Returns to Scale and Efficiency in Production: A Distance Function Approach to Southern Illinois Hog Farms

  • R. Färe
  • W. Herr
  • D. Njinkeu
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 332)


In this paper, we introduce a parametric specification of a ray-homothetic input distance function. We choose to parametrice our distance function in such a manner that it becomes log-linear in the parameters. This choice enables us to utilize a generalized version of Aigner and Chu (1968) to compute the parameters of the function as solutions to a linear programming problem. The purpose of these theoretical developments are to formulate a framework for the measurements of scale elasticity and input efficiency. The analysis follows ideas introduced by Farrell (1957) and it is applied to the U.S. agricultural sector. The approach followed in this paper allows for a multiple output technology and does not require knowledge of prices. In addition, our methodology allows us to explicitly study the notion of scale elasticity and technical efficiency with respect to output size (in a multi-output setting) and output mix.


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  1. Aigner, D., and S. Chu (1968) “On Estimating the Industry Production Function,” American Economic Review, 58:4, 826–839.Google Scholar
  2. Britton, D.K. and H.B. Hill ( 1975 ) Size and Efficiency in Farming, Farnborough: Saxon House cited by Dawson (1985).Google Scholar
  3. Dawson, P.J. (1985) “Measuring Technical Efficiency From Production Functions: Some Further Estimates,” Journal of Agricultural Economics 36, 31–40.CrossRefGoogle Scholar
  4. Dawson, P.J. (1987) “Farm Specific Technical Efficiency in the England and Wales Dairy Sector,” European Review of Agricultural Economics, 14(4): 383–394.CrossRefGoogle Scholar
  5. Eichhorn, W. (1969) “Eine Verallgemeinerung des Begriffs der Homogenen Produktionsfunktion,” Unternehmensforschung, 13, 99–109.CrossRefGoogle Scholar
  6. Ekanayake, S.A.B. and S.K. Jayasuriya (1987) “Measurement of Firm Specific Technical Efficiency: A comparison of Methods,” Journal of Agricultural Economics.Google Scholar
  7. Färe, R. (1988) Fundamentals of Production Theory, Lecture Notes in Economics and Mathematical Systems, Vol. 311, Springer-Verlag, Berlin.Google Scholar
  8. Färe, R., S. Grosskopf, and C.A.K. Lovell (1985) The Measurement of Efficiency of Production, Kluwer-Nijhoff, Boston.Google Scholar
  9. Färe, R., S. Grosskopf, and C.A.K. Lovell (1986) “Scale Economics and Duality,” Zeitschrift far Nationalökonomie, 46, 175–182.CrossRefGoogle Scholar
  10. Färe, R., and R.W. Shephard (1977) “Ray-Homothetic Production Functions,” Econometrica, 45:1, 133–146.CrossRefGoogle Scholar
  11. Farrell, M.J. (1957) “The Measurement of Productive Efficiency,” Journal of Royal Statistical Society, Series A (General), 120, 253–281.CrossRefGoogle Scholar
  12. Lund, P.J. and P.G. Hill (1979) “Farm Size, Efficiency and Economics of Size,” Journal of Agricultural Economics, 30, 145–158.CrossRefGoogle Scholar
  13. Njinkeu, D. (forthcoming) “On Firm Specific Technical Efficiency: A Monte Carlo Comparison,” European Review of Agricultural Economics.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1989

Authors and Affiliations

  • R. Färe
    • 1
  • W. Herr
    • 1
  • D. Njinkeu
    • 1
  1. 1.Southern Illinois UniversityUSA

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