A COMPLETE THEORY OF COMPARATIVE STATICS FOR DIFFERENTIABLE OPTIMIZATION PROBLEMS

M. Hossein Partovi and Michael Caputo

Metroeconomica, 2006, vol. 57, issue 1, 31-67

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.

Date: 2006
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