The Dynamics of Growth and Distribution in a Spatially Heterogeneous World
Paulo Brito ()
No 2004/14, Working Papers Department of Economics from ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa
This paper tries to reconcile growth and geographical economics by dealing directly with capital accumulation through time and space and by seeing growth convergence and spatial agglomeration as jointly generated by dynamic processes displaying pattern formation. It presents a centralized economy in which a Bergson-Samuelson- Millian central planner finds a flow of optimal distributions of consumption, subject to a spatial-temporal capital accumulation budget constraint. The main conclusions are: first, if the behavioral parameters are symmetric, but there is an asymmetric distribution of the capital stock, then the long run asymptotic distribution will be spatially homogeneous; second, if there is homogeneous distribution of the capital stock, but there is an asymmetric shock in any parameter, then the economy will converge towards a spatially heterogeneous asymptotic state; third, spatially heterogeneous asymptotic states will only emerge exogenously, not endogenously; fourth, the spatial propagation mechanism can give birth, when the production function is close to linear, to a Turing instability, which implies that for some parameter values, a conditionally stable spacetime distribution should display spatial pattern formation.
Keywords: Optimal growth and distribution; Spatial growth; Optimal control of partial differential equations; Traveling waves; Fourier transforms; Turing instability. (search for similar items in EconPapers)
JEL-codes: C6 D9 E1 R1 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-geo and nep-mac
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Journal Article: The dynamics of growth and distribution in a spatially heterogeneous world (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:ise:isegwp:wp142004
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More papers in Working Papers Department of Economics from ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa Department of Economics, ISEG - Lisbon School of Economics and Management, Universidade de Lisboa, Rua do Quelhas 6, 1200-781 LISBON, PORTUGAL.
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