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Asymptotic Linearity of Consumption Functions and Computational Efficiency

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  • Qingyin Ma
  • Alexis Akira Toda

Abstract

We prove that the consumption functions in optimal savings problems are asymptotically linear if the marginal utility is regularly varying. We also analytically characterize the asymptotic marginal propensities to consume (MPCs) out of wealth. Our results are useful for obtaining good initial guesses when numerically computing consumption functions, and provide a theoretical justification for linearly extrapolating consumption functions outside the grid.

Suggested Citation

  • Qingyin Ma & Alexis Akira Toda, 2020. "Asymptotic Linearity of Consumption Functions and Computational Efficiency," Papers 2002.09108, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:2002.09108
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    Cited by:

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    2. Ezra Karger & Aastha Rajan, 2020. "Heterogeneity in the Marginal Propensity to Consume: Evidence from Covid-19 Stimulus Payments," Working Paper Series WP-2020-15, Federal Reserve Bank of Chicago, revised 21 Feb 2021.
    3. 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.
    4. Alexis Akira Toda, 2023. "Unbounded Markov Dynamic Programming with Weighted Supremum Norm Perov Contractions," Papers 2310.04593, arXiv.org.
    5. Platell, Monique & Martin, Karen & Fisher, Colleen & Cook, Angus, 2020. "Comparing adolescent and service provider perceptions on the barriers to mental health service use: A sequential mixed methods approach," Children and Youth Services Review, Elsevier, vol. 115(C).
    6. Yang, C.C. & Zhao, Xueya & Zhu, Shenghao, 2023. "Tax progressivity and the Pareto tail of income distributions," Economics Letters, Elsevier, vol. 231(C).

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