Optimal agglomerations in dynamic economics

We study rational expectations equilibrium problems and social optimum problems in infinite horizon spatial economies in the context of a Ramsey type capital accumulation problem with geographical spillovers. We identify sufficient local and global conditions for the emergence (or not) of optimal ag...

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Bibliographic Details
Published in:Journal of mathematical economics 2014-08, Vol.53, p.1-15
Main Authors: Brock, William A., Xepapadeas, Anastasios, Yannacopoulos, Athanasios N.
Format: Article
Language:English
Subjects:
Agglomeration
Capital accumulation
Capital formation
Economics
Equilibrium
Externality
Geographic location
Hilbert space
Location of industry
Mathematical problems
Monotone operators
Rational expectations
Rational expectations equilibrium
Social optimum
Spatial distribution
Spatial spillovers
Spillover induced instability
Spillovers
Studies
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Summary:We study rational expectations equilibrium problems and social optimum problems in infinite horizon spatial economies in the context of a Ramsey type capital accumulation problem with geographical spillovers. We identify sufficient local and global conditions for the emergence (or not) of optimal agglomeration, using techniques from monotone operator theory and spectral theory in infinite dimensional Hilbert spaces. We show that agglomerations may emerge, with any type of returns to scale (increasing or decreasing) and with the marginal productivity of private capital increasing or decreasing with respect to the spatial externality. This is a fairly general result indicating the importance of the network structure of the spatial externality relative to the properties of the aggregate production function. Our analytical methods can be used to systematically study optimal potential agglomeration and clustering in dynamic economics.
ISSN:0304-4068
1873-1538
DOI:10.1016/j.jmateco.2014.04.005