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

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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7334.

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Date of creation: 2006
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Handle: RePEc:pra:mprapa:7334

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

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References

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  1. 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.
  2. Boucekkine, Raouf & Del Rio, Fernando & Licandro, Omar, 2000. "Vintage capital and the dynamics of the AK model," CEPREMAP Working Papers (Couverture Orange) 0003, CEPREMAP.
  3. BOUCEKKINE, Raouf & DEL RIO, Fernando & MARTINEZ, Blanca, 2006. "Technological progress obsolescence and depreciation," CORE Discussion Papers 2006027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
  5. 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.
  6. Michael Gort & Jeremy Greenwood & Peter Rupert, 1999. "Measuring the Rate of Technological Progress in Structures," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 2(1), pages 207-230, January.
  7. Raouf Boucekkine & Marc Germain & Omar Licandro, . "Replacement echoes in the vintage capital growth model," Working Papers 96-16, FEDEA.
  8. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
  9. Askenazy, Philippe & Le Van, 1997. "A model of optimal growth strategy," CEPREMAP Working Papers (Couverture Orange) 9707, CEPREMAP.
  10. 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.
  11. Kocherlakota, Narayana R. & Yi, Kei-Mu, 1995. "Can convergence regressions distinguish between exogenous and endogenous growth models?," Economics Letters, Elsevier, vol. 49(2), pages 211-215, August.
  12. 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.
  13. Giuseppe Freni & Fausto Gozzi & Neri Salvadori, 2004. "Existence of Optimal Strategies in linear Multisector Models," Discussion Papers 2004/29, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
  14. Sergio T. Rebelo, 1990. "Long Run Policy Analysis and Long Run Growth," NBER Working Papers 3325, National Bureau of Economic Research, Inc.
  15. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
  16. Parente Stephen L., 1994. "Technology Adoption, Learning-by-Doing, and Economic Growth," Journal of Economic Theory, Elsevier, vol. 63(2), pages 346-369, August.
  17. Boyan Jovanovic & Rafael Rob, 1997. "Solow vs. Solow: Machine Prices and Development," NBER Working Papers 5871, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. 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.
  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. Raouf BOUCEKKINE & Giorgio FABBRI & Fausto GOZZI, 2009. "Maintenance and investment : Complements or Substitutes ? A Reappraisal," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2009010, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  4. Fabbri, Giorgio & Iacopetta, Maurizio, 2007. "Dynamic Programming, Maximum Principle and Vintage Capital," MPRA Paper 5115, 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.

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