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A COMPLETE THEORY OF COMPARATIVE STATICS FOR DIFFERENTIABLE OPTIMIZATION PROBLEMS
Author(s) -
Partovi M. Hossein,
Caputo Michael R.
Publication year - 2006
Publication title -
metroeconomica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.256
H-Index - 29
eISSN - 1467-999X
pISSN - 0026-1386
DOI - 10.1111/j.1467-999x.2006.00232.x
Subject(s) - comparative statics , differentiable function , uniqueness , statics , maximization , mathematical optimization , mathematical economics , constraint (computer aided design) , mathematics , economics , physics , mathematical analysis , geometry , classical mechanics , macroeconomics
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.