The shape of ray average cost and its role in multioutput scale economies: some generalizations

Giovanni Cesaroni, Kristiaan Kerstens, Jafar Sadeghi and Ignace van de Woestyne
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Giovanni Cesaroni: Universitas Mercatorum
Jafar Sadeghi: RMCC - Royal Military College of Canada - Royal Military College of Canada
Ignace van de Woestyne: ORSTAT - Operations Research and Business Statistics - KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven

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Abstract: Establishing a link between the so-called ‘neoclassical' and ‘axiomatic' approaches to production theory, we deal with some central and unresolved issues concerning scale economies in multi-output technologies. First, we extend Panzar and Willig's (1977) results on the duality between primal and dual scale elasticity measures, which helps pointing out the unknown role played in this regard by the monotonicity of the local degree of homogeneity of the technology. Second, under a general representation of a convex technology – allowing for non-differentiability of the cost function and multiple optima – we determine the shape of the ray average cost function. Third, in the same setting, we determine an unambiguous relationship between cost scale elasticity and cost scale efficiency, and therefore between local and global scale economies. Fourth, we develop a complete map of values taken by primal and dual scale elasticities and point out that the equality between returns to scale and scale economies local measures breaks down in a convex technology at points where the cost function is not differentiable. This highlights the importance of considering non-differentiability when analysing scale economies in production technologies.

Keywords: ray average cost; scale economies; returns to scale; Data envelopment analysis (search for similar items in EconPapers)
Date: 2025
New Economics Papers: this item is included in nep-eff
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Published in Applied Economics, 2025, ⟨10.1080/00036846.2025.2536874⟩

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Working Paper: The Shape of Ray Average Cost and Its Role in Multioutput Scale Economies: Some Generalisations (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05369076

DOI: 10.1080/00036846.2025.2536874

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