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A Scale Elasticity Measure for Directional Distance Function and its Dual

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Abstract

In this paper we introduce a scale elasticity measure based on directional distance function for multi-output-multi-input technologies and explore its fundamental properties. Specifically, we derive necessary and sufficient condition for equivalence of the scale elasticity measure based on the directional distance function with the input oriented and output oriented scale elasticity measures. We also establish duality relationship between the scale elasticity measure based on the directional distance function with a scale elasticity measure based on the profit function. This theoretical result is valuable for empirical researchers as it provides a testable analytical condition for when (and only when) the alternative primal and dual definitions of scale elasticity for multi-output-multi-input technologies yield equivalent conclusions about economies or diseconomies of scale.

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  • 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.
  • Handle: RePEc:qld:uqcepa:66
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    File URL: http://www.uq.edu.au/economics/cepa/docs/WP/WP062011.pdf
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    1. Chau, Nancy H. & Färe, Rolf, 2011. "Shadow pricing market access: A trade benefit function approach," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1631-1663, July.
    2. Nancy H. Chau & Rolf F”re & Shawna Grosskopf, 2003. "Trade restrictiveness and efficiency," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(3), pages 1079-1095, August.
    3. Fare, Rolf & Grosskopf, Shawna & Noh, Dong-Woon & Weber, William, 2005. "Characteristics of a polluting technology: theory and practice," Journal of Econometrics, Elsevier, vol. 126(2), pages 469-492, June.
    4. Färe, Rolf & Grosskopf, Shawna & Hayes, Kathy J. & Margaritis, Dimitris, 2008. "Estimating demand with distance functions: Parameterization in the primal and dual," Journal of Econometrics, Elsevier, vol. 147(2), pages 266-274, December.
    5. 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.
    6. Rolf Fare & Daniel Primont, 2006. "Directional duality theory Directional duality theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 239-247, September.
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    Cited by:

    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.
    3. Valentin Zelenyuk, 2011. "Scale Efficiency: Equivalence of Primal and Dual Measures," CEPA Working Papers Series WP092011, School of Economics, University of Queensland, Australia.

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