A Scale Elasticity Measure for Directional Distance Function and its Dual
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.
|Date of creation:||2011|
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- 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.
- Rolf Fare & Daniel Primont, 2006. "Directional duality theory Directional duality theory," Economic Theory, Springer, vol. 29(1), pages 239-247, September.
- Chau, Nancy H. & Fare, Rolf, 2008.
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6218, University of Bonn, Center for Development Research (ZEF).
- 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.
- Chau, Nancy H. & Fare, Rolf, 2007. "Shadow Pricing Market Access: A Trade Benefit Function Approach," Working Papers 127015, Cornell University, Department of Applied Economics and Management.
- 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.
- 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.
- 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, 08.
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