Journal of Productivity Analysis

, Volume 13, Issue 2, pp 93–103 | Cite as

Theory and Application of Directional Distance Functions

  • Rolf Färe
  • Shawna Grosskopf


In 1957 Farrell demonstrated how cost inefficiency could be decomposed into two mutually exclusive and exhaustive components: technical and allocative inefficiency. This result is consequence of the fact that—as shown by Shephard—the cost function and the input distance function (the reciprocal of Farrell's technical efficiency measure) are ‘dual’ to each other. Similarly, the revenue function and the output distance function are dual providing the basis for the decomposition of revenue inefficiency into technical and allocative components (see for example, Färe, Grosskopf and Lovell (1994)). Here we extend those results to include the directional distance function and its dual, the profit function. This provides the basis for defining and decomposing profit efficiency. As we show, the output and input distance functions (reciprocals of Farrell efficiency measures) are special cases of the directional distance function. We also show how to use the directional distance function as a tool for measuring capacity utilization using DEA type techniques.


Cost Function Distance Function Technical Efficiency Efficiency Measure Capacity Utilization 
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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Rolf Färe
    • 1
  • Shawna Grosskopf
    • 2
  1. 1.Department of Economics and Department of Agricultural and Resource EconomicsOSUCorvallis
  2. 2.Department of EconomicsOregon State UniversityCorvallis

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