Scale, Indivisibilities and Production Function in Data Envelopment Analysis

Abstract

This paper critically re-examines the concept of returns to scale vis-à-vis economies of scale since the writings of Adam Smith by relating the former to the concept of production unit and the latter to the concept of firm. Though to date some valuable progress has been made exploring the economic theory underlying DEA models, these developments have remained in their infancy and have not found enough application. An attempt is made here to examine the DEA model of efficiency measurement and its application from an economic viewpoint. We show here that the presence of indivisibilities in all multi-stage production processes makes the technology structure non-convex, and therefore, the standard convex DEA production models (e.g., CCR and BCC) fail to exhibit increasing returns due to indivisibilities. However, the non-convex technology embedded in FDH model helps revealing process indivisibilities arising from task-specific processes whereas a homogeneous characterization of production function fails to do so.

Keywords: returns to scale, economies of scale, process indivisibility, data envelopment analysis

JEL Classification: D24, C61