Fabbri, Giorgio and Gozzi, Fausto (2006): Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version.
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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.
Item Type:  MPRA Paper 

Original Title:  Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version. 
Language:  English 
Keywords:  Endogenous growth; Vintage capital; AK model; Dynamic programming 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis O  Economic Development, Innovation, Technological Change, and Growth > O4  Economic Growth and Aggregate Productivity 
Item ID:  7334 
Depositing User:  Giorgio Fabbri 
Date Deposited:  26 Feb 2008 00:05 
Last Modified:  26 Sep 2019 13:54 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/7334 
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Vintage Capital in the AK growth model: a Dynamic Programming approach. (deposited 22 Apr 2007)
 Vintage Capital in the AK growth model: a Dynamic Programming approach. Extended version. (deposited 26 Feb 2008 00:05) [Currently Displayed]