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

  • Fabbri, Giorgio
  • Gozzi, Fausto

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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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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  1. Patrick K. Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," NBER Technical Working Papers 0211, National Bureau of Economic Research, Inc.
  2. 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.
  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. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
  5. 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.
  6. 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.
  7. Raouf Boucekkine & Omar Licandro & Luis A. Puch & Fernando del Rio, . "Vintage capital and the dynamics of the AK model," Working Papers 2000-01, FEDEA.
  8. Boyan Jovanovic & Rafael Rob, 1997. "Solow vs. Solow: Machine Prices and Development," NBER Working Papers 5871, National Bureau of Economic Research, Inc.
  9. Sergio T. Rebelo, 1990. "Long Run Policy Analysis and Long Run Growth," NBER Working Papers 3325, National Bureau of Economic Research, Inc.
  10. Mauro Bambi, 2006. "Endogenous Growth and Time-to-Build: the AK Case," Economics Working Papers ECO2006/17, European University Institute.
  11. 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.
  12. 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.
  13. Parente Stephen L., 1994. "Technology Adoption, Learning-by-Doing, and Economic Growth," Journal of Economic Theory, Elsevier, vol. 63(2), pages 346-369, August.
  14. 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.
  15. 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.
  16. 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.
  17. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, vol. 85(1), pages 24-51, March.
  18. 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.
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