IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v186y2008i2p451-465.html
   My bibliography  Save this article

On the dynamics of capital accumulation across space

Author

Listed:
  • Camacho, Carmen
  • Zou, Benteng
  • Briani, Maya

Abstract

We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the optimal trajectories of capital and consumption across space and time by maximizing an objective function with both space and time discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. We end up with a system of two parabolic differential equations with the corresponding boundary conditions. Then, we study the roles of initial capital and technology distributions over space in various scenarios.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Camacho, Carmen & Zou, Benteng & Briani, Maya, 2008. "On the dynamics of capital accumulation across space," European Journal of Operational Research, Elsevier, vol. 186(2), pages 451-465, April.
    • Handle: RePEc:eee:ejores:v:186:y:2008:i:2:p:451-465
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(07)00212-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(1), pages 20-45, February.
    2. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    3. Mossay, Pascal, 2003. "Increasing returns and heterogeneity in a spatial economy," Regional Science and Urban Economics, Elsevier, vol. 33(4), pages 419-444, July.
    4. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
    5. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    6. Pascal Mossay, 2003. "Increasing Returns And Heterogeneity In A Spatial Economy," Working Papers. Serie AD 2003-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    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


    Cited by:

    1. Carmen Camacho & Agustín Pérez-Barahona, 2012. "Land use dynamics and the environment," Post-Print halshs-00674020, HAL.
    2. João Juchem Neto & Julio Claeyssen, 2015. "Capital-induced labor migration in a spatial Solow model," Journal of Economics, Springer, vol. 115(1), pages 25-47, May.
    3. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2015. "Pollution diffusion and abatement activities across space and over time," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 48-63.
    4. Herb Kunze & Davide La Torre & Simone Marsiglio, 2019. "A Multicriteria Macroeconomic Model with Intertemporal Equity and Spatial Spillovers," Papers 1911.08247, arXiv.org.
    5. 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.
    6. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    7. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "Managing spatial linkages and geographic heterogeneity in dynamic models with transboundary pollution," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    8. Javier de Frutos & Guiomar Martín-Herrán, 2016. "Pollution control in a multiregional setting: a differential game with spatially distributed controls," Gecomplexity Discussion Paper Series 201601, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2016.
    9. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.
    10. Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    11. Giorgio Fabbri, 2014. "Ecological Barriers and Convergence: A Note on Geometry in Spatial Growth Models," Documents de recherche 14-05, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    12. Giorgio Fabbri, 2014. "Ecological Barriers and Convergence: A Note on Geometry in Spatial Growth Models," Documents de recherche 14-05, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    13. Brock, William A. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2014. "Optimal agglomerations in dynamic economics," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 1-15.
    14. Gilberto Gonz'alez-Parra & Benito Chen-Charpentier & Abraham J. Arenas & Miguel Diaz-Rodriguez, 2015. "Mathematical modeling of physical capital using the spatial Solow model," Papers 1504.04388, arXiv.org.
    15. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    16. Fabbri, Giorgio, 2016. "Geographical structure and convergence: A note on geometry in spatial growth models," Journal of Economic Theory, Elsevier, vol. 162(C), pages 114-136.
    17. Gilberto González-Parra & Benito Chen-Charpentier & Abraham J. Arenas & Miguel Díaz-Rodríguez, 2022. "Mathematical Modeling of Physical Capital Diffusion Using a Spatial Solow Model: Application to Smuggling in Venezuela," Economies, MDPI, vol. 10(7), pages 1-16, July.
    18. Carmen Camacho, 2013. "Spatial migration," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00801109, HAL.
    19. Juchem Neto, J.P. & Claeyssen, J.C.R. & Pôrto Júnior, S.S., 2018. "Economic agglomerations and spatio-temporal cycles in a spatial growth model with capital transport cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 76-86.
    20. Juchem Neto, Joao Plinio & Claeyssen, Julio Cesar Ruiz & Porto Junior, Sabino da Silva, 2014. "A spatial Solow model with transport cost," MPRA Paper 59766, University Library of Munich, Germany.
    21. de Frutos, Javier & Martín-Herrán, Guiomar, 2019. "Spatial vs. non-spatial transboundary pollution control in a class of cooperative and non-cooperative dynamic games," European Journal of Operational Research, Elsevier, vol. 276(1), pages 379-394.
    22. W.A. Brock & A. Xepapadeas & A.N. Yannacopoulos, 2014. "Optimal Control in Space and Time and the Management of Environmental Resources," Annual Review of Resource Economics, Annual Reviews, vol. 6(1), pages 33-68, October.
    23. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    24. Herb Kunze & Davide Torre & Simone Marsiglio, 2022. "Sustainability and spatial spillovers in a multicriteria macroeconomic model," Annals of Operations Research, Springer, vol. 311(2), pages 1067-1084, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(1), pages 20-45, February.
    2. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2019. "Growth and agglomeration in the heterogeneous space: a generalized AK approach," Journal of Economic Geography, Oxford University Press, vol. 19(6), pages 1287-1318.
    3. Albeverio, Sergio & Mastrogiacomo, Elisa, 2022. "Large deviation principle for spatial economic growth model on networks," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    4. Benteng Zou & Carmen Camacho, 2004. "The spatial Solow model," Economics Bulletin, AccessEcon, vol. 18(2), pages 1-11.
    5. José M. Gaspar, 2018. "A prospective review on New Economic Geography," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 61(2), pages 237-272, September.
    6. P M Picard & T Tabuchi, 2003. "Natural Agglomeration," Economics Discussion Paper Series 0329, Economics, The University of Manchester.
    7. Akamatsu, Takashi & Takayama, Yuki & Ikeda, Kiyohiro, 2012. "Spatial discounting, Fourier, and racetrack economy: A recipe for the analysis of spatial agglomeration models," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1729-1759.
    8. Mossay, Pascal, 2013. "A theory of rational spatial agglomerations," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 385-394.
    9. Pierre Picard & Takatoshi Tabuchi, 2010. "Self-organized agglomerations and transport costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 565-589, March.
    10. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2015. "Pollution diffusion and abatement activities across space and over time," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 48-63.
    11. Akamatsu, Takashi & Takayama, Yuki, 2009. "A Simplified Approach to Analyzing Multi-regional Core-Periphery Models," MPRA Paper 21739, University Library of Munich, Germany, revised 29 Oct 2009.
    12. Mossay, P. & Picard, P.M., 2011. "On spatial equilibria in a social interaction model," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2455-2477.
    13. Takashi Akamatsu & Tomoya Mori & Yuki Takayama, 2015. "Agglomerations in a multi-region economy: Poly-centric versus mono-centric patterns," KIER Working Papers 929, Kyoto University, Institute of Economic Research.
    14. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," Working Papers halshs-01982243, HAL.
    15. Sofia B. S. D. Castro & João Correia-da-Silva & José M. Gaspar, 2022. "Economic geography meets Hotelling: the home-sweet-home effect," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 183-209, February.
    16. Breinlich, Holger & Ottaviano, Gianmarco I.P. & Temple, Jonathan R.W., 2014. "Regional Growth and Regional Decline," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 4, pages 683-779, Elsevier.
    17. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico & Fausto Gozzi, 2020. "Optimal location of economic activity and population density: The role of the social welfare function," AMSE Working Papers 2003, Aix-Marseille School of Economics, France.
    18. Ohtake, Kensuke, 2023. "Agglomeration and welfare of the Krugman model in a continuous space," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 137-142.
    19. Herb Kunze & Davide La Torre & Simone Marsiglio, 2019. "A Multicriteria Macroeconomic Model with Intertemporal Equity and Spatial Spillovers," Papers 1911.08247, arXiv.org.
    20. Mossay, Pascal, 2006. "Stability of spatial adjustments across local exchange economies," Regional Science and Urban Economics, Elsevier, vol. 36(4), pages 431-449, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:186:y:2008:i:2:p:451-465. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.