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 relatively higher. We extend Pontryagin s maximum principle to account for transition dynamics governed by a nonlinear partial di⁄erential equation emerging from spatial capital ows. 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 ows induce the emergence of optimal spatial patterns, while for a low utility discount, a at earth steady state is socially optimal. Furthermore, when spatial heterogeneities exist due to total factor productivity di⁄erences across locations, we identify conditions under which the spatial capital ows could intensify or weaken spatial inequalities