Notes on some inequalities in economics

Rolf Färe and Shawna Grosskopf
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Rolf Färe: Department of Economics and Department of Agricultural and Resource Economics,Oregon State University, Corvallis, OR 97331, USA

Economic Theory, 2000, vol. 15, issue 1, 227-233

Abstract: Inequalities created by relating gauge (distance) functions and their dual support functions have been used in economics and operations research/management science to measure efficiency and productivity. The most familiar example is the Farrell (1957) measure of cost efficiency and its decomposition into technical and allocative components, which can be shown to be an application of the Mahler (1939) inequalities, although Farrell was probably unaware of the connection. In this short paper we add to this literature by providing explicit relationships between distance functions and support functions to form five different inequalities. These inequalities are derived from three support functions: the cost function, the revenue function and the profit function, and three gauge (distance) functions: the input distance function, the output distance function and the directional (technology) distance function.

Keywords: Mahler inequality; Distance functions; Duality. (search for similar items in EconPapers)
JEL-codes: D20 D69 (search for similar items in EconPapers)
Date: 1999-11-22
Note: Received: April 13, 1998; revised version: July 17, 1998
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