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 maximum 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. Despite 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.
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|Date of creation:||2013|
|Publication status:||Published in Journal of Economic Theory, Elsevier, 2013, 148 (6), pp.2719-2736. 〈10.1016/j.jet.2013.09.013〉|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00973387|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- 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.
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- 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).
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- 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," Discussion Papers (ECON - Département des Sciences Economiques) 2006038, Université catholique de Louvain, Département des Sciences Economiques.
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