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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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    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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