Stochastic congestion pricing and urban spatial structure in a monocentric city: A risk-adjusted equilibrium model

Urban congestion is characterized by a dynamic and stochastic environment, particularly evident in the daily traffic flow on road networks during peak hours. The introduction of stochastic elements can significantly influence the determination of the urban spatial structure and associated land price gradients. This study proposes a novel methodology for a circular monocentric city setting, in which the impact of uncertainty in money and time congestion pricing on households’ residential location decisions is analyzed. The analytical results demonstrate that, given a concave utility function, monetary uncertainty steepens the decline, and time-cost uncertainty tends to flatten it. Both mechanisms can increase the optimal city size within model parameters. This is attributed to the need to reduce land prices to offset fluctuations in commuting costs, which may yield welfare gains. Higher uncertainty leads to an expansion of city size (for a larger population) and an increase in total land rent income compared to the deterministic scenario. Regarding policy implications, the model suggests that policymakers should develop pricing models that better characterize potential random traffic congestion to assess its possible impact on the urban model. Based on the analytical findings, we conduct numerical simulations and sensitivity analysis to validate the proposed stochastic congestion-pricing model for urban spatial structures.