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Consumption with liquidity constraints: An analytical characterization

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  • Holm, Martin Blomhoff

Abstract

How do liquidity constraints affect households? This is a well-researched subject with remarkably few theoretical results. This paper bridges this gap by providing a closed form expression for consumption with liquidity constraints for a wide class of utility functions (HARA). Using this expression, I prove that the consumption function is strictly concave in wealth if a relevant liquidity constraint exists. Moreover, households respond to a tightening of the liquidity constraint by reducing consumption, becoming more sensitive to wealth changes, and having a “more” concave consumption function in wealth. These results thus provide theoretical underpinnings for how contractions in credit supply affect households.

Suggested Citation

  • Holm, Martin Blomhoff, 2018. "Consumption with liquidity constraints: An analytical characterization," Economics Letters, Elsevier, vol. 167(C), pages 40-42.
    • Handle: RePEc:eee:ecolet:v:167:y:2018:i:c:p:40-42
    DOI: 10.1016/j.econlet.2018.03.004
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    References listed on IDEAS

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    1. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, November.
    2. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    3. Carroll, Christopher D. & Holm, Martin B. & Kimball, Miles S., 2021. "Liquidity constraints and precautionary saving," Journal of Economic Theory, Elsevier, vol. 195(C).
    4. Seater, John J., 1997. "An optimal control solution to the liquidity constraint problem," Economics Letters, Elsevier, vol. 54(2), pages 127-134, February.
    5. Park, Myung-Ho, 2006. "An analytical solution to the inverse consumption function with liquidity constraints," Economics Letters, Elsevier, vol. 92(3), pages 389-394, September.
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    Citations

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    Cited by:

    1. Dongjing Chen & Xiaotong Guo, 2023. "Impact of the Digital Economy and Financial Development on Residents’ Consumption Upgrading: Evidence from Mainland China," Sustainability, MDPI, vol. 15(10), pages 1-25, May.
    2. Jordan Roulleau-Pasdeloup, 2025. "Explicit Consumption Functions with Borrowing Constraints: a Continuous Time Approach," Papers 2511.03452, arXiv.org.
    3. Krueger, Dirk & Malkov, Egor & Perri, Fabrizio, 2024. "How do households respond to income shocks?," Journal of Economic Dynamics and Control, Elsevier, vol. 168(C).
    4. Krueger, Dirk & Malkov, Egor & Perri, Fabrizio, 2024. "Reprint of: How do households respond to income shocks?," Journal of Economic Dynamics and Control, Elsevier, vol. 169(C).
    5. Chen Lian, 2023. "Mistakes in Future Consumption, High MPCs Now," American Economic Review: Insights, American Economic Association, vol. 5(4), pages 563-581, December.
    6. Krueger, Dirk & Malkov, Egor & Perri, Fabrizio, 2023. "How Do Households Respond to Income Shocks?," CEPR Discussion Papers 18614, C.E.P.R. Discussion Papers.
    7. Andrew Lyasoff, 2023. "The Time-Interlaced Self-Consistent Master System of Heterogeneous-Agent Models," Papers 2303.12567, arXiv.org, revised May 2025.
    8. Andreas Fagereng & Martin B. Holm & Gisle J. Natvik, 2021. "MPC Heterogeneity and Household Balance Sheets," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(4), pages 1-54, October.
    9. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lions & Benjamin Moll, 2017. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach," NBER Working Papers 23732, National Bureau of Economic Research, Inc.
    10. Fischer, Thomas, 2019. "Determinants of Wealth Inequality and Mobility in General Equilibrium," Working Papers 2019:22, Lund University, Department of Economics.
    11. Chen Lian, 2021. "Mistakes in Future Consumption, High MPCs Now," NBER Working Papers 29517, National Bureau of Economic Research, Inc.
    12. Chunkai Zhao & Xing Li & Jianfeng Yan, 2024. "The effect of digital finance on Residents' happiness: the case of mobile payments in China," Electronic Commerce Research, Springer, vol. 24(1), pages 69-104, March.
    13. Carroll, Christopher D. & Holm, Martin B. & Kimball, Miles S., 2021. "Liquidity constraints and precautionary saving," Journal of Economic Theory, Elsevier, vol. 195(C).
    14. Liu, Haoyu & Li, Lun, 2023. "On the concavity of consumption function under habit formation," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    15. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    16. Meiqi Zhao & Mengxia Zhang, 2025. "Marketization and Household Consumption Upgrading: Evidence from China," Sustainability, MDPI, vol. 17(21), pages 1-32, October.

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    More about this item

    Keywords

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    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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