IDEAS home Printed from https://ideas.repec.org/p/hhs/bergec/2007_005.html
   My bibliography  Save this paper

Slopes of Shadow Prices and Lagrange Multipliers

Author

Listed:

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.uib.no/filearchive/No.%2005-07.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Evstigneev, I.V. & Flam, S.D., 2000. "Sharing Nonconvex Costs," Norway; Department of Economics, University of Bergen 1300, Department of Economics, University of Bergen.
    2. Flam, S. D. & Jourani, A., 2003. "Strategic behavior and partial cost sharing," Games and Economic Behavior, Elsevier, vol. 43(1), pages 44-56, April.
    3. Henriet, Dominique & Rochet, Jean-Charles, 1987. "Some reflections on insurance pricing," European Economic Review, Elsevier, vol. 31(4), pages 863-885, June.
    4. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    5. 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.
    6. GABSZEWICZ, Jean & GRAZZINI, Lisa, 2000. "Strategic multilateral exchange and taxes," CORE Discussion Papers 2000063, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    More about this item

    Keywords

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

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hhs:bergec:2007_005. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Kjell Erik Lommerud). General contact details of provider: http://edirc.repec.org/data/iouibno.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.