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Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version

Author

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  • Fabbri, Giorgio
  • Gozzi, Fausto

Abstract

This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [18]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathematical difficulties. So far, in this approach, the model is studied by the Maximum Principle; here we develop the Dynamic Programming approach to the same problem by obtaining sharper results and we provide more insight about the economic implications of the model. We explicitly find the value function, the closed loop formula that relates capital and investment, the optimal consumption paths and the long run equilibrium. The short run fluctuations of capital and investment and the relations with the standard AK model are analyzed. Finally the applicability to other models is also discussed.

Suggested Citation

  • Fabbri, Giorgio & Gozzi, Fausto, 2006. "Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version," MPRA Paper 7334, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:7334
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    File URL: https://mpra.ub.uni-muenchen.de/7334/1/MPRA_paper_7334.pdf
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    References listed on IDEAS

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    4. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers ECO2006/17, European University Institute.
    5. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June.
    6. Raouf Boucekkine & David De La Croix & Omar Licandro, 2004. "MODELLING VINTAGE STRUCTURES WITH DDEs: PRINCIPLES AND APPLICATIONS," Mathematical Population Studies, Taylor & Francis Journals, vol. 11(3-4), pages 151-179.
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    11. Emilio Barucci & Fausto Gozzi, 2001. "Technology adoption and accumulation in a vintage-capital model," Journal of Economics, Springer, vol. 74(1), pages 1-38, February.
    12. Freni, Giuseppe & Gozzi, Fausto & Pignotti, Cristina, 2008. "Optimal strategies in linear multisector models: Value function and optimality conditions," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 55-86, January.
    13. Raouf Boucekkine & Fernando del Río & Blanca Martínez, 2009. "Technological progress, obsolescence, and depreciation," Oxford Economic Papers, Oxford University Press, vol. 61(3), pages 440-466, July.
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    18. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
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    Citations

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    Cited by:

    1. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
    2. Anton Bondarev, 2012. "The long-run dynamics of product and process innovations for a multi-product monopolist," Economics of Innovation and New Technology, Taylor & Francis Journals, vol. 21(8), pages 775-799, November.
    3. Fabbri, Giorgio & Iacopetta, Maurizio, 2007. "Dynamic Programming, Maximum Principle and Vintage Capital," MPRA Paper 5115, University Library of Munich, Germany.
    4. Fabbri, Giorgio & Faggian, Silvia & Gozzi, Fausto, 2006. "On the Dynamic Programming approach to economic models governed by DDE's," MPRA Paper 2825, University Library of Munich, Germany.
    5. Silvia Faggian, 2008. "Equilibrium Points for Optimal Investment with Vintage Capital," Working Papers 182, Department of Applied Mathematics, Università Ca' Foscari Venezia.

    More about this item

    Keywords

    Endogenous growth; Vintage capital; AK model; Dynamic programming;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity

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