α-Returns to scale and multi-output production technologies

Jean-Philippe Boussemart (1) , Walter Briec (2) , Nicolas Peypoch (2) , Christophe Tavéra (3)

1 UMR CNRS 8179
2 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
3 CREM - Centre de recherche en économie et management

This contribution proposes a specification of strictly increasing and decreasing returns to scale in multioutput technologies. Along this line a notion of a-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].

Mots clés: returns to scale; distance function; productivity growth; Malmquist index

Domaines: Economies et finances

Jean-Philippe Boussemart, Walter Briec, Nicolas Peypoch, Christophe Tavéra. α-Returns to scale and multi-output production technologies. European Journal of Operational Research, 2009, 197 (1), pp.332-339. ⟨10.1016/j.ejor.2008.05.028⟩. ⟨halshs-00418883⟩