Spatial externality and indeterminacy

Emmanuelle Augeraud-Véron (1) , Arnaud Ducrot (2)

1 GREThA - Groupe de Recherche en Economie Théorique et Appliquée
2 LMAH - Laboratoire de Mathématiques Appliquées du Havre

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.

Mots clés: Characteristic equation; Convolution; Economics; Existence and uniqueness; Existence and uniqueness of solution; Indeterminacy; Long distance interactions; Non-local equations; Spatial externalities; Standard deviation

Domaines: Economies et finances

Emmanuelle Augeraud-Véron, Arnaud Ducrot. Spatial externality and indeterminacy. Mathematical Modelling of Natural Phenomena, In press, 14 (1), 31 p. ⟨10.1051/mmnp/2019003⟩. ⟨hal-02306568⟩