# The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

# Gauge Functions

• Peter Newman
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_764

## Abstract

Consider the standard two-product diagram which depicts an opportunity set P with production frontier fr(P). For any point x1 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 $$\overline{x}\in \mathrm{fr}(P)$$ which is just a scale change of x1, 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(x1 | 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).

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