Growth and agglomeration in the heterogeneous space: A generalized AK approach

Raouf Boucekkine (1) , Giorgio Fabbri (2) , Salvatore Federico (3) , Fausto Gozzi (4)

1 GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille
2 GAEL - Laboratoire d'Economie Appliquée de Grenoble
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 Dipartimento di Scienze Economiche e Aziendali

We provide an optimal growth spatio-temporal setting with capital accumulation and diffusion across space in order to study the link between economic growth triggered by capital spatio-temporal dynamics and agglomeration across space. The technology is AK, K being broad capital. The social welfare function is Benthamite. In sharp contrast to the related literature, which considers homogeneous space, we derive optimal location outcomes for any given space distributions for technology and population. Both the transitional spatio-temporal dynamics and the asymptotic spatial distributions are computed in closed form. Concerning the latter, we find, among other results, that: (i) due to inequality aversion, the consumption per capital distribution is much flatter than the distribution of capital per capita; (ii) endogenous spillovers inherent in capital spatio-temporal dynamics occur as capital distribution is much less concentrated than the (pre-specified) technological distribution ; (iii) the distance to the center (or to the core) is an essential determinant of the shapes of the asymptotic distributions, that is relative location matters.

Mots clés: Growth; agglomeration; heterogeneous and continuous space; capital mobility; infinite dimensional optimal control problems Journal of Economic Literature

Domaines: Economies et finances

Raouf Boucekkine, Giorgio Fabbri, Salvatore Federico, Fausto Gozzi. Growth and agglomeration in the heterogeneous space: A generalized AK approach. 2018. ⟨hal-01713905⟩