We introduce knowledge spillovers as an externality in the production function of competitive firms operating in a finite spatial domain under adjustment costs. Spillovers are spatial as productive knowledge flows more easily among firms located nearby. When knowledge spillovers are not...

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...