Endogenous Growth, Spatial Dynamics and Convergence: A Refinement

Raouf Boucekkine (), Carmen Camacho () and Weihua Ruan ()
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Carmen Camacho: PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - ENPC - École nationale des ponts et chaussées - IP Paris - Institut Polytechnique de Paris
Weihua Ruan: Purdue University Northwest

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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)
Date: 2025-09
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Published in Annals of Economics and Statistics, 2025, 159, pp.79-105. ⟨10.2307/48839155⟩

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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)
Working Paper: Endogenous growth, spatial dynamics and convergence: A refinement (2025)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:halshs-05666834

DOI: 10.2307/48839155

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