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The New Palgrave Dictionary of Economics pp 1–10Cite as

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Gauge Functions

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Abstract

Consider the standard two-product diagram which depicts an opportunity set P with production frontier fr(P). For any point x 1 inside P it would be useful to have a measure of just how inefficient it is, i.e. to gauge how far it is from the frontier. A simple way of doing this is, first to find that point \( \overline{x}\in \mathrm{f}\mathrm{r}(P) \) which is just a scale change of x 1, so that \( {x}^1={\lambda}_1\overline{x} \) for some λ1 ∈ [0, 1). Then a function J(. | P) that calibrates any such point with respect to P is defined by putting J(x 1 | P) = λ1. For this to be a sensible measure of efficiency, it should obviously have the property that J(x | P) = 1 if and only if (iff) x ∈ fr(P).

This chapter was originally published in The New Palgrave: A Dictionary of Economics, 1st edition, 1987. Edited by John Eatwell, Murray Milgate and Peter Newman

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    Peter Newman

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    Newman, P. (1987). Gauge Functions. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95121-5_764-1

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    • DOI: https://doi.org/10.1057/978-1-349-95121-5_764-1

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