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Optimal Savings with Preference for Wealth

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  • Qingyin Ma
  • Alexis Akira Toda

Abstract

The consumption function maps current wealth and the exogenous state to current consumption. We prove the existence and uniqueness of a consumption function when the agent has a preference for wealth. When the period utility functions are restricted to power functions, we prove that the consumption function is asymptotically linear as wealth tends to infinity and provide a complete characterization of the asymptotic slopes. When the risk aversion with respect to wealth is less than that for consumption, the asymptotic slope is zero regardless of other model parameters, implying wealthy households save a large fraction of their income, consistent with empirical evidence.

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  • Qingyin Ma & Alexis Akira Toda, 2025. "Optimal Savings with Preference for Wealth," Papers 2509.12195, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2509.12195
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    References listed on IDEAS

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    3. Brock, William A, 1970. "An Axiomatic Basis for the Ramsey- Weizsacker Overtaking Criterion," Econometrica, Econometric Society, vol. 38(6), pages 927-929, November.
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