Slopes of Shadow Prices and Lagrange Multipliers

Sjur Flåm, Hubertus Th. Jongen () and Oliver Stein ()
Additional contact information
Hubertus Th. Jongen: RWTH Aachen University, Germany, Postal: Mathematics, Section C, Templergraben 55,, 52056 Aachen, Germany,, http://www.mathc.rwth-aachen.de/jongen/jongene.html
Oliver Stein: Karlsruhe Institute of Technology, Postal: Karlsruhe Institute of Technology, P.O. Box 3640, , 76021 Karlsruhe, Germany, http://kop.ior.kit.edu/english/stein.php

No 05/07, Working Papers in Economics from University of Bergen, Department of Economics

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.

Keywords: Sensitivity; optimal value function; shadow price; Karush-Kuhn-Tucker system; matrix inversion. (search for similar items in EconPapers)
JEL-codes: C60 C71 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2007-02-28
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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