An optimal control problem with state constraints in a spatio-temporal economic growth model on networks

Alessandro Calvia, Fausto Gozzi, Marta Leocata, Georgios I. Papayiannis, Anastasios Xepapadeas and Athanasios N. Yannacopoulos

Journal of Mathematical Economics, 2024, vol. 113, issue C

Abstract: We introduce a spatial economic growth model where space is described as a network of interconnected geographic locations and we study a corresponding finite-dimensional optimal control problem on a graph with state constraints. Economic growth models on networks are motivated by the nature of spatial economic data, which naturally possess a graph-like structure: this fact makes these models well-suited for numerical implementation and calibration. The network setting is different from the one adopted in the related literature, where space is modeled as a subset of a Euclidean space, which gives rise to infinite dimensional optimal control problems. After introducing the model and the related control problem, we prove existence and uniqueness of an optimal control and a regularity result for the value function, which sets up the basis for a deeper study of the optimal strategies. Then, we focus on specific cases where it is possible to find, under suitable assumptions, an explicit solution of the control problem. Finally, we discuss the cases of networks of two and three geographic locations.

Keywords: Optimal control problems; Value function; Graphs and networks; Viscosity and regular solutions of HJB equations; Spatial economic growth models; AK production function (search for similar items in EconPapers)
Date: 2024
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Working Paper: An optimal control problem with state constraints in a spatio-temporal economic growth model on networks (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:113:y:2024:i:c:s0304406824000533

DOI: 10.1016/j.jmateco.2024.102991

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