User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

Bridging the gap between growth theory and the new economic geography: the spatial ramsey model

Primary tabs

Boucekkine, Raouf [UCL] Camacho Pérez, Maria del Carmen [UCL]

We study a Ramsey problem in infinite and continuous time and space. The problem is discounted both temporally and spatially. Capital flows to locations with higher marginal return. We show that the problem amounts to optimal control of parabolic partial differential equations (PDEs). We rely on the existing related mathematical literature to derive the Pontryagin conditions. Using explicit representations of the solutions to the PDEs, we first show that the resulting dynamic system gives rise to an ill-posed problem in the sense of Hadamard. We then turn to the spatial Ramsey problem with linear utility. The obtained properties are significantly different from those of the nonspatial linear Ramsey model due to the spatial dynamics induced by capital mobility.

Document type Article de périodique (Journal article)
Access type Accès restreint
Publication date 2009
Language Anglais
Journal information "Macroeconomic Dynamics" - Vol. 13, no. 1, p. 20-45 (Février 2009)
Peer reviewed yes
Publisher Cambridge University Press (Cambridge, United Kingdom)
issn 1365-1005
e-issn 1469-8056
Publication status Publié
Affiliations UCL - EUEN/CORE - Center for operations research and econometrics
UCL - ESPO/ECON - Département des sciences économiques
Keywords Ramsey Model ; Economic Geography ; Parabolic Equations ; Optimal Control
Links
  1. Bandle Catherine, Pozio M. A., Tesei Alberto, The Asymptotic Behavior of the Solutions of Degenerate Parabolic Equations, 10.2307/2000679
  2. Beckmann Martin, A Continuous Model of Transportation, 10.2307/1907646
  3. Fujita, The Spatial Economy. Cities, Regions and International Trade. (1999)
  4. Fujita Masahisa, Thisse Jacques-Francois, Economics of Agglomeration : Cities, Industrial Location, and Regional Growth, ISBN:9780511805660, 10.1017/cbo9780511805660
  5. Gaines R.E, Existence of solutions to Hamiltonian dynamical systems of optimal growth, 10.1016/0022-0531(76)90029-6
  6. Hadamard, Lectures on the Cauchy Problem in Linear Partial Differential Equations. (1923)
  7. Isard, Spatial Dynamics and Optimal Space-Time Development. (1979)
  8. Krugman Paul, Increasing Returns and Economic Geography, 10.1086/261763
  9. Krugman Paul, On the number and location of cities, 10.1016/0014-2921(93)90017-5
  10. Krugman, The Self-Organizing Economy, Appendix: A Central Place Model. (1996)
  11. Mossay Pascal, Increasing returns and heterogeneity in a spatial economy, 10.1016/s0166-0462(02)00041-8
  12. Pao, Nonlinear Parabolic and Elliptic Equations. (1992)
  13. Puu Tonu, Outline of a Trade Cycle Model in Continuous Space and Time, 10.1111/j.1538-4632.1982.tb00050.x
  14. Raymond J. P., Zidani H., Pontryagin's Principle for State-Constrained Control Problems Governed by Parabolic Equations with Unbounded Controls, 10.1137/s0363012996302470
  15. Raymond, Differential and Integral Equations, 13, 1039 (2000)
  16. Ten Raa Thijs, The initial value problem for the trade cycle in euclidian space, 10.1016/0166-0462(86)90022-0
  17. Wen Guochun, Zou Benteng, Initial-irregular oblique derivative problems for nonlinear parabolic complex equations of second order with measurable coefficients, 10.1016/s0362-546x(98)00258-2
  18. Wen, Initial-Boundary Value Problems for Nonlinear Parabolic Equations in Higher Dimensional Domains. (2002)
Bibliographic reference Boucekkine, Raouf ; Camacho Pérez, Maria del Carmen. Bridging the gap between growth theory and the new economic geography: the spatial ramsey model . In: Macroeconomic Dynamics, Vol. 13, no. 1, p. 20-45 (Février 2009)
Permanent URL http://hdl.handle.net/2078.1/23218