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The Wong-Viner envelope theorem for subdifferentiable functions

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  • Horsley, Anthony
  • Wrobel, Andrew J.

Abstract

The Wong-Viner Envelope Theorem on the equality of long-run and short-run marginal costs (LRMC and SRMC) is reformulated for convex but generally nondifferentiable cost functions. 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., to identify suitable SRMCs as LRMCs. This goal is achieved by equating the profit-imputed values of the fixed inputs to their prices. Thus reformulated, the theorem is proved from a lemma on the sections of the joint subdifferential of a bivariate convex function. The new technique is linked to the Partial Inversion Rule of convex calculus.

Suggested Citation

  • Horsley, Anthony & Wrobel, Andrew J., 2005. "The Wong-Viner envelope theorem for subdifferentiable functions," LSE Research Online Documents on Economics 19309, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:19309
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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-imputed valuation of fixed inputs; general equilibrium; public utility pricing.;
    All these keywords.

    JEL classification:

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

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