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[alpha]-Returns to scale and multi-output production technologies


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  • Boussemart, Jean-Philippe
  • Briec, Walter
  • Peypoch, Nicolas
  • Tavéra, Christophe


This contribution proposes a specification of strictly increasing and decreasing returns to scale in multi-output technologies. Along this line a notion of [alpha]-returns to scale is derived from that of homogeneous multi-output technology. For a large class of technologies we establish necessary and sufficient conditions characterizing strictly increasing and strictly decreasing returns to scale to scale. Furthermore, a relationship between input, output and graph distance functions is established. These connections lead naturally to a link between the various Malmquist indexes and the Chavas-Cox productivity index. Finally, we show that these concepts can be implemented in a DEA context using a piecewise homogeneous constant elasticity substitution-transformation model due to [Färe, R., Grosskopf, S., Njinkeu, D., 1988b. On piecewise reference technologies. Management Science 34, 1507-1511].

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 197 (2009)
Issue (Month): 1 (August)
Pages: 332-339

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Handle: RePEc:eee:ejores:v:197:y:2009:i:1:p:332-339

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Keywords: D24 Returns to scale Distance function Productivity growth Malmquist index;

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Cited by:
  1. Sheng, Yu & Zhao, Shiji & Nossal, Katarina, 2011. "Productivity and farm size in Australian agriculture: reinvestigating the returns to scale," 2011 Conference (55th), February 8-11, 2011, Melbourne, Australia 100711, Australian Agricultural and Resource Economics Society.
  2. Pestana Barros, Carlos & Peypoch, Nicolas, 2010. "Productivity changes in Portuguese bus companies," Transport Policy, Elsevier, vol. 17(5), pages 295-302, September.
  3. Hervé Leleu & James Moises & Vivian Valdmanis, 2011. "Optimal productive size of hospital’s intensive care units," Working Papers 2011-ECO-01, IESEG School of Management.
  4. Jean-Philippe Boussemart & Walter Briec & Hervé Leleu, 2008. "Linear programming solutions and distance functions under a constant returns to scale technology," Working Papers 2008-ECO-06, IESEG School of Management.


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