Consumption Habits and Humps

Holger Kraft, Claus Munk, Frank Thomas Seifried, Sebastian Wagner

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We show that the optimal consumption of an individual over the life cycle can have the hump shape (inverted U-shape) observed empirically if the preferences of the individual exhibit internal habit formation. In the absence of habit formation, an impatient individual would prefer a decreasing consumption path over life. However, because of habit formation, a high initial consumption would lead to high required consumption in the future. To cover the future required consumption, wealth is set aside, but the necessary amount decreases with age which allows consumption to increase in the early part of life. At some age, the impatience outweighs the habit concerns so that consumption starts to decrease. We derive the optimal consumption strategy in closed form, deduce sufficient conditions for the presence of a consumption hump, and characterize the age at which the hump occurs. Numerical examples illustrate our findings. We show that our model can quantitatively reproduce the hump observed in US consumption data from the Consumer Expenditure Survey.
Original languageEnglish
JournalEconomic Theory
Issue number2
Pages (from-to)305–330
Number of pages26
Publication statusPublished - Aug 2017

Bibliographical note

Published online: 13 June 2016


  • Consumption hump
  • Life-cycle utility maximization
  • Habit formation
  • Impatience

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