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

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  • Walter Briec
  • Kristiaan Kerstens
  • Philippe Venden 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

  • Walter Briec & Kristiaan Kerstens & Philippe Venden Eeckaut, 2004. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Journal of Economics, Springer, vol. 81(2), pages 155-192, February.
    • Handle: RePEc:kap:jeczfn:v:81:y:2004:i:2:p:155-192
    DOI: 10.1007/s00712-003-0620-y
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