On Convergence in the Spatial AK Growth Models

TL;DR

This paper broadens the understanding of convergence in spatial AK growth models by removing restrictive assumptions, allowing for time-varying technology, and providing explicit solutions for capital distribution dynamics.

Contribution

It demonstrates that convergence results hold under more general conditions and introduces explicit solutions for the evolution of spatial capital distribution.

Findings

Convergence does not depend on specific social planner assumptions.

Results hold with time-varying technology parameters.

Provides explicit solutions for spatial capital dynamics.

Abstract

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.