Reference : Bridging the gap between growth theory and the new economic geo-graphy : The spatial ...
Scientific journals : Article
Business & economic sciences : Quantitative methods in economics & management
Bridging the gap between growth theory and the new economic geo-graphy : The spatial Ramsey model
Boucckine, Raouf [Catholic University of Louvain ; University of Glasgow]
Camacho, Carmen [CNRS, University Pairs 1, France > Centre d'Economie de la Sorbonne]
Zou, Benteng mailto [University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Center for Research in Economic Analysis (CREA) >]
Macroeconomic Dynamics
Cambridge University Press
Yes (verified by ORBilu)
[en] Ramsey model ; Economic geography ; parabolic equations ; optimal control
[en] We study a Ramsey problem in in¯nite 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 (1923). We then turn to the spatial Ramsey problem with linear utility. The obtained properties are significantly different from those of the non-spatial linear Ramsey model due to
the spatial dynamics induced by capital mobility.

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