The Dynamics of Growth and Distribution in a Spatially Heterogeneous World

This paper tries to reconcile growth and geographical economics by dealing directly with capital accumulation through time and space and by seeing growth convergence and spatial agglomeration as jointly generated by dynamic processes displaying pattern formation. It presents a centralized economy in which a Bergson-Samuelson- Millian central planner finds a flow of optimal distributions of consumption, subject to a spatial-temporal capital accumulation budget constraint. The main conclusions are: first, if the behavioral parameters are symmetric, but there is an asymmetric distribution of the capital stock, then the long run asymptotic distribution will be spatially homogeneous; second, if there is homogeneous distribution of the capital stock, but there is an asymmetric shock in any parameter, then the economy will converge towards a spatially heterogeneous asymptotic state; third, spatially heterogeneous asymptotic states will only emerge exogenously, not endogenously; fourth, the spatial propagation mechanism can give birth, when the production function is close to linear, to a Turing instability, which implies that for some parameter values, a conditionally stable spacetime distribution should display spatial pattern formation.