Scandinavian Working Papers in Economics

Memorandum,
Oslo University, Department of Economics

No 15/2007: Farrell Revisited: Visualising the DEA Production Frontier

Finn R. Førsund (), Sverre A. Kittelsen and Vladimir E. Krivonozhko
Additional contact information
Finn R. Førsund: Dept. of Economics, University of Oslo, Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Sverre A. Kittelsen: Ragnar Frisch Centre of Economic Research, Postal: Gaustadallèen 21 , N-0349 Oslo, Norway
Vladimir E. Krivonozhko: Institute for Systems Analysis, Postal: Moscow

Abstract: The contributions of the paper are threefold: i) compare with mathematical rigour the Charnes, Cooper, and Rhodes DEA model and the Farrell model exhibiting constant returns to scale, ii) reinterpret the contribution of Farrell and Fieldhouse that extended the analysis to variables returns to scale and establish the connection with the approach in Banker, Charnes and Cooper, iii) provide graphical visualisation of properties of the frontier function. Both papers by Farrell emphasised the importance of graphical visualisation of non-parametric frontier functions, but, to our knowledge, this is seldom followed up in the literature. We use a graphical package (EffiVision) with a numerical representation of the frontier functions, representing the contemporary development of visualisation. By making suitable cuts through the DEA frontier in multidimensional space, various graphical representations of features of economic interest can be done. Development of ray average cost function and scale elasticity are novel illustrations.

Keywords: Farrell efficiency measure; DEA; variable returns to scale; visualisation; grouping method

JEL-codes: C61; D24

31 pages, February 1, 2007

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Published as
Finn R. Førsund, Sverre A. Kittelsen and Vladimir E. Krivonozhko, (2009), 'Farrell Revisited: Visualising properties of DEA Production Frontiers', Journal of the Operational Research Society, vol 60, pages 1535-1545

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