TITLE:
Kinetic Model of City Size Distribution Including a Value Function
AUTHORS:
Xue Xia, Liangli Chen
KEYWORDS:
City-Size Distribution, Value Function, Boltzmann-Type Equation, Fokker-Planck Equation, Utility Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.4,
April
10,
2026
ABSTRACT: This study adopts a kinetic model incorporating a value function to explore the evolution of the city size distribution. Specifically, the value function consistent with prospect theory is utilized to characterize the internal population changes of cities. Based on the interaction rules of population dynamics, we establish the Boltzmann equation and its corresponding Fokker-Planck equation; thereafter, we theoretically analyze population movements by solving these equations. Assuming that the urban population consists of working and non-working people, we employ a utility function to describe cities’ preferences for these two population groups. Numerical analysis is performed, and some key parameters are estimated using real-world data to verify the rationality of the proposed model.