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Slopes of Shadow Prices and Lagrange Multipliers

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Abstract

Many economic models and optimization problems generate (endogenous) shadow prices - alias dual variables or Lagrange multipliers. Frequently the “slopes” of resulting price curves - that is, multiplier derivatives - are of great interest. These objects relate to the Jacobian of the optimality conditions. That particular matrix often has block structure. So, we derive explicit formulas for the inverse of such matrices and, as a consequence, for the multiplier derivatives.

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  • Flåm, Sjur Didrik & Jongen, Hubertus Th. & Stein, Oliver, 2007. "Slopes of Shadow Prices and Lagrange Multipliers," Working Papers in Economics 05/07, University of Bergen, Department of Economics.
    • Handle: RePEc:hhs:bergec:2007_005
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    1. Jean J. Gabszewicz, 2002. "Strategic Multilateral Exchange," Books, Edward Elgar Publishing, number 756.
    2. Evstigneev, I.V. & Flam, S.D., 2000. "Sharing Nonconvex Costs," Norway; Department of Economics, University of Bergen 1300, Department of Economics, University of Bergen.
    3. Flam, S. D. & Jourani, A., 2003. "Strategic behavior and partial cost sharing," Games and Economic Behavior, Elsevier, vol. 43(1), pages 44-56, April.
    4. Jean-Pierre Aubin, 1984. "Lipschitz Behavior of Solutions to Convex Minimization Problems," Mathematics of Operations Research, INFORMS, vol. 9(1), pages 87-111, February.
    5. Carlo Carraro & Vito Fragnelli (ed.), 2004. "Game Practice and the Environment," Books, Edward Elgar Publishing, number 3344.
    6. Henriet, Dominique & Rochet, Jean-Charles, 1987. "Some reflections on insurance pricing," European Economic Review, Elsevier, vol. 31(4), pages 863-885, June.
    7. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    8. Magill, Michael & Shafer, Wayne, 1991. "Incomplete markets," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 30, pages 1523-1614, Elsevier.
    9. GABSZEWICZ, Jean & GRAZZINI, Lisa, 2000. "Strategic multilateral exchange and taxes," LIDAM Discussion Papers CORE 2000063, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Vadim Borokhov, 2014. "On the properties of nodal price response matrix in electricity markets," Papers 1404.3678, arXiv.org, revised Jan 2015.

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    More about this item

    Keywords

    Sensitivity; optimal value function; shadow price; Karush-Kuhn-Tucker system; matrix inversion.;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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