IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v146y2023ics0165188922002871.html
   My bibliography  Save this article

Spatial growth theory: Optimality and spatial heterogeneity

Author

Listed:
  • Xepapadeas, Anastasios
  • Yannacopoulos, Athanasios N.

Abstract

Spatiotemporal dynamics are introduced in a standard Ramsey model of optimal growth in which capital moves toward locations where the marginal productivity of capital is relatively higher and initiate a study of the effects of nonlinear capital transport in terms of a linearized analysis around steady state solution solutions.

Suggested Citation

  • Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2023. "Spatial growth theory: Optimality and spatial heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
  • Handle: RePEc:eee:dyncon:v:146:y:2023:i:c:s0165188922002871
    DOI: 10.1016/j.jedc.2022.104584
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188922002871
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jedc.2022.104584?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Richard Baldwin & Rikard Forslid & Philippe Martin & Gianmarco Ottaviano & Frederic Robert-Nicoud, 2005. "Economic Geography and Public Policy," Economics Books, Princeton University Press, edition 1, number 7524.
    3. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    4. Benteng Zou & Carmen Camacho, 2004. "The spatial Solow model," Economics Bulletin, AccessEcon, vol. 18(2), pages 1-11.
    5. 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.
    6. Raouf Boucekkine & Giorgio Fabbri & Salvatore Federico, 2016. "Optimal Economic Growth Through Capital Accumulation in a Spatially Heterogeneous Environment," AMSE Working Papers 1641, Aix-Marseille School of Economics, France.
    7. Xanthi-Isidora Kartala & Nikolaos Englezos & Athanasios N. Yannacopoulos, 2020. "Future Expectations Modeling, Random Coefficient Forward–Backward Stochastic Differential Equations, and Stochastic Viscosity Solutions," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 403-433, May.
    8. Quah, Danny T, 1996. "Twin Peaks: Growth and Convergence in Models of Distribution Dynamics," Economic Journal, Royal Economic Society, vol. 106(437), pages 1045-1055, July.
    9. 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.
    10. Cuong Van & Raouf Boucekkine & Cagri Saglam, 2007. "Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 497-509, September.
    11. 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.
    12. Lucas, Robert E, Jr, 1990. "Why Doesn't Capital Flow from Rich to Poor Countries?," American Economic Review, American Economic Association, vol. 80(2), pages 92-96, May.
    13. Masahisa Fujita & Paul Krugman & Anthony J. Venables, 2001. "The Spatial Economy: Cities, Regions, and International Trade," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262561476, December.
    14. Martin, Philippe & Ottaviano, Gianmarco I P, 2001. "Growth and Agglomeration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 947-968, November.
    15. Benveniste, L. M. & Scheinkman, J. A., 1982. "Duality theory for dynamic optimization models of economics: The continuous time case," Journal of Economic Theory, Elsevier, vol. 27(1), pages 1-19, June.
    16. Treb Allen & Costas Arkolakis, 2014. "Trade and the Topography of the Spatial Economy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1085-1140.
    17. Desmet, Klaus & Rossi-Hansberg, Esteban, 2009. "Spatial growth and industry age," Journal of Economic Theory, Elsevier, vol. 144(6), pages 2477-2502, November.
    18. 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.
    19. 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.
    20. Conley, Timothy G & Ligon, Ethan, 2002. "Economic Distance and Cross-Country Spillovers," Journal of Economic Growth, Springer, vol. 7(2), pages 157-187, June.
    21. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 407-437.
    22. Brock, William & Xepapadeas, Anastasios, 2010. "Pattern formation, spatial externalities and regulation in coupled economic-ecological systems," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 149-164, March.
    23. 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.
    24. BOUCEKKINE, Raouf & FABBRI, Giorgio & PINTUS, Patrick, 2012. "On the optimal control of a linear neutral differential equation arising in economics," LIDAM Reprints CORE 2449, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    25. Masahisa Fujita & Tomoya Mori, 2005. "Frontiers of the New Economic Geography," Papers in Regional Science, Wiley Blackwell, vol. 84(3), pages 377-405, August.
    26. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    27. Richard E. Baldwin & Philippe Martin & Gianmarco I. P. Ottaviano, 2021. "Global Income Divergence, Trade, and Industrialization: The Geography of Growth Take-Offs," World Scientific Book Chapters, in: Firms and Workers in a Globalized World Larger Markets, Tougher Competition, chapter 2, pages 25-57, World Scientific Publishing Co. Pte. Ltd..
    28. Walter Nonneman & Patrick Vanhoudt, 1996. "A Further Augmentation of the Solow Model and the Empirics of Economic Growth for OECD Countries," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(3), pages 943-953.
    29. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    30. Raouf Boucekkine & Carmen Camacho & Fabbri Giorgio, 2013. "On the optimal control of some parabolic partial differential equations arising in economics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00973388, HAL.
    31. 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.
    32. Danny Quah, 1996. "Twin Peaks: Growth and Convergence in Models of Distribution Dynamics," CEP Discussion Papers dp0280, Centre for Economic Performance, LSE.
    33. Baldwin, Richard E. & Krugman, Paul, 2004. "Agglomeration, integration and tax harmonisation," European Economic Review, Elsevier, vol. 48(1), pages 1-23, February.
    34. Robert E. Lucas Jr., 2003. "Macroeconomic Priorities," American Economic Review, American Economic Association, vol. 93(1), pages 1-14, March.
    35. Klaus Desmet & Esteban Rossi‐Hansberg, 2010. "On Spatial Dynamics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 43-63, February.
    36. Quah, Danny, 1996. "Twin peaks : growth and convergence in models of distribution dynamics," LSE Research Online Documents on Economics 2278, London School of Economics and Political Science, LSE Library.
    37. Paul Krugman, 1998. "Space: The Final Frontier," Journal of Economic Perspectives, American Economic Association, vol. 12(2), pages 161-174, Spring.
    38. 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.
    39. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
    40. 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.
    41. Magill, Michael J. P., 1977. "Some new results on the local stability of the process of capital accumulation," Journal of Economic Theory, Elsevier, vol. 15(1), pages 174-210, June.
    42. Yannacopoulos, Athanasios N., 2008. "Rational expectations models: An approach using forward-backward stochastic differential equations," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 251-276, February.
    43. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2745-2787, September.
    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. Spyridon Tsangaris & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2022. "Spatial externalities, R&D spillovers, and endogenous technological change," DEOS Working Papers 2225, Athens University of Economics and Business.
    2. Alessandro Calvia & Fausto Gozzi & Marta Leocata & Georgios I. Papayiannis & Anastasios Xepapadeas & Athanasios N. Yannacopoulos, 2023. "An optimal control problem with state constraints in a spatio-temporal economic growth model on networks," Papers 2304.11568, arXiv.org.

    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. Xepapadeas, A. & Yannacopoulos, A.N., 2016. "Spatial growth with exogenous saving rates," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 125-137.
    2. Anastasios Xepapadeas & Athanasios Yannacopoulos & Andreas Ioannidis, 2014. "Spatial Growth: The Distribution of Capital across Locations when Saving Rates are Exogenous," DEOS Working Papers 1412, Athens University of Economics and Business.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," Working Papers halshs-01982243, HAL.
    9. 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.
    10. 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.
    11. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    12. repec:esx:essedp:729 is not listed on IDEAS
    13. Giorgio FABBRI, 2014. "Ecological Barriers and Convergence: a Note on Geometry in Spatial Growth Models," LIDAM Discussion Papers IRES 2014014, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    14. 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.
    15. Carmen Camacho & Agustín Pérez-Barahona, 2017. "The diffusion of economic activity across space: a new approach," PSE Working Papers halshs-01670532, HAL.
    16. Wilfried Koch, 2004. "Effets de voisinage dans le modèle de Solow avec des externalités spatiales," Working Papers hal-01526536, HAL.
    17. Spyridon Tsangaris & Anastasios Xepapadeas & Athanasios Yannacopoulos, 2022. "Spatial externalities, R&D spillovers, and endogenous technological change," DEOS Working Papers 2225, Athens University of Economics and Business.
    18. 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.
    19. 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.
    20. 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.
    21. 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.

    More about this item

    Keywords

    Ramsey model; spatiotemporal dynamics; flat earth; pattern formation;
    All these keywords.

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • R11 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Regional Economic Activity: Growth, Development, Environmental Issues, and Changes
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

    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:dyncon:v:146:y:2023:i:c:s0165188922002871. 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/jedc .

    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.