On Convergence in the Spatial AK Growth Models

Recent research in economic theory attempts to study optimal economic growth and spatial location of economic activity in a unified framework. So far, the key result of this literature - asymptotic convergence, even in the absence of decreasing returns to capital - relies on specific assumptions about the objective of the social planner. We show that this result does not depend on such restrictive assumptions and obtains for a broader class of objective functions. We also generalize this finding, allowing for the time-varying technology parameter, and provide an explicit solution for the dynamics of spatial distribution of the capital stock.