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On the concavity of consumption function under habit formation

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  • Liu, Haoyu
  • Li, Lun

Abstract

This paper studies the concavity of the consumption function of a habit-forming consumer with convex absolute risk tolerance. Compared with a model without habit formation, we show the conditions required for concave consumption are weaker if habit parameters are above a certain threshold. Contrary to the results of a standard consumption-saving model with time-separable utility, we show that the consumer’s consumption function can be convex when young and becomes concave when old. These results advance our understanding of the (non-)concavity of consumption function when preferences are not time-separable.

Suggested Citation

  • Liu, Haoyu & Li, Lun, 2023. "On the concavity of consumption function under habit formation," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    • Handle: RePEc:eee:mateco:v:106:y:2023:i:c:s0304406823000228
    DOI: 10.1016/j.jmateco.2023.102829
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    References listed on IDEAS

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