A Non-Envelope Theorem with Linearly Homogeneous Constraints

Eduardo Dávila and Andreas Schaab
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Eduardo Dávila: Yale University
Andreas Schaab: University of California - Berkeley

No 2405, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper shows that it is possible to define an unambiguous notion of the direct effect of a parameter perturbation on the value of an optimization problem’s objective away from an optimum for problems with linearly homogeneous constraints. This notion of the direct effect relies on reformulating the optimization problem using shares as choice variables, and has the interpretation of holding choice variables — when formulated as shares — fixed. This short paper contains one formal “non-envelope†theorem and four applications to i) consumer demand, ii) cost minimization, iii) planning in exchange economies, and iv) planning in production economies.

Pages: 20 pages
Date: 2024-09
New Economics Papers: this item is included in nep-dcm
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