Abstract
Although nobody seems to have recognized it at the time, 1953 was a banner year for duality theory, which in turn facilitated a veritable revolution in the application of consumer and producer theory some two decades later.1 Sten Malmquist (1953) and Ronald W. Shephard (1953) independently introduced the notion of a distance function (also called a gauge function and a transformation function2) to economists.3 In production theory, the (input) distance function is simply the maximal radial contraction (equivalently, the minimal radial expansion) of an input vector consistent with the technological feasibility of producing a given output vector. In utility theory, it is the maximal radial contraction (or minimal radial expansion) of a consumption vector consistent with the attainment of a particular utility level.
I am grateful to Rolf Färe, Shawna Grosskopf, Craig Gundersen, Marc Mecurio, and especially Bert Balk for many insightful comments on an earlier draft. As I have not always followed their advice, they bear no blame for the remaining inadequacies.
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Russell, R.R. (1998). Distance Functions in Consumer and Producer Theory. In: Färe, R., Grosskopf, S., Russell, R.R. (eds) Index Numbers: Essays in Honour of Sten Malmquist. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4858-0_2
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