AUGERAUD VERON, Emmanuelle; DUCROT, ARNAUD

doi:10.1051/mmnp/2019003

Groupe de Recherche en Economie Théorique et Appliquée [GREThA]

DUCROT, ARNAUD

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Article de revue

Ce document a été publié dans

Mathematical Modelling of Natural Phenomena. 2019, vol. 14, n° 1, p. 31 p.

Résumé en anglais

We study conditions for existence and uniqueness of solutions in some space-structured economic models with long-distance interactions between locations. The solution of these models satisfies non local equations, in which the interactions are modeled by convolution terms. Using properties of the spectrum location obtained by studying the characteristic equation, we derive conditions for the existence and uniqueness of the solution. This enables us to characterize the degree of indeterminacy of the system being considered. We apply our methodology to a theoretical one-sector growth model with increasing returns, which takes into account technological interdependencies among countries that are modeled by spatial externalities. When symmetric interaction kernels are considered, we prove that conditions for which indeterminacy occurs are the same as the ones needed when no interactions are taken into account. For Gaussian kernels, we study the impact of the standard deviation parameter on the degree of indeterminacy. We prove that when some asymmetric kernels are considered, indeterminacy can occur with classical assumptions on supply and demand curves. © The authors. Published by EDP Sciences, 2019.< Réduire

Mots clés en anglais

Characteristic equation

Convolution

Economics

Existence and uniqueness

Existence and uniqueness of solution

Indeterminacy

Long distance interactions

Non-local equations

Spatial externalities

Standard deviation

URI

https://oskar-bordeaux.fr/handle/20.500.12278/30

DOI

http://dx.doi.org/10.1051/mmnp/2019003

Unités de recherche

Groupe de Recherche en Economie Théorique et Appliquée (GREThA) - UMR 5113

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Spatial externality and indeterminacy

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Résumé en anglais

Mots clés en anglais

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DOI

Unités de recherche