Benefit and Distance Functions

Abstract

We explore the relationship between Shephard's input distance function and Luenberger's benefit function. We point out that the latter can be recognized in a production context as a directional input distance function which can exhaustively characterize production technologies under appropriate assumptions on input disposability. McFadden's composition rules for input sets and input distance functions are then extended to the directional input distance function. Working Paper 95-09 Scientific Article No. , Contribution No. from the Maryland Agricultural Experiment Station.

Input saving possibilities and practices contributing to more efficient beef production in Sweden

“…Therefore, the input distance function definition suggests the degree to which the inputs used exceed the input requirement for an observed production enterprise, which is identified as a cost, or inefficiency (Greene 2008). Generalization of Shepard's radial form of the input distance functions has been done by Chambers et al (1996Chambers et al ( , 1998 through the introduction of a directional input distance function (DIDF). The DIDF measures the amount that one can translate an input vector radially from itself to the technology frontier in a reassigned direction, assuming that the translation is allowed towards all of the points on the frontier that dominate the observed decision-making unit (Färe et al 2008).…”

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“…, , v w x the output directional distance function allowing a simultaneous increase in good and a reduction of bad output (Chambers et al, 1996(Chambers et al, , 1998Chung et al, 1997) can be defined as: …”

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“…Subject to Chambers et al (1996) defined a similar model without considering undesirable outputs as formulated in Model (8) below:…”