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Asymptotic linearity of consumption functions and computational efficiency

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  • Ma, Qingyin
  • Toda, Alexis Akira

Abstract

We prove that the consumption functions in optimal savings problems are asymptotically linear if the marginal utility is regularly varying, or loosely speaking, behaves like a power function for wealthy agents. 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.

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  • Ma, Qingyin & Toda, Alexis Akira, 2022. "Asymptotic linearity of consumption functions and computational efficiency," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    • Handle: RePEc:eee:mateco:v:98:y:2022:i:c:s0304406821001257
    DOI: 10.1016/j.jmateco.2021.102562
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