Abstract
The use of elasticities of substitution between inputs is a standard method for addressing the effect of a change in the mix of inputs used for production from a technical or cost standpoint. Most estimation methods use parametric production or cost functions or frontiers to estimate these elasticities. A potentially useful nonparametric alternative is data envelopment analysis (DEA). The purpose of this paper is to derive elasticities of input substitution for both technical and cost frontiers using DEA, extending the use of this approach in the field of economics and associated fields. The paper provides derivations for both Hicksian (production and cost frontier) and Morishima (cost frontier) elasticities of input substitution, as well as a parsimonious method for estimating them using DEA. The derivations are presented using an agricultural example form Kansas, USA.
Highlights
Agricultural production is characterized by increases in productivity and frequent changes in price
From the technological perspective, this measurement shows how a per unit change in the marginal rate of technical substitution alters the ratio of inputs, while maintaining a fixed level of output
In the case of a cost function, the elasticity of substitution shows how a shift in input prices shifts the ratio of inputs. It relates a percentage change in the ratio of inputs being used to an incremental increase in the ratio of the marginal products of the inputs [1]
Summary
Data Availability Statement: All relevant data are within the manuscript and its Supporting Information files. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. There was no additional external funding received for this study
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