Lie Symmetries and Essential Restrictions in Economic Optimization

Eran Yashiv and Gadi Perets

No 12611, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: In optimization problems in Economics there are explicit or implicit assumptions about the underlying structure. In particular, one typically assumes that optimal behavior will remain invariant, in a sense to be precisely defined. Inter alia, this relates to the rationale for empirical estimation of invariant structural models. This paper has three goals. First, to show how relevant restrictions pertaining to this invariance can be derived using the algebraic technique of Lie symmetries of differential equations. Importantly, the symmetries provide solutions of the optimization problems in question or generate rich information with respect to the properties of the solutions, when no closed-form solutions exist. Second, to provide an example of implementation of this algebra, using an issue of substance, thereby gaining insight on a key topic in utility theory and consumer-investor choice. Third, to outline topics that are at the research frontier, which would be amenable to such analysis, thereby providing a road map for a potentially important new literature.

Keywords: Economic optimization; Invariance; Lie symmetries; Differential equations; Consumption and portfolio choice; Hara utility; Structural econometrics; Macroeconomics; Finance (search for similar items in EconPapers)
Date: 2018-01
New Economics Papers: this item is included in nep-upt
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Citations: View citations in EconPapers (1)

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