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Necessity of Hyperbolic Absolute Risk Aversion for the Concavity of Consumption Functions

Carroll and Kimball (1996) have shown that, in the class of utility functions that are strictly increasing, strictly concave, and have nonnegative third derivatives, hyperbolic absolute risk aversion (HARA) is sufficient for the concavity of consumption functions in general consumption-saving problems. This paper shows that HARA is necessary, implying the concavity of consumption is not a robust prediction outside the HARA class.

preprint2020arXivOpen access
Alexis Akira Toda
econ.TH
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Alexis Akira Toda

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