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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. Seater, John J., 1997. "An optimal control solution to the liquidity constraint problem," Economics Letters, Elsevier, vol. 54(2), pages 127-134, February.
    4. Carroll, Christopher D. & Holm, Martin B. & Kimball, Miles S., 2021. "Liquidity constraints and precautionary saving," Journal of Economic Theory, Elsevier, vol. 195(C).
    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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    Cited by:

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    2. 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.
    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. Liu, Haoyu & Li, Lun, 2023. "On the concavity of consumption function under habit formation," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    5. Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    6. Dirk Krueger & Egor Malkov & Fabrizio Perri, 2023. "How Do Households Respond to Income Shocks?," Staff Report 655, Federal Reserve Bank of Minneapolis.
    7. Andrew Lyasoff, 2023. "Self-Aware Transport of Economic Agents," Papers 2303.12567, arXiv.org, revised Jan 2024.
    8. 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.
    9. Fischer, Thomas, 2019. "Determinants of Wealth Inequality and Mobility in General Equilibrium," Working Papers 2019:22, Lund University, Department of Economics.
    10. Chen Lian, 2021. "Mistakes in Future Consumption, High MPCs Now," NBER Working Papers 29517, National Bureau of Economic Research, Inc.

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    More about this item

    Keywords

    Consumption; Liquidity constraints;

    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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