The spatial evolution of economic activities and the emergence of cities

• 成果类型: Article
• 署名作者: Fiaschi, Davide; Ricci, Cristiano
• 署名单位: University of Pisa
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2025.105971
• 发表日期: 2025
• 关键词: Spatial general equilibrium; Spatial agglomeration; Spatial spillovers; Aggregation-diffusion equations; metastability; Complex landscapes

摘要

This paper examines the spatial agglomeration of workers and income in a continuous spacetime framework. Local markets feature spatial spillovers and both exogenous and endogenous amenities. Workers relocate to maximise their instantaneous utility, constrained by mobility costs. In the limit of infinite workers, short-run equilibria are described by a partial differential equation (PDE). The PDE reveals spatial dynamics influenced by initial conditions, path dependence, and metastability (persistence), where prolonged stability is disrupted by sharp transitions to new distributions. We characterise conditions for spatial agglomeration in stationary equilibria and demonstrate that social utility consistently increases over time, suggesting efficient spatial allocations. Numerical results replicate key patterns, such as city formation, dependence on historical spatial patterns, and nonlinear out-of-equilibrium dynamics.