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The Mordukhovich Normal Cone and the Foundations of Welfare Economics

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  • Khan, M Ali

Abstract

The statement that Pareto optimal allocations require the equalization of marginal rates of substitution, or in an economy with public goods, require the equalization of the aggregate of the marginal rates in consumption to those in production, is formalized through the use of the Mordukhovich normal cone. Since this cone is strictly contained, in general, in the Clarke normal cone, the results generalize earlier work of Khan and Vohra, Quinzii, Yun, and Cornet. The results are an application of Mordukhovich's 1980 theorem on necessary conditions for optimality in constrained optimization problems involving functions that are not necessarily differentiable or quasi-concave. As such, the results suggest a distinction between the mathematical programming approach to the "second welfare theorem," as in the work of Hicks, Lange, and Samuelson, and that based on the separation of sets, as pioneered by Arrow and Debreu. Copyright 1999 by Blackwell Publishing Inc.

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Bibliographic Info

Article provided by Association for Public Economic Theory in its journal Journal of Public Economic Theory.

Volume (Year): 1 (1999)
Issue (Month): 3 ()
Pages: 309-38

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Handle: RePEc:bla:jpbect:v:1:y:1999:i:3:p:309-38

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Cited by:
  1. M Ali Khan, 2007. "Perfect Competition," Microeconomics Working Papers 22207, East Asian Bureau of Economic Research.
  2. repec:hal:journl:halshs-00113335 is not listed on IDEAS
  3. Jean-Marc Bonnisseau & Bertrand Crettez, 2007. "On the Characterization of Efficient Production Vectors," Economic Theory, Springer, vol. 31(2), pages 213-223, May.
  4. Jean-Marc Bonnisseau & Bernard Cornet & Marc-Olivier Czarnecki, 2005. "The marginal pricing rule revisited," Cahiers de la Maison des Sciences Economiques b06021, Université Panthéon-Sorbonne (Paris 1).
  5. Bonnisseau, J.-M. & Cornet, B., 2008. "Existence of equilibria with a tight marginal pricing rule," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 613-624, July.
  6. Khan, M. Ali Khan, 2007. "Perfect Competition," MPRA Paper 2202, University Library of Munich, Germany.
  7. Jean-Marc Bonnisseau & Bernard Cornet, 2006. "Existence of equilibria with a tight marginal," Cahiers de la Maison des Sciences Economiques b06022, Université Panthéon-Sorbonne (Paris 1).
  8. repec:hal:journl:halshs-00113332 is not listed on IDEAS

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