Nonconvexity in Production and Cost Functions: An Exploratory and Selective Review
The purpose of this contribution is to provide an overview of developments in nonconvex production technologies and economic value functions, with special attention to the cost function. Apart from a somewhat selective review of theoretical issues, the em
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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technologies and Distance Functions: Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Axiom of Convexity: Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convexity and Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convexity and Time Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Convexity and Managerial Practice: Some Skepticism Around . . . . . . . . . . . . . . . . . . . . . . . Nonparametric Nonconvex Technologies and Value Functions: Free Disposal Assumption and Minimum Extrapolation Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . Technologies: FDH and Its Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Economic Value Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Efficiency Decompositions and the Testing of Convexity: A Priori Relations . . . . . . . . . . . Empirical Evidence on FDH and Its Extensions: The Impact of Convexity . . . . . . . . . . . . . FDH and Its Extensions: Further Methodological Refinements . . . . . . . . . . . . . . . . . . . . . . . Mitigating Convexity: A Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Convexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Regular Ultra Passum Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . From Generalized Convexity to Nonconvexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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∗ We
acknowledge the most helpful comments of R. Chambers and G. Cesaroni on an earlier version. The usual disclaimer applies. W. Briec University of Perpignan, LAMPS, Perpignan, France e-mail: [email protected] K. Kerstens () IESEG School of Management, CNRS, Université de Lille, UMR 9221-LEM, Lille, France e-mail: [email protected] I. Van de Woestyne Research Unit MEES, KU Leuven, Brussel, Belgium e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 S. C. Ray et al. (eds.), Handbook of Production Economics, https://doi.org/10.1007/978-981-10-3450-3_15-1
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Semilattice Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preliminary Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Re
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