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

Giorgio Fabbri () and Fausto Gozzi

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Endogenous growth; Vintage capital; AK model; Dynamic programming. (search for similar items in EconPapers)
JEL-codes: C61 O4 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-dev and nep-dge
Date: 2006
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http://mpra.ub.uni-muenchen.de/2863/ orginal version
http://mpra.ub.uni-muenchen.de/7334/ revised version

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