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Scale Efficiency: Equivalence of Primal and Dual Measures

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Abstract

In this paper we address an issue of equivalence of primal and dual measures of scale efficiency in general production theory framework. We find that particular types of homotheticity, which we refer to as scale homotheticity, provide necessary and sufficient condition for such equivalence. Specifically, we show that the input scale homotheticity of technology is necessary and sufficient condition for equivalence of primal and dual scale efficiency measures in the input/cost oriented case. Similarly, the output scale homotheticity of technology is necessary and sufficient condition for equivalence of primal and dual scale efficiency measures in the output/revenue oriented case. We also discuss the case when technology is both input scale homothetic and output scale homothetic, as well as indicate about some relationships of scale homotheticity with the homotheticity notions that have already been used in economic theory.

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  • Valentin Zelenyuk, 2011. "Scale Efficiency: Equivalence of Primal and Dual Measures," CEPA Working Papers Series WP092011, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uqcepa:75
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    File URL: https://economics.uq.edu.au/files/5193/WP092011.pdf
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    3. Valentin Zelenyuk, 2011. "A Note on Equivalences in Measuring Returns to Scale in Multi-output-multi-input Technologies," CEPA Working Papers Series WP052011, School of Economics, University of Queensland, Australia.
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    9. Léopold Simar & Valentin Zelenyuk, 2007. "Statistical inference for aggregates of Farrell-type efficiencies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(7), pages 1367-1394.
    10. Valentin Zelenyuk, 2011. "A Scale Elasticity Measure for Directional Distance Function and its Dual," CEPA Working Papers Series WP062011, School of Economics, University of Queensland, Australia.
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    1. Zelenyuk, Valentin, 2015. "Aggregation of scale efficiency," European Journal of Operational Research, Elsevier, vol. 240(1), pages 269-277.
    2. 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.

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