Introduction

In this chapter we model technology with the input correspondence u → L(u). We assume that x ∈ L(u) and measure production efficiency by calculating where in the input set L(u) the input vector x is located. Thus we take the observed output vector u as given and adopt a resource conservation approach toward efficiency measurement. We refer to this approach as input based, since inputs are the choice variables, and we measure efficiency in terms of maximum feasible shrinkage of an observed input vector, feasibility being determined by the input set L(u).

Shrinkage can be given many interpretations. Throughout most of the chapter shrinkage is accomplished radially, i.e., by an equiproportionate reduction in all inputs. In Section 3.1 input-based efficiency measures that are radial and independent of prices are introduced. We obtain a measure of technical efficiency, and show how it can be decomposed into three components that measure the separate contributions of scale efficiency, congestion of inputs, and “pure” technical efficiency. Each of these measures is calculated relative to the input set L(u) that takes output as given.

In Section 3.2 we introduce input prices and develop a radial, price dependent measure of cost efficiency. This measure is then decomposed into two parts, technical efficiency (which itself has three components) and allocative efficiency. This enables us to attribute potential cost saving to elimination of waste and adjustments to the input mix.

A difficulty with radial measurement of technical efficiency is that a radially shrunken input vector need not necessarily belong to the efficient subset of the input set.