Endogenous Growth, Spatial Dynamics and Convergence: A Refinement

Raouf Boucekkine (), Carmen Camacho and Weihua Ruan
Additional contact information
Carmen Camacho: Paris School of Economics and CNRS, France.
Weihua Ruan: Department of mathematics, Purdue University Northwest, USA

No 2533, AMSE Working Papers from Aix-Marseille School of Economics, France

Abstract: The dynamics of capital distribution across space are an important topic in economic geography and, more recently, in growth theory. In particular, the spatial AK model has been intensively studied in the latter stream. It turns out that the positivity of optimal capital stocks over time and space for any initial capital spatial distribution has not been entirely settled even in the simple linear AK case. We use Ekeland’s variational principle together with Pontryagin’s maximum principle to solve an optimal spatiotemporal AK model with a state constraint (non-negative capital stock), where the capital law of motion follows a diffusion equation. We derive the necessary optimality conditions to ensure the solution satisfies the state constraints for all times and locations. The maximum principle enables the reduction of the infinite-horizon optimal control problem to a finite-horizon problem, ultimately proving the uniqueness of the optimal solution with positive capital and the non-existence of such a solution when the time discount rate is either too large or too small.

Keywords: Diffusion and growth; Convergence; optimal control; State constraint; Ekeland’s variational principle (search for similar items in EconPapers)
JEL-codes: C61 O44 Q15 Q56 R11 (search for similar items in EconPapers)
Pages: 23 pages
Date: 2025-12
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.amse-aixmarseille.fr/sites/default/fil ... rs/wp_2025_nr_33.pdf (application/pdf)

Related works:
Journal Article: Endogenous Growth, Spatial Dynamics and Convergence: A Refinement (2025)
Working Paper: Endogenous growth, spatial dynamics and convergence: A refinement (2025)
Working Paper: Endogenous growth, spatial dynamics and convergence: A refinement (2025)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:aim:wpaimx:2533

Access Statistics for this paper

More papers in AMSE Working Papers from Aix-Marseille School of Economics, France AMU-AMSE - 5-9 Boulevard Maurice Bourdet, CS 50498 - 13205 Marseille Cedex 1. Contact information at EDIRC.
Bibliographic data for series maintained by Gregory Cornu ().