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A Remark On Clarke'S Normal Cone And The Marginal Cost Pricing Rule

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  • Elyès Jouini

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper constructs a closed set Y in R' such that for all y in the boundary of Y Clarke's normal cone to Y at y is equal to R'+. If Y is the production set of a tirm, then the marginal cost pricing rule imposes no restriction. The existence of Y is shown to be equivalent to the existence of a Lipschitzian function f from Rt-1 to R such that the generalized gradient of / is everywhere equal to the convex hull of 0 and the simplex of Rt-1.

Suggested Citation

  • Elyès Jouini, 1989. "A Remark On Clarke'S Normal Cone And The Marginal Cost Pricing Rule," Post-Print halshs-00167132, HAL.
    • Handle: RePEc:hal:journl:halshs-00167132
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    Cited by:

    1. Yun, Kwan Koo, 1995. "The Dubovickii-Miljutin Lemma and characterizations of optimal allocations in non-smooth economies," Journal of Mathematical Economics, Elsevier, vol. 24(5), pages 435-460.
    2. Jean-Marc Bonnisseau & Bernard Cornet & Marc-Olivier Czarnecki, 2007. "The marginal pricing rule revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 579-589, December.
    3. Jean-Marc Bonnisseau, 2000. "The Marginal Pricing Rule in Economies with Infinitely Many Commodities," Econometric Society World Congress 2000 Contributed Papers 0262, Econometric Society.
    4. Jouini, Elyes, 1992. "An index theorem for nonconvex production economies," Journal of Economic Theory, Elsevier, vol. 57(1), pages 176-196.
    5. Beardon, Alan F. & Rowat, Colin, 2013. "Efficient sets are small," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 367-374.
    6. 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).
    7. 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.
    8. Antonio Villar, 1994. "Existence and efficiency of equilibrium in economics with increasing returns to scale: an exposition," Investigaciones Economicas, Fundación SEPI, vol. 18(2), pages 205-243, May.
    9. Jean-Marc Bonnisseau & Bernard Cornet & Marc-Olivier Czarnecki, 2007. "The marginal pricing rule revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 579-589, December.
    10. repec:hal:journl:halshs-00113332 is not listed on IDEAS

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    Keywords

    pricing rule; marginal cost;

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