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A theory of the saving rate of the rich

Author

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  • Ma, Qingyin
  • Toda, Alexis Akira

Abstract

Empirical evidence suggests that the rich have higher propensity to save than do the poor. While this observation may appear to contradict the homotheticity of preferences, we theoretically show that that is not the case. Specifically, we consider an income fluctuation problem with homothetic preferences and general shocks and prove that consumption functions are asymptotically linear, with an exact analytical characterization of asymptotic marginal propensities to consume (MPC). We provide necessary and sufficient conditions for the asymptotic MPCs to be zero. We calibrate a model with standard constant relative risk aversion utility and show that zero asymptotic MPCs are empirically plausible, implying that our mechanism has the potential to accommodate a large saving rate of the rich and high wealth inequality (small Pareto exponent) as observed in the data.

Suggested Citation

  • Ma, Qingyin & Toda, Alexis Akira, 2021. "A theory of the saving rate of the rich," Journal of Economic Theory, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:jetheo:v:192:y:2021:i:c:s0022053121000107
    DOI: 10.1016/j.jet.2021.105193
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    Cited by:

    1. Ahmed, Muhammad Ashfaq & Nawaz, Nasreen, 2023. "Policy Formulation for an Optimal Level of Savings in a Dynamic Setting," MPRA Paper 121352, University Library of Munich, Germany, revised 29 Oct 2023.
    2. Marcello D’Amato & Christian Di Pietro & Marco M. Sorge, 2024. "Left and right: a tale of two tails of the wealth distribution," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(4), pages 1389-1433, December.
    3. Qingyin Ma & Xinxin Zhang, 2026. "Optimal Savings under Transition Uncertainty and Learning Dynamics," Papers 2603.08663, arXiv.org.
    4. Jordan Roulleau-Pasdeloup, 2025. "Explicit Consumption Functions with Borrowing Constraints: a Continuous Time Approach," Papers 2511.03452, arXiv.org.
    5. Yang, C.C. & Zhao, Xueya & Zhu, Shenghao, 2023. "Tax progressivity and the Pareto tail of income distributions," Economics Letters, Elsevier, vol. 231(C).
    6. Tjeerd de Vries & Alexis Akira Toda, 2022. "Capital and Labor Income Pareto Exponents Across Time and Space," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 68(4), pages 1058-1078, December.
    7. Alexis Akira Toda, 2024. "Unbounded Markov dynamic programming with weighted supremum norm Perov contractions," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 141-156, December.
    8. Tomohiro HIRANO & Ryo Jinnai & Alexis Akira Toda, 2023. "Necessity of Rational Asset Price Bubbles in Two Sector Growth Economies," CIGS Working Paper Series 23-002E, The Canon Institute for Global Studies.
    9. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    10. Ma, Qingyin & Stachurski, John & Toda, Alexis Akira, 2022. "Unbounded dynamic programming via the Q-transform," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    11. Ji Hyung Lee & Yuya Sasaki & Alexis Akira Toda & Yulong Wang, 2021. "Fixed-k Tail Regression: New Evidence on Tax and Wealth Inequality from Forbes 400," Papers 2105.10007, arXiv.org, revised Sep 2022.
    12. Lee, Byoungchan, 2023. "Wealth Inequality and Endogenous Growth," Journal of Monetary Economics, Elsevier, vol. 133(C), pages 132-148.
    13. Tomohiro Hirano & Alexis Akira Toda, 2025. "Bubble Necessity Theorem," Journal of Political Economy, University of Chicago Press, vol. 133(1), pages 111-145.
    14. Lu, Xiang & Wang, Xudong, 2025. "Inequality measures in wealth exchange models based on saving propensity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 680(C).
    15. Thomas J. Sargent & John Stachurski, 2024. "Dynamic Programming: Finite States," Papers 2401.10473, arXiv.org.
    16. Toda, Alexis Akira & Walsh, Kieran James, 2024. "Recent advances on uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 113(C).

    More about this item

    Keywords

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    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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