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Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity

Author

Listed:
  • W. Briec
  • K. Kerstens

    (LEM - Lille - Economie et Management - Université de Lille, Sciences et Technologies - CNRS - Centre National de la Recherche Scientifique)

  • P. Vanden Eeckaut

Abstract

This contribution is the first systematic attempt to develop a series of nonparametric, deterministic technologies and cost functions without maintaining convexity. Specifically, we introduce returns to scale assumptions into an existing non-convex technology and, dual to these various technologies, define non-convex cost functions. These non-convex cost functions are never lower than their convex counterparts. Both non-convex technologies and cost functions (total, ray-average and marginal) are characterised by simple, closed form expressions. Furthermore, a local duality result is established between a local cost function and the input distance function. Finally, nonparametric goodness-of-fit tests for the convexity axiom are developed. This is a first step towards making convexity a statistically testable hypothesis.
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Suggested Citation

  • W. Briec & K. Kerstens & P. Vanden Eeckaut, 2006. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Post-Print hal-00211174, HAL.
    • Handle: RePEc:hal:journl:hal-00211174
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