Bridging the gap between growth theory and the new economic geography: the spatial Ramsey model
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 (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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- 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, January.
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- Paulo Brito, 2004. "The Dynamics of Growth and Distribution in a Spatially Heterogeneous World," Working Papers Department of Economics 2004/14, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
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