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Consumption Habits and Humps

SAFE Working Paper No. 15

37 Pages Posted: 4 May 2013 Last revised: 11 Jul 2015

Holger Kraft

Goethe University Frankfurt

Claus Munk

Copenhagen Business School

Frank Thomas Seifried

University of Trier

Sebastian Wagner

Goethe University Frankfurt

Multiple version iconThere are 2 versions of this paper

Date Written: July 10, 2015

Abstract

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 U.S. consumption data from the Consumer Expenditure Survey.

Keywords: Consumption hump, life-cycle utility maximization, habit formation, impatience

JEL Classification: D91, D11, D14

Suggested Citation

Kraft, Holger and Munk, Claus and Seifried, Frank Thomas and Wagner, Sebastian, Consumption Habits and Humps (July 10, 2015). SAFE Working Paper No. 15. Available at SSRN: https://ssrn.com/abstract=2259613 or http://dx.doi.org/10.2139/ssrn.2259613

Holger Kraft (Contact Author)

Goethe University Frankfurt ( email )

Faculty of Economics and Business Administration
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany

Claus Munk

Copenhagen Business School ( email )

Department of Finance
Solbjerg Plads 3
Frederiksberg, DK-2000
Denmark

HOME PAGE: http://sites.google.com/site/munkfinance/

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

Sebastian Wagner

Goethe University Frankfurt ( email )

Faculty of Economics and Business Administration
Theodor-W.-Adorno-Platz 3
Frankfurt am Main, 60323
Germany

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