Spatial dynamics and convergence: The spatial AK model
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.
|Date of creation:||2013|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +33 1 69 47 71 77
Fax: +33 1 69 47 70 50
Web page: http://epee.univ-evry.fr
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009.
"Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model,"
Cambridge University Press, vol. 13(01), pages 20-45, February.
- Raouf, BOUCEKKINE & Carmen, CAMACHO & Benteng, ZOU, 2006. "Bridging the Gap between Growth Theory and the New Economic Geography : The Spatial Ramsey Model," Discussion Papers (ECON - Département des Sciences Economiques) 2006038, Université catholique de Louvain, Département des Sciences Economiques.
- BOUCEKKINE, Raouf & CAMACHO, Carmen & ZOU, Benteng, . "Bridging the gap between growth theory and the new economic geography: The spatial Ramsey model," CORE Discussion Papers RP -2090, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- BOUCEKKINE, Raouf & CAMACHO, Carmen & ZOU, Benteng, 2006. "Bridging the gap between growth theory and the new economic geography: the spatial Ramsey model," CORE Discussion Papers 2006072, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Raouf Boucekkine & C. Camacho & B. Zou, 2007. "Bridging the gap between growth theory and the new economic geography: The spatial Ramsey model," Working Papers 2007_27, Business School - Economics, University of Glasgow.
- Raouf Boucekkine & Carmen Camacho & Benteng Zou, 2006. "Bridging the gap between growth theory and the new economic geography: The spatial Ramsey model," DEGIT Conference Papers c011_039, DEGIT, Dynamics, Economic Growth, and International Trade.
- Paulo Brito, 2004. "The Dynamics of Growth and Distribution in a Spatially Heterogeneous World," Working Papers Department of Economics 2004/14, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
- Silvia Faggian, 2008. "Maximum Principle for Boundary Control Problems Arising in Optimal Investment with Vintage Capital," Working Papers 181, Department of Applied Mathematics, Università Ca' Foscari Venezia.
- Klaus Desmet & Esteban Rossi-Hansberg, 2010.
"On Spatial Dynamics,"
Journal of Regional Science,
Wiley Blackwell, vol. 50(1), pages 43-63.
- Anastasios Xepapadeas & William Brock, 2009.
"General Pattern Formation in Recursive Dynamical Systems Models in Economics,"
2009.49, Fondazione Eni Enrico Mattei.
- Brock, William & Xepapadeas, Anastasios, 2008. "General Pattern Formation in Recursive Dynamical Systems Models in Economics," MPRA Paper 12305, University Library of Munich, Germany.
- Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
- Chatterjee, Satyajit, 1994. "Transitional dynamics and the distribution of wealth in a neoclassical growth model," Journal of Public Economics, Elsevier, vol. 54(1), pages 97-119, May.
When requesting a correction, please mention this item's handle: RePEc:eve:wpaper:13-09. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Samuel Nosel)
If references are entirely missing, you can add them using this form.