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

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.