Spatial growth theory: Optimality and spatial heterogeneity

Spatiotemporal dynamics are introduced in a standard Ramsey model of optimal growth in which capital moves toward locations where the marginal productivity of capital is rel- atively higher and initiate a study of the effects of nonlinear capital transport in terms of a linearized analysis around steady state solution solutions. The potential spatial heterogeneity of optimal growth, as seen from the point of view of an optimizing social planner, is examined. Our results suggest that for a high utility discount rate, the spatial capital flows induce the emergence of optimal spatial patterns, while for a low utility discount, a flat earth steady state is socially optimal. Furthermore, when spa- tial heterogeneities exist due to total factor productivity differences across locations, we identify conditions under which the spatial capital flows could intensify or weaken spatial inequalities.