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Optimal growth when consumption takes time

Author

Listed:
  • Thai Ha-Huy

    (EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne)

  • Cuong Le Van

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, VCREME - Van Xuan Center of Research in Economics, Management and Environment, IPAG Business School, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Thi-Do-Hanh Nguyen

    (Hai Phong University)

Abstract

This article establishes a growth model in which consumption takes time. The agent faces a time constraint, i.e; her/his available amount of time must be optimally share between consuming time and working time. By using a dynamic programming argument, it is proved that the optimal capital sequences are monotonic and have property that converges to steady state. We also compare this model to the one agent growth model with elastic labor. We obtain that (i) When the quantity of time to consume one unit of consumption increases, the agent devotes less time for labour. (ii) When the quantity of time to consume one unit of consumption is smaller that the threshod, it is better for the economy to spend time to consume than to enjoy leisure. We have more time for labour. This implies more output and more consumption. We reverse the situation when the quantity of time to consume one unit of consumption is larger than the threshold. We give an example to illustrate this result. Finally, if both models have the same technology which is of constant returns to scale, then they have the same ratios capital stock per head and consumption per head.

Suggested Citation

  • Thai Ha-Huy & Cuong Le Van & Thi-Do-Hanh Nguyen, 2023. "Optimal growth when consumption takes time," Working Papers halshs-04310371, HAL.
    • Handle: RePEc:hal:wpaper:halshs-04310371
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04310371
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    References listed on IDEAS

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    2. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
    3. Cuong Le Van & Anh-Ngoc Nguyen & Ngoc-Minh Nguyen, 2014. "Growth Strategy with Social Capital and Physical Capital- Theory and Evidence: the Case of Vietnam," Documents de travail du Centre d'Economie de la Sorbonne 14045, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
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    1. Dam, My & Ha-Huy, Thai & Le Van, Cuong & Nguyen, Thi Tuyet Mai, 2020. "Economic dynamics with renewable resources and pollution," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 14-26.

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