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A Non-Envelope Theorem with Linearly Homogeneous Constraints

Author

Listed:
  • Eduardo Dávila

    (Yale University)

  • Andreas Schaab

    (University of California - Berkeley)

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.

Suggested Citation

  • Eduardo Dávila & Andreas Schaab, 2024. "A Non-Envelope Theorem with Linearly Homogeneous Constraints," Cowles Foundation Discussion Papers 2405, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2405
    as

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    File URL: https://cowles.yale.edu/sites/default/files/2024-09/d2405.pdf
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    References listed on IDEAS

    as
    1. Silberberg, Eugene, 1974. "A revision of comparative statics methodology in economics, or, how to do comparative statics on the back of an envelope," Journal of Economic Theory, Elsevier, vol. 7(2), pages 159-172, February.
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