The dynamics of growth and distribution in a spatially heterogeneous world

Distributional extensions of the benchmark AK endogenous growth model and of the Ramsey model are presented in this paper. The resulting geographic growth model - a forward-backward parabolic partial differential equation (PDE) over a bounded spatial domain - is governed by two main driving forces: a spatial friction in the reallocation of physical capital, and a spatial arbitrage driving the reallocation of savings. The spatial AK model solution, starting from an unequal distribution of capital, displays convergence over time to a spatially homogeneous balanced growth path with positive growth rates. The spatial Ramsey model potentially contains both diffusive and agglomerative spatial forces. If there are no agglomerative forces, the solution displays convergence to a spatially homogenous steady state, but if an agglomerative force exists, there is increasing spatial concentration of capital over time. This shows that convergence in the aggregate can be consistent with different distribution profiles over locations. An additional contribution of the paper is to develop a distributive comparative dynamics analysis for a spatially heterogeneous productivity shock. It is shown that, although there is redistribution of consumption across locations, technological inequality is persistent.