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Samuelson's Approach to Revealed Preference Theory: Some Recent Advances

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  • Demuynck, Thomas

    (ECARES, Université Libre de Bruxelles)

  • Hjertstrand, Per

    (Research Institute of Industrial Economics (IFN))

Abstract

Since Paul Samuelson introduced the theory of revealed preference, it has become one of the most important concepts in economics. This chapter surveys some recent contributions in the revealed preference literature. We depart from Afriat's theorem, which provides the conditions for a data set to be consistent with the utility maximization hypothesis. We provide and motivate a new condition, which we call the Varian inequalities. The advantage of the Varian inequalities is that they can be formulated as a set of mixed integer linear inequalities, which are linear in the quantity and price data. We show how the Varian inequalities can be used to derive revealed preference tests for weak separability, and show how it can be used to formulate tests of the collective household model. Finally, we discuss measurement errors in the observed data and measures of goodness-of-fit, power and predictive success.

Suggested Citation

  • Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    • Handle: RePEc:hhs:iuiwop:1274
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    Cited by:

    1. Victor H. Aguiar & Per Hjertstrand & Roberto Serrano, 2020. "Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies," Working Papers 2020-16, Brown University, Department of Economics.
    2. Victor H. Aguiar & Per Hjertstrand & Roberto Serrano, 2020. "Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies," Working Papers 2020-16, Brown University, Department of Economics.
    3. Demuynck, Thomas, 2021. "A Markov Chain Monte Carlo procedure to generate revealed preference consistent datasets," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    4. Hjertstrand, Per & Swofford, James L. & Whitney, Gerald A., 2023. "Testing for Weak Separability and Utility Maximization with Incomplete Adjustment," Journal of Economic Dynamics and Control, Elsevier, vol. 152(C).
    5. Thomas Demuynck & Tom Potoms, 2022. "Testing revealed preference models with unobserved randomness: a column generation approach," Working Papers ECARES 2022-42, ULB -- Universite Libre de Bruxelles.
    6. Hjertstrand, Per, 2019. "Power Against Random Expenditure Allocation for Revealed Preference Tests," Working Paper Series 1309, Research Institute of Industrial Economics, revised 30 Apr 2021.
    7. Aguiar, Victor H. & Hjertstrand, Per & Serrano, Roberto, 2020. "A Rationalization of the Weak Axiom of Revealed Preference," Working Paper Series 1321, Research Institute of Industrial Economics.
    8. Hjertstrand, Per, 2022. "Nonparametric Analysis of the Mixed-Demand Model," Working Paper Series 1430, Research Institute of Industrial Economics.
    9. Raghav Malhotra, 2022. "(Functional)Characterizations vs (Finite)Tests: Partially Unifying Functional and Inequality-Based Approaches to Testing," Papers 2208.03737, arXiv.org, revised Dec 2023.
    10. Hjertstrand, Per, 2021. "Power against random expenditure allocation for revealed preference tests," Journal of Economic Behavior & Organization, Elsevier, vol. 188(C), pages 36-45.

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    More about this item

    Keywords

    Afriats theorem; Collective household model; GARP; Mixed integer linear programing; Revealed preference; Varian inequalities; Weak separability;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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