Geographical poverty core formation in a spatial Solow growth model

Abstract

This paper develops the concept of poverty core, a novel framework that extends the traditional notion of poverty traps by incorporating the dynamics of irreversibility and complete capital depletion. While poverty traps describe self-reinforcing cycles of deprivation that hinder economic mobility, a poverty core emerges when an already vulnerable system experiences a random exogenous shock—such as a natural disaster, armed conflict, financial collapse, or health crisis—that destroys natural, physical, and human capital beyond the threshold required for recovery. Unlike poverty traps, which may be escaped through gradual investment or policy intervention, a poverty core represents an absorbing state of destitution where normal economic mechanisms are no longer sufficient to restore livelihoods. To formally model the transition from poverty traps to poverty cores, we extend the Solow growth framework by incorporating divergence operators and introducing a nonlinear depreciation function that accounts for capital depletion under extreme shocks. This modification captures how spatial and structural economic vulnerabilities amplify depreciation rates beyond sustainable levels, leading to economic divergence instead of convergence. The model demonstrates that under specific conditions—where capital loss surpasses a critical threshold—economic collapse becomes irreversible, mathematically distinguishing poverty cores from conventional poverty traps. Our findings contribute to the literature on economic fragility, disaster-induced poverty, and sustainability by providing a new theoretical and mathematical framework to identify cases where poverty becomes irreversible. Recognizing poverty cores as distinct from traditional traps is essential for designing effective interventions in post-shock environments, ensuring that affected communities are not left in perpetual economic collapse. • ‘Poverty Core’: A novel economic framework differentiating poverty cores from traditional poverty traps. • Capital depletion in finite time. • Irreversible poverty and economic collapse.