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Relaxed Optimization: How Close Is a Consumer to Satisfying First-Order Conditions?

Author

Listed:
  • Geoffroy de Clippel

    (Department of Economics, Brown University)

  • Kareen Rozen

Abstract

We propose relaxing the first-order conditions in optimization to approximate rational consumer choice. We assess the magnitude of departures with a new, axiomatically founded measure that admits multiple interpretations. Standard inequality tests of rationality for any given reference class of preferences can be conveniently repurposed to measure goodness-of-fit with that class. Another advantage of our approach is that it is applicable in any context where the first-order approach is meaningful (e.g., convex budget sets arising from progressive taxation). We apply these ideas to shed new light on existing portfolio-choice data.

Suggested Citation

  • Geoffroy de Clippel & Kareen Rozen, 2023. "Relaxed Optimization: How Close Is a Consumer to Satisfying First-Order Conditions?," The Review of Economics and Statistics, MIT Press, vol. 105(4), pages 883-898, July.
    • Handle: RePEc:tpr:restat:v:105:y:2023:i:4:p:883-898
    DOI: 10.1162/rest_a_01088
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    Cited by:

    1. Choi, Syngjoo & Cipriani, Marco & Guarino, Antonio & Kariv, Shachar, 2025. "Douglas Gale’s contribution to social learning, decision under risk and uncertainty, monotone games and networks," Journal of Financial Intermediation, Elsevier, vol. 62(C).
    2. Dziewulski, Paweł, 2025. "A revealed preference approach to approximate utility maximisation," Journal of Economic Theory, Elsevier, vol. 228(C).
    3. Mingshi Chen & Tracy Xiao Liu & You Shan & Shu Wang & Songfa Zhong & Yanju Zhou, 2025. "How General Are Measures of Choice Consistency? Evidence from Experimental and Scanner Data," Papers 2505.05275, arXiv.org, revised Sep 2025.
    4. Matthew Polisson & John K. -H. Quah, 2024. "Rationalizability, Cost-Rationalizability, and Afriat's Efficiency Index," Papers 2406.10136, arXiv.org, revised Jul 2024.
    5. Dziewulski, Paweł & Lanier, Joshua & Quah, John K.-H., 2024. "Revealed preference and revealed preference cycles: A survey," Journal of Mathematical Economics, Elsevier, vol. 113(C).

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