Spatial growth theory: Optimality and spatial heterogeneity

Spatiotemporal dynamics are introduced in a standard Ramsey model of optimal growth which capital moves towards locations where the marginal productivity capita is relatively higher. We extend Pontryagin's maximum principle to account for transition governed by nonlinear partial differential equation emerging spatial flows. The potential heterogeneity as seen from point view an optimizing social planner examined. Our results suggest that high utility discount rate flows induce emergence patterns while hor low flat-earth steady state socially optimal. Furthermore, when heterogeneities exist due total factor differences across locations, we identify conditions under could intensify or weaken inequalities.