Spatial externality and indeterminacy

Abstract

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.

Distributed optimal control models in environmental economics: a review

“…Last but not least, Fabbri [43] has specifically studied the impact of the shape of the domain on the optimal solution in this class of spatial growth models. In this issue, Augeraud-Véron and Ducrot [14] assess the impact of inter-regional disparities when the engine of growth is a learning by doing externality, modeled through non-local interactions. It is in particular shown that, depending on the type of interaction considered, local indeterminacy may occur.…”