A COMPLETE THEORY OF COMPARATIVE STATICS FOR DIFFERENTIABLE OPTIMIZATION PROBLEMS |
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| Authors: | M Hossein Partovi Michael R Caputo |
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| Institution: | 1. California State University and University of Central Florida;2. M. Hossein Partovi
Department of Physics and Astronomy
California State University
Sacramento
CA 95819‐6041
USA
E‐mail: hpartovi@saclink.csus.edu;3. Michael R. Caputo
Department of Economics
University of Central Florida
PO Box 161400
Orlando
FL 32816‐1400
USA
E‐mail: michael.caputo@bus.ucf.edu;4. Earlier versions of this work ( Partovi and Caputo, 1998) have been presented at North Carolina State University, University of California, Berkeley, University of California, Davis, University of Tennessee, Knoxville, University of Maryland, East Carolina University and University of Central Florida, as well as at the North American Meeting of the Econometric Society held at the California Institute of Technology, 25–29 June 1997, the 72nd Annual Western Economic Association International Conference held in Seattle, Washington, 9–13 July 1997, and the Southeast Economic Theory Conference held at Georgetown University, 12–14 November 1999. We are grateful to several colleagues and an anonymous referee for helpful comments on the organization and presentation of the contents of this paper. In particular, we would like to mention Susan Athey, Martine Quinzii, Walter N. Thurman and Juaquim Silvestre. M.H.P.'s work was in part supported by research awards from California State University, Sacramento. |
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| 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. |
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