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A Complete Theory Of Comparative Statics For Differentiable Optimization Problems

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  • M. Hossein Partovi
  • Michael R. Caputo

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.

Suggested Citation

  • M. Hossein Partovi & Michael R. Caputo, 2006. "A Complete Theory Of Comparative Statics For Differentiable Optimization Problems," Metroeconomica, Wiley Blackwell, vol. 57(1), pages 31-67, February.
  • Handle: RePEc:bla:metroe:v:57:y:2006:i:1:p:31-67
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    Cited by:

    1. Michael R. Caputo & Dmitriy Popov, 2014. "Comparative Statics Of A Monopolistic Firm Facing Rate-Of-Return And Command-And-Control Pollution Constraints," Bulletin of Economic Research, Wiley Blackwell, vol. 66(S1), pages 17-35, December.
    2. repec:bpj:bejtec:v:18:y:2018:i:1:p:13:n:13 is not listed on IDEAS
    3. 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: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(3), pages 401-421, September.
    4. Michael Caputo & Chen Ling, 2015. "Intrinsic Comparative Dynamics of Locally Differentiable Feedback Stackelberg Equilibria," Dynamic Games and Applications, Springer, vol. 5(1), pages 1-25, March.
    5. Michael R. Caputo, 2016. "Intrinsic Comparative Statics of a Nash Bargaining Solution," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-11, December.
    6. Caputo, Michael R. & Paris, Quirino, 2008. "Comparative statics of the generalized maximum entropy estimator of the general linear model," European Journal of Operational Research, Elsevier, vol. 185(1), pages 195-203, February.
    7. Larson, Douglas M. & Shaikh, Sabina L., 1999. "Empirical Specification Requirements For Two-Constraint Models Of Recreation Demand," 1999 Annual meeting, August 8-11, Nashville, TN 21629, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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