W. Eichhorn et al. Würzburg-Wien 1982 (this volume).Google Scholar
  9. Färe, R., and C.A.K. Lovell: Measuring the Technical Efficiency of Production. Journal of Economic Theory 19 (1), 1978, 150–162.CrossRefGoogle Scholar
  10. Farrell, M.J.: The Measurement of Productive Efficiency. Journal of the Royal Statistical Society, Series A General, 120 (3), 1957, 253–281.CrossRefGoogle Scholar
  11. Försund, F.R., C.A.K. Lovell and P. Schmidt: A Survey of Frontier Production Functions and of Their Relationship to Efficiency Measurement. Journal of Econometrics 13 (1), 1980, 5–26.CrossRefGoogle Scholar
  12. Koopmans, T.C.: Analysis of Production as an Efficient Combination of Activities. Activity Analysis of Production and Allocation. Co wies Commission for Research in Economics Monograph No. 13. Ed. by T.C. Koopmans. New York 1951.Google Scholar
  13. Kopp, R.: The Measurement of Productive Efficiency: A Reconsideration. Resources for the Future. Washington, D.C., 1980.Google Scholar
  14. Samuelson, P.S.: The Fundamental Singularity Theorem for Non-Joint Production. International Economic Review 7 (1), 1966, 34–41.CrossRefGoogle Scholar
  15. Shephard, R. W.: The Theory of Cost and Production Functions. Princeton 1970.Google Scholar
  16. Shephard, R. W.: Semi-Homogeneous Production Functions and Scaling of Production. Lecture Notes in Economics and Mathematical Systems 99. Berlin 1974.Google Scholar
  17. Vincze, E.: Über das Problem der Berechnung der Wirtschaftlichkeit. Acta Technica Academiae Scientiarum Hungarieae 28, 1960, 33–41.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Rolf Färe
  • C. A. Knox Lovell
  • Kimberly Zieschang

There are no affiliations available

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