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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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    4. Yang, C.C. & Zhao, Xueya & Zhu, Shenghao, 2023. "Tax progressivity and the Pareto tail of income distributions," Economics Letters, Elsevier, vol. 231(C).
    5. Lee, Byoungchan, 2023. "Wealth Inequality and Endogenous Growth," Journal of Monetary Economics, Elsevier, vol. 133(C), pages 132-148.

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