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A Complete Theory Of Comparative Statics For Differentiable Optimization Problems


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  • M. Hossein Partovi
  • Michael R. Caputo


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.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Metroeconomica.

Volume (Year): 57 (2006)
Issue (Month): 1 (02)
Pages: 31-67

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Handle: RePEc:bla:metroe:v:57:y:2006:i:1:p:31-67

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Cited by:
  1. Michael Caputo & Dmitriy Popov, 2010. "Comparative Statics of a Monopolistic Firm Facing Rate-of-Return and Command-and-Control Pollution Constraints," Working Papers 2010-06, University of Central Florida, Department of Economics, revised Jun 2012.
  2. Manuel Besada & Javier García & Miguel Mirás & Carmen Vázquez, 2011. "Generalized marginal rate of substitution in multiconstraint consumer’s problems and their reciprocal expenditure problems," SERIEs, Spanish Economic Association, vol. 2(3), pages 401-421, September.


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