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The Measurement of Efficiency Relative to a Frontier Production Function

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  • Wesley D. Seitz

Abstract

A method is presented for estimating a frontier production function allowing economies and diseconomies of scale using linear programming techniques. The general applicability of this function is illustrated by considering the neutral and nonneutral cases. Indexes of technical, price, and economic efficiency of production of observations of equal scale are introduced. Three equivalent efficiency indexes are offered which measure the efficiency of alternative scale activities. Utilization of the efficiency indexes in determining the nature of the production function, causes of observed inefficiency, and the degree and nature of technological advance are discussed.

Suggested Citation

  • Wesley D. Seitz, 1970. "The Measurement of Efficiency Relative to a Frontier Production Function," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 52(4), pages 505-511.
    • Handle: RePEc:oup:ajagec:v:52:y:1970:i:4:p:505-511.
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    File URL: http://hdl.handle.net/10.2307/1237257
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    Cited by:

    1. Kerstens, Kristiaan & Sadeghi, Jafar & Toloo, Mehdi & Van de Woestyne, Ignace, 2022. "Procedures for ranking technical and cost efficient units: With a focus on nonconvexity," European Journal of Operational Research, Elsevier, vol. 300(1), pages 269-281.
    2. Toshiyuki Sueyoshi, 1999. "DEA Duality on Returns to Scale (RTS) in Production and Cost Analyses: An Occurrence of Multiple Solutions and Differences Between Production-Based and Cost-Based RTS Estimates," Management Science, INFORMS, vol. 45(11), pages 1593-1608, November.
    3. Finn Førsund & Lennart Hjalmarsson, 2004. "Are all Scales Optimal in DEA? Theory and Empirical Evidence," Journal of Productivity Analysis, Springer, vol. 21(1), pages 25-48, January.
    4. French, Ben C., 1977. "PART II. The Analysis of Productive Efficiency in Agricultural Marketing: Models, Methods, and Progress," AAEA Monographs, Agricultural and Applied Economics Association, number 337214, january.
    5. Sharma, Khem R. & Leung, PingSun & Zane, Lynn, 1999. "Performance Measurement Of Hawaii State Public Libraries: An Application Of Data Envelopment Analysis (Dea)," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 28(2), pages 1-9, October.
    6. R. K. Ige, 2014. "Allocative Efficiency of Resources in the Production of Maize among Small Scale Farmers in Odogbolu Local Government Area of Ogun State, Nigeria," International Journal of Management Sciences, Research Academy of Social Sciences, vol. 4(9), pages 383-387.
    7. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane," European Journal of Operational Research, Elsevier, vol. 181(2), pages 549-570, September.
    8. Forsund, Finn R. & Sarafoglou, Nikias, 2005. "The tale of two research communities: The diffusion of research on productive efficiency," International Journal of Production Economics, Elsevier, vol. 98(1), pages 17-40, October.
    9. Bruno De Borger & Kristiaan Kerstens & Diego Prior & Ignace Van de Woestyne, 2013. "Static efficiency decompositions and capacity utilization: integrating economic and technical capacity notions," Applied Economics, Taylor & Francis Journals, vol. 45(24), pages 3529-3529, August.
    10. Spielman, Kimberly & Whipple, Glen & McLemore, Dan, 1982. "Estimation Of A Long Run Average Cost Curve Using A Frontier Function: An Application To The Tennessee Livestock Auction Market Industry," 1982 Annual Meeting, August 1-4, Logan, Utah 279185, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Finn Førsund & Nikias Sarafoglou, 2002. "On the Origins of Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 17(1), pages 23-40, January.
    12. Valentin Zelenyuk, 2011. "Scale Efficiency: Equivalence of Primal and Dual Measures," CEPA Working Papers Series WP092011, School of Economics, University of Queensland, Australia.
    13. Lars Jonasson, 1997. "A Policy Oriented Multi‐Input And Multi‐Output Measure Of Overall Efficiency And Its Decomposition," Journal of Agricultural Economics, Wiley Blackwell, vol. 48(1‐3), pages 52-64, January.
    14. Weaver, Robert D., 1979. "Survey of Promising Developments in Supply Response: Pre- and Post-Data Econometric Methods for Integration of Neo-Classical Theory with Sample Evidence," Staff Paper Series 256836, Pennsylvania State University, Department of Agricultural Economics and Rural Sociology.
    15. F R Førsund & S A C Kittelsen & V E Krivonozhko, 2009. "Farrell revisited–Visualizing properties of DEA production frontiers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1535-1545, November.
    16. Bhende, M.J. & Kalirajan, K.P., 2007. "Technical Efficiency of Major Food and Cash Crops in Karnataka (India)," Indian Journal of Agricultural Economics, Indian Society of Agricultural Economics, vol. 62(2), pages 1-17.
    17. Valentin Zelenyuk, 2014. "Scale efficiency and homotheticity: equivalence of primal and dual measures," Journal of Productivity Analysis, Springer, vol. 42(1), pages 15-24, August.
    18. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1918-1946, February.
    19. Forsund, Finn R & Hjalmarsson, Lennart, 1979. "Generalised Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Economic Journal, Royal Economic Society, vol. 89(354), pages 294-315, June.
    20. Førsund, Finn R. & Kittelsen, Sverre A. & Krivonozhko, Vladimir E., 2007. "Farrell Revisited: Visualising the DEA Production Frontier," Memorandum 15/2007, Oslo University, Department of Economics.
    21. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    22. McLemore, Dan L. & Whipple, Glen D. & Spielman, Kimberly, 1983. "Ols And Fronteir Function Estimates Of Long-Run Average Cost For Tennessee Livestock Auction Markets," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 15(2), pages 1-5, December.
    23. Zelenyuk, Valentin, 2020. "Aggregation of inputs and outputs prior to Data Envelopment Analysis under big data," European Journal of Operational Research, Elsevier, vol. 282(1), pages 172-187.
    24. Kent Olson & Linh Vu, 2009. "Economic efficiency in farm households: trends, explanatory factors, and estimation methods," Agricultural Economics, International Association of Agricultural Economists, vol. 40(5), pages 587-599, September.

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