Long-run economic growth in the delay spatial Solow model

ABSTRACT

This paper analyses the long-term dynamics of the Solow model with spatial dependence of the physical capital, time delay and pollution effect due to capital accumulation. Previous studies not including spatial dependence showed that the dynamics can be cyclic or chaotic, in which cases the description of the long-run system’s behaviour becomes difficult or unfeasible. We provide sufficient conditions for the existence of a delay-independent global attractor and an easy way to estimate it. We also introduce new and extend known results for the existence of a global attractor in the absence of spatial dependence. Additionally, we complement known global stability results for a family of difference equations with applications in different fields.

KEYWORDS:

• Solow’s growth model
• spatial dependence
• global stability
• delay reaction–diffusion equations

JEL:

• C02
• C32
• E13
• O41

ACKNOWLEDGEMENTS

We thank the anonymous reviewers for their suggestions, which helped to improve the paper.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Escuela Técnica Superior de Ingenieros Industriales (UNED) [grant number 2022-ETSII-UNED-16]; and the Agencia Estatal de Investigación, Spain, and European Regional Development Fund, UE [grant numbers MTM2017-85054-C2-2-P and PID2021-122442NB-I00].