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The Wong-Viner Envelope Theorem for subdifferentiable functions

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  • Anthony Horsley
  • Andrew J Wrobel

Abstract

The Wong-Viner Envelope Theorem on the equality of long-run and short-run marginalcosts (LRMC and SRMC) is reformulated for convex but generally nondifferentiable costfunctions. The marginal cost can be formalized as the multi-valued subdifferential a.k.a.the subgradient set but, in itself, this is insufficient to extend the result effectively, i.e., toidentify suitable SRMCs as LRMCs. This goal is achieved by equating the profit-imputedvalues of the fixed inputs to their prices. Thus reformulated, the theorem is proved froma lemma on the sections of the joint subdifferential of a bivariate convex function. Thenew technique is linked to the Partial Inversion Rule of convex calculus.

Suggested Citation

  • Anthony Horsley & Andrew J Wrobel, 2005. "The Wong-Viner Envelope Theorem for subdifferentiable functions," STICERD - Theoretical Economics Paper Series 489, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stitep:489
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    References listed on IDEAS

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    1. Horsley, Anthony & Wrobel, Andrew J., 2002. "Efficiency rents of pumped-storage plants and their uses for operation and investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 109-142, November.
    2. Anthony Horsley & Andrew Wrobel, 2005. "Continuity of the equilibrium price density and its uses in peak-load pricing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 839-866, November.
    3. Horsley, Anthony & Wrobel, Andrew J., 1999. "Efficiency rents of storage plants in peak-load pricing, ii: hydroelectricity," LSE Research Online Documents on Economics 19342, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Horsley, Anthony & Wrobel, Andrew J., 2005. "A practical short-run approach to market equilibrium," LSE Research Online Documents on Economics 19313, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    Wong-Viner Envelope Theorem; nondifferentiable joint costs; profit-imputedvaluation of fixed inputs; general equilibrium; public utility pricing.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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