Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies

Kristof De Witte*, Rui C. Marques

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

26 Citations (Web of Science)


Knowledge on the scale economies drives the incentives of regulators, governments and individual utilities to scale-up or scale-down the scale of operations. This paper considers the returns to scale (rts) in non-convex frontier models. In particular, we evaluate rts assumptions in a free disposal hull model, which accounts for uncertainty and heterogeneity in the sample. Additionally, we provide a three-step framework to empirically analyze the existence and extent of rts in real world applications. In a first step, the presence of scale (and scope) economies is verified. Secondly, rts for individual observations are examined while in a third step we derive the optimal scale for a sector as a whole. The framework is applied to the portuguese drinking water sector where we find the optimal scale to be situated around 7–10 million m3.
Original languageEnglish
Pages (from-to)213-226
JournalJournal of Productivity Analysis
Issue number3
Publication statusPublished - Jun 2011


  • Free Disposal Hull
  • Economies of scale
  • Optimal size
  • Water sector

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