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

  • Walter Briec

    ()

  • Kristiaan Kerstens

    ()

  • Philippe Venden Eeckaut

    ()

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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File URL: http://hdl.handle.net/10.1007/s00712-003-0620-y
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Article provided by Springer in its journal Journal of Economics.

Volume (Year): 81 (2004)
Issue (Month): 2 (02)
Pages: 155-192

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Handle: RePEc:kap:jeczfn:v:81:y:2004:i:2:p:155-192
DOI: 10.1007/s00712-003-0620-y
Contact details of provider: Web page: http://www.springer.com

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