Global Economies of Scale in Nonconvex Cost Functions: New Proposals and Empirical Illustration

Giovanni Cesaroni, Kristiaan Kerstens (), Amin Mostafaee () and Majid Soleimani-Damaneh ()
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Kristiaan Kerstens: Corresponding author: Univ. Lille, CNRS, IESEG School of Management, UMR 9221 - LEM - Lille Économie Management, F-59000 Lille, France, Tel: +33 320545892 (switchboard), Fax: +33 320574855
Amin Mostafaee: Department of Mathematics, NT.C., Islamic Azad University, Tehran, Iran
Majid Soleimani-Damaneh: Corresponding author: School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, Enghelab Avenue, Tehran, Iran, & ICOL: Industrial and Computational Optimization Lab., University of Tehran, Iran

No 2026-EQM-06, Working Papers from IESEG School of Management

Abstract: Economies of Scale (ES), defined in terms of minimal Ray Average Cost (RAC) and optimal scale size, is a key concept in economics. We refine global ES by considering two new notions, called Global Sub-Increasing ES (G-SIES) and Global Sub-Decreasing ES (G-SDES), which both depend on the behaviour of the RAC function in a nonconvex setting. These notions provide qualitative information about the optimal scale size and position an observation relative to the true flexible returns to scale technology. After presenting a motivating example and defining G-SIES and G-SDES, we characterize these new notions. Then, we calculate a stability interval (region) for the new ES classification against output changes. We establish several technical theorems and design polynomial-time enumeration algorithms which determine the ES of the units under evaluation and provide stability intervals. These results are illustrated by numerical examples and by two empirical studies on real-world data sets from the electricity generation and distribution sectors.

Keywords: Data Envelopment Analysis; Free Disposal Hull; Sub-global economies of scale; RAC function; Stability. (search for similar items in EconPapers)
Pages: 47 pages
Date: 2026-08
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