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

Listed author(s):
  • 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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File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00453-0
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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
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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  1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
  2. Forsund, Finn R & Hjalmarsson, Lennart, 1979. "Generalised Farrell Measures of Efficiency: An Application to Milk Processing in Swedish Dairy Plants," Economic Journal, Royal Economic Society, vol. 89(354), pages 294-315, June.
  3. Baumol, William J, 1982. "Contestable Markets: An Uprising in the Theory of Industry Structure," American Economic Review, American Economic Association, vol. 72(1), pages 1-15, March.
  4. W. Briec & K. Kerstens & P. Vanden Eeckaut, 2006. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Post-Print hal-00211174, HAL.
  5. R. Färe & S. Grosskopf & D. Njinkeu, 1988. "Note---On Piecewise Reference Technologies," Management Science, INFORMS, vol. 34(12), pages 1507-1511, December.
  6. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
  7. Fare, Rolf & Grosskopf, Shawna & Zaim, Osman, 2002. "Hyperbolic efficiency and return to the dollar," European Journal of Operational Research, Elsevier, vol. 136(3), pages 671-679, February.
  8. Jean-Paul Chavas & Thomas L. Cox, 1999. "A Generalized Distance Function and the Analysis of Production Efficiency," Wisconsin-Madison Agricultural and Applied Economics Staff Papers 422, Wisconsin-Madison Agricultural and Applied Economics Department.
  9. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
  10. Lau, Lawrence J., 1978. "Applications of Profit Functions," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.), Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 3 McMaster University Archive for the History of Economic Thought.
  11. Charnes, A. & Cooper, W. W. & Seiford, L. & Stutz, J., 1982. "A multiplicative model for efficiency analysis," Socio-Economic Planning Sciences, Elsevier, vol. 16(5), pages 223-224.
  12. Jose Zofio & C. A. Knox Lovell, 2001. "Graph efficiency and productivity measures: an application to US agriculture," Applied Economics, Taylor & Francis Journals, vol. 33(11), pages 1433-1442.
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