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  • Raouf Boucekkine (a1), Carmen Camacho (a2) and Benteng Zou (a3)

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.

Corresponding author
Address Correspondence to Carmen Camacho, Department of Economics, Catholic University of Louvain, Place Montesquieu, 3, B-1348 Louvain-la-Neuve, Belgium. e-mail:
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C. Bandle , M.A. Pozio , and A. Tesei (1987) The asymptotic behavior of the solutions of degenerate parabolic equations. Transactions of the American Mathematical Society 303, 2, 487501.

M. Beckman (1952) A continuous model of transportation. Econometrica 20, 643660.

R. Gaines (1976) Existence of solutions to Hamiltonian dynamical systems of optimal growth. Journal of Economic Theory 12, 114130.

P. Krugman (1991) Increasing returns and economic geography. Journal of Political Economy 99, 483499.

P. Krugman (1993) On the number and location of cities. European Economic Review 37, 293298.

P. Mossay (2003) Increasing returns and heterogeneity in a spatial economy. Regional Science and Urban Economics 33, 419444.

C.V. Pao (1992) Nonlinear Parabolic and Elliptic Equations. New York: Plenum Press.

T. Puu (1982) Outline of a trade cycle model in continuous space and time. Geographical Analysis 14, 19.

J.P. Raymond and H. Zidani (1998) Pontryagin's principle for state-constrained control problems governed by parabolic equations with unbounded controls. SIAM Journal of Control and Optimization, 36 (6), 18531879.

T. Ten Raa (1986) The initial value problem for the trade cycle in euclidean space. Regional Science and Urban Economics, 16 (4), 527546.

G.C. Wen and B. Zou (2000) Initial-irregular oblique derivative problems for nonlinear parabolic complex equations of second order with measurable coefficients. Nonlinear Analysis TMA, 39, 937953.

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Macroeconomic Dynamics
  • ISSN: 1365-1005
  • EISSN: 1469-8056
  • URL: /core/journals/macroeconomic-dynamics
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