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BRIDGING THE GAP BETWEEN GROWTH THEORY AND THE NEW ECONOMIC GEOGRAPHY: THE SPATIAL RAMSEY MODEL

Published online by Cambridge University Press:  01 February 2009

Raouf Boucekkine ,
Carmen Camacho  and
Benteng Zou
Raouf Boucekkine
Affiliation:
Catholic University of Louvain and University of Glasgow
Carmen Camacho*
Affiliation:
Catholic University of Louvain
Benteng Zou
Affiliation:
University of Luxembourg
*
Address Correspondence to Carmen Camacho, Department of Economics, Catholic University of Louvain, Place Montesquieu, 3, B-1348 Louvain-la-Neuve, Belgium. e-mail: carmen.camacho@uclouvain.be.
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Abstract

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.

Keywords

Ramsey ModelEconomic GeographyParabolic EquationsOptimal Control
Type
Articles
Information
Macroeconomic Dynamics , Volume 13 , Issue 1 , February 2009 , pp. 20 - 45
Copyright
Copyright © Cambridge University Press 2009

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