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Properties of Critical Points and Operators in Economics

Abstract: 'The study of the local characteristics of equilibrium positions generated bythe constrained maximization of some criterion functions (such as utility,profit, cost, etc.) goes back to Antonelli's paper [2] of 1886. Certain localproperties have proved to be particularly fruitful for economie theory sincethe early works of Slutsky, Hicks, and Samuelson [9]; they have been formulatedin terms of a matrix uf "compensated" terms and they concern the propertiesof partial derivatives of the demand function in some neighborhood of theequilibrium.

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Munich Personal RePEc Archive
Properties of critical points and
operators in economics
Chichilnisky, Graciela and Kalman, P.J.
Online at
MPRA Paper No. 7976, posted 29 Mar 2008 07:02 UTC

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Abstract: A new comparative statics formalism using generalized compensated derivatives is presented that, in contrast to existing methodologies, directly yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. The formalism provides a natural and powerful method of constructing comparative statics results, free of constraints and unrestricted in scope. New results on envelope relations, invariance conditions, rank inequalities and non-uniqueness are derived that greatly extend their utility and reach. The methodology is illustrated by deriving the comparative statics of multiple linear constraint utility maximization models and the principal-agent problem with hidden actions, both highly nontrivial and hitherto unsolved problems.

18 citations

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