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Business cycle fluctuations and learning-by-doing externalities in a one-sector model

Author

Listed:
  • Hippolyte d'Albis

    (LERNA - Economie des Ressources Naturelles - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

  • Emmanuelle Augeraud-Véron

    (MIA - Mathématiques, Image et Applications - EA 3165 - ULR - La Rochelle Université)

  • Alain Venditti

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract
We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with Arrow [5], to be a good index of experience. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation. This is obtained for reasonable parameter values, notably for both the elasticity of output with respect to the externality and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.

Suggested Citation

  • Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Alain Venditti, 2009. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Working Papers halshs-00432267, HAL.
    • Handle: RePEc:hal:wpaper:halshs-00432267
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00432267
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    References listed on IDEAS

    as
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    Cited by:

    1. Fabbri Giorgio & Federico Salvatore, 2014. "On the Infinite-Dimensional Representation of Stochastic Controlled Systems with Delayed Control in the Diffusion Term," Mathematical Economics Letters, De Gruyter, vol. 2(3-4), pages 33-43, November.
    2. Frédéric Dufourt & Kazuo Nishimura & Alain Venditti, 2016. "Sunspot fluctuations in two-sector models: New results with additively separable preferences," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 67-83, March.
    3. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Working Papers hal-03145949, HAL.
    4. Bambi, Mauro & Gozzi, Fausto & Licandro, Omar, 2014. "Endogenous growth and wave-like business fluctuations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 68-111.
    5. Manjira Datta & Kevin Reffett & Łukasz Woźny, 2018. "Comparing recursive equilibrium in economies with dynamic complementarities and indeterminacy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 593-626, October.
    6. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Multiple solutions in systems of functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 50-56.
    7. Fabbri, Giorgio, 2017. "International borrowing without commitment and informational lags: Choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 103-114.
    8. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Papers 2102.09851, arXiv.org, revised Feb 2021.
    9. Usman, Umer & Batabyal, Amitrajeet A., 2014. "Goods production, learning by doing, and growth in a region with creative and physical capital," International Review of Economics & Finance, Elsevier, vol. 33(C), pages 92-99.
    10. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Backward- versus Forward-Looking Feedback Interest Rate Rules," Documents de travail du Centre d'Economie de la Sorbonne 12051, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    11. Augeraud-Veron, Emmanuelle & Boucekkine, Raouf & Gozzi, Fausto & Venditti, Alain & Zou, Benteng, 2024. "Fifty years of mathematical growth theory: Classical topics and new trends," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    12. Frédéric Zumer & Jacques Le Cacheux & Marc Flandreau, 1998. "Stability without a pact? Lessons from the European Gold Standard, 1880-1913," Sciences Po publications n°98-01, Sciences Po.
    13. William Lefebvre & Enzo Miller, 2021. "Linear-Quadratic Stochastic Delayed Control and Deep Learning Resolution," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 134-168, October.
    14. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Post-Print hal-03145949, HAL.

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    More about this item

    Keywords

    One-sector infinite-horizon model; learning-by-doing externalities; inelastic labor; business cycle fluctuations; Hopf bifurcation;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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