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Internal habits formation and optimality

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  • Bambi, Mauro
  • Gozzi, Fausto

Abstract

In a very influential model with internal habits, Carroll et al., (2017, 2000), establish that an increase in economic growth may cause a positive change in savings. The optimality of this result, and of many other contributions using a similar framework, has been questioned by some authors who have observed that the parametrization used in these models always implies a utility function not jointly concave in consumption and habits. In this paper, we revisit the optimality issue and, using advanced techniques in Dynamic Programming, we answer the following long-standing open questions: (i) Is the solution found in Carroll et al., (2017, 2000) optimal? (ii) Is it also unique or do other optimal solutions exist?

Suggested Citation

  • Bambi, Mauro & Gozzi, Fausto, 2020. "Internal habits formation and optimality," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 165-172.
  • Handle: RePEc:eee:mateco:v:91:y:2020:i:c:p:165-172
    DOI: 10.1016/j.jmateco.2020.09.008
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    References listed on IDEAS

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    1. Diaz, Antonia & Pijoan-Mas, Josep & Rios-Rull, Jose-Victor, 2003. "Precautionary savings and wealth distribution under habit formation preferences," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1257-1291, September.
    2. Jody Overland & Christopher D. Carroll & David N. Weil, 2000. "Saving and Growth with Habit Formation," American Economic Review, American Economic Association, vol. 90(3), pages 341-355, June.
    3. Emmanuelle Augeraud-Veron & Mauro Bambi & Fausto Gozzi, 2017. "Solving Internal Habit Formation Models Through Dynamic Programming in Infinite Dimension," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 584-611, May.
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