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Slopes of shadow prices and Lagrange multipliers

Sjur D. Flåm, Hubertus Th. Jongen and Oliver Stein

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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