Advanced Search
MyIDEAS: Login to save this paper or follow this series

Spatial dynamics and convergence: The spatial AK model

Contents:

Author Info

  • Raouf Boucekkine

    ()
    (Aix-Marseille University (Aix-Marseille School of Economics) and Université catholique de Louvain (IRES and CORE))

  • Carmen Camacho

    ()
    (CNRS, Université Paris 1-Panthéon Sorbonne and IRES, Université catholique de Louvain)

  • Giorgio Fabbri

    ()
    (EPEE, Université d’Evry-Val-d’Essonne (TEPP, FR-CNRS 3126))

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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://epee.univ-evry.fr/RePEc/2013/13-09.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne in its series Documents de recherche with number 13-09.

as in new window
Length: 17 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:eve:wpaper:13-09

Contact details of provider:
Postal: 4, bld Francois Mitterand, 91025 Evry Cedex
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

Related research

Keywords: Economic Growth; Spatial Dynamics; Optimal Control; Partial-Differential Equations;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
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.:
as in new window
  1. Klaus Desmet & Esteban Rossi-Hansberg, 2009. "On Spatial dynamics," Working Papers 2009-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  2. 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.
  3. 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.
  4. 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.
  5. Anastasios Xepapadeas & William Brock, 2009. "General Pattern Formation in Recursive Dynamical Systems Models in Economics," Working Papers 2009.49, Fondazione Eni Enrico Mattei.
  6. 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.
  7. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. repec:hal:journl:halshs-00674020 is not listed on IDEAS
  2. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Optimal Agglomerations in Dynamic Economics," DEOS Working Papers 1403, Athens University of Economics and Business.
  3. Brock, William A. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2014. "Spatial externalities and agglomeration in a competitive industry," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 143-174.
  4. William Brock & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," DEOS Working Papers 1402, Athens University of Economics and Business.
  5. Raouf Boucekkine & Carmen Camacho & Giorgio Fabbri, 2013. "On the optimal control of some parabolic partial differential equations arising in economics," Documents de recherche 13-10, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
  6. Carmen Camacho & Agustín Pérez-Barahona, 2012. "Land use dynamics and the environment," Documents de travail du Centre d'Economie de la Sorbonne 12012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  7. BOUCEKKINE, Raouf & FABBRI, Giorgio & PINTUS, Patrick, . "On the optimal control of a linear neutral differential equation arising in economics," CORE Discussion Papers RP -2449, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. repec:hal:wpaper:halshs-00831042 is not listed on IDEAS
  9. Paulo Brito, 2012. "Global Endogenous Growth and Distributional Dynamics," DEGIT Conference Papers c017_053, DEGIT, Dynamics, Economic Growth, and International Trade.
  10. Gani Aldashev & Serik Aldashev & Timoteo Carletti, 2014. "On Convergence in the Spatial AK Growth Models," Papers 1401.4887, arXiv.org.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

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 you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.