Marginal Rates and Two-dimensional Level Curves in DEA

Dan Rosen, Claire Schaffnit and Joseph Paradi

Journal of Productivity Analysis, 1998, vol. 9, issue 3, 205-232

Abstract: Of great importance to management, the computation of trade-offs presents particular difficulties within DEA since the piecewise linear nature of the envelopment surfaces does not allow for unique derivatives at every point. We present a comprehensive framework for analyzing marginal rates, and directional derivatives in general, on DEA frontiers. A useful characterization of these derivatives at given points can be provided in terms of the ranges they can take; equivalently, the bounds of these ranges correspond to derivatives “to the right”and “to the left” at these points. We present two approaches for their computation: first, the dual equivalents calculation of minimum and maximum multiplier ratios / finite differences, and then a modified simplex tableau method. The simplex tableau method provides a more general application of the method introduced by Hackman et al. (1994) to generate any two-dimensional section of the isoquant and is a practical tool to generate level plots of the frontier. By giving a complete picture of trade-offs and allowing a better visualization of high dimensional production possibility sets, these tools can be very useful for managerial applications. Copyright Kluwer Academic Publishers 1998

Keywords: Data Envelopment Analysis; marginal rates; trade-offs; partial derivatives; piecewise linear surfaces; returns to scale (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (24)

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DOI: 10.1023/A:1018382904489

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