Spatial dynamics and convergence: The spatial AK model

Raouf Boucekkine (), Carmen Camacho and Giorgio Fabbri

No 13-09, Documents de recherche from Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne

Abstract: We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Spatio-temporal capital dynamics are described by a parabolic partial differential equation. The application of the maxi- mum principle leads to necessary but non-sufficient first-order conditions. Thanks to the linearity of the production technology and the special spatial setting considered, the value-function of the problem is found explicitly, and the (unique) optimal control is identified in feedback form. De- spite constant returns to capital, we prove that the spatio-temporal dynamics, induced by the willingness of the planner to give the same (detrended) consumption over space and time, lead to convergence in the level of capital across locations in the long-run.

Keywords: Economic Growth; Spatial Dynamics; Optimal Control; Partial-Differential Equations (search for similar items in EconPapers)
JEL-codes: C60 O11 R11 R12 R13 (search for similar items in EconPapers)
Pages: 17 pages
Date: 2013
New Economics Papers: this item is included in nep-dge and nep-ure
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (84)

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Related works:
Journal Article: Spatial dynamics and convergence: The spatial AK model (2013)
Working Paper: Spatial dynamics and convergence: The spatial AK model (2013)
Working Paper: Spatial dynamics and convergence: The spatial AK model (2013)
Working Paper: Spatial dynamics and convergence: The spatial AK model (2013)
Working Paper: Spatial dynamics and convergence: The spatial AK model (2013)
Working Paper: Spatial dynamics and convergence: The spatial AK model (2013)
Working Paper: Spatial dynamics and convergence: the spatial AK model (2010)
Working Paper: Spatial dynamics and convergence: the spatial AK model (2010)
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