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The Wong-Viner Envelope Theorem for subdifferentiable functions


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  • Anthony Horsley
  • Andrew J Wrobel


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.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Theoretical Economics Paper Series with number /2005/489.

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Date of creation: Apr 2005
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Handle: RePEc:cep:stitep:/2005/489

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

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  1. Anthony Horsley & Andrew J. Wrobel, 2000. "Efficiency rents of pumped-storage plants and their uses for operation and investment decisions," LSE Research Online Documents on Economics 19336, London School of Economics and Political Science, LSE Library.
  2. Anthony Horsley & Andrew J. Wrobel, 2001. "Continuity of the equilibrium price density and its uses in peak-load pricing," LSE Research Online Documents on Economics 19330, London School of Economics and Political Science, LSE Library.
  3. Anthony Horsley & Andrew J. Wrobel, 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. Anthony Horsley & Andrew J. Wrobel, 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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