Scale, Indivisibilities and Production Function in Data Envelopment Analysis

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. To date, the economic theory underlying DEA models has never been explored in any systematic manner. Hence one observes a significant divergence between the econometric and the DEA approaches for the estimation of production frontier. 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 scale economies due to such 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 achieve the same.http://www.grips.ac.jp/list/facultyinfo/tone_kaoru