The Transformation Function, Technical Efficiency, and the CCR Ratio

Subhash Ray

No 2017-09, Working papers from University of Connecticut, Department of Economics

Abstract: Charnes, Cooper, and Rhodes define the ratio of the virtual output to the virtual input as a measure of the technical efficiency of a multiple output multiple input firm. The aggregation weights used in constructing the virtual output and the virtual input may be arbitrarily chosen so long as the weights are non-negative and using these weights no firm’s input-output bundle shows efficiency exceeding 100%. In production economics, the ratio of aggregate output to aggregate input is a measure of total factor productivity and a direct link of the CCR ratio to technical efficiency is not obvious. Usually the CCR ratio is rationalized as efficiency by showing its equivalence to the Farrell efficiency measure. This paper offers a direct derivation of the CCR ratio measure of efficiency from a Transformation Function. We also show how the Banker, Charnes, Cooper (BCC) measure under variable returns to scale can be derived from the Transformation Function.

Keywords: Supporting hyperplane; Convexity; Degree of Increasing Returns (search for similar items in EconPapers)
JEL-codes: C60 D24 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2017-06
New Economics Papers: this item is included in nep-eff
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Citations: View citations in EconPapers (1)

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Journal Article: The transformation function, technical efficiency, and the CCR ratio (2019)
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