A COMPLETE THEORY OF COMPARATIVE STATICS FOR DIFFERENTIABLE OPTIMIZATION PROBLEMS

M. Hossein Partovi and Michael R. Caputo ()

Metroeconomica, 2006, vol. 57, issue 1, pages 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. Copyright Blackwell Publishing Ltd 2006.

Date: 2006
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