Boundary and interior spikes in economic agglomeration of a spatial Solow model with capital-induced labor migration

Abstract

Economic geography seeks to explore uneven spatial development commonly known as economic agglomeration, where economic activities concentrate in specific regions. While a variety of factors have been studied to explain the emergence of core–periphery economic patterns, labor mobility emerges as a fundamental and indispensable driver of such heterogeneity within the spatial economic framework. The spatial Solow model under consideration incorporates both wealth diffusion and labor migration to analyze the spatio-temporal economic growth. Labor migration is influenced by a combination of an unbiased random walk without economic incentives and a biased movement toward regions with better economic opportunities due to uneven capital distribution. In the regime of a large capital-induced labor migration rate, we first prove the existence of a steady state with a single boundary spike, and then prove its linearized stability using its asymptotic profile; moreover, this spike can be reflected and periodically extended to construct more stationary configurations with aggregates featuring interior spike and/or double-boundary spike. Further theoretical analysis shows that the single interior spike is inherently unstable and the double boundary spike is linearly stable. These results suggest that intense capital-induced labor migration can drive and stabilize economic agglomerations, concentrating wealth and labor in specific areas. Numerical simulations support these findings, revealing additional spatio-temporal dynamics such as phase transitions and spike insertion, and showcase the framework’s ability to capture complex economic behaviors.