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