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Slopes of Shadow Prices and Lagrange Multipliers

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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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File URL: http://www.uib.no/filearchive/No.%2005-07.pdf
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Paper provided by University of Bergen, Department of Economics in its series Working Papers in Economics with number 05/07.

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Length: 15 pages
Date of creation: 28 Feb 2007
Handle: RePEc:hhs:bergec:2007_005
Contact details of provider: Postal:
Institutt for økonomi, Universitetet i Bergen, Postboks 7802, 5020 Bergen, Norway

Phone: (+47)55589200
Fax: (+47)55589210
Web page: http://www.uib.no/econ/en
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  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 J. & GRAZZINI, Lisa, "undated". "Strategic multilateral exchange and taxes," CORE Discussion Papers RP 1511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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