On the uniqueness of the optimal path in a discrete-time model à la Lucas (1988)

Stefano Bosi (), Carmen Camacho () and Thai Ha-Huy
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Stefano Bosi: EPEE - Centre d'Etudes des Politiques Economiques - UEVE - Université d'Évry-Val-d'Essonne - Université Paris-Saclay, Université Paris-Saclay, UEVE - Université d'Évry-Val-d'Essonne
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 - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, 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 - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: In a simple discrete-time version of the Lucas (1988) model, we prove, first, that the Balanced Growth Path (BGP) is optimal and, second, that the optimal solution is unique. After briefly discussing the results obtained in some of the continuous-time versions of the Lucas model, we address the issues of existence and uniqueness of the optimal solution in discrete time. Making use of the supermodularity of the value function, we prove that the optimal solution must be monotonically increasing. This feature does indeed suit the BGP, although nothing can ensure yet its optimality. After providing the exact expression of the BGP, we do prove both its optimality and its uniqueness.

Keywords: Human capital; Balanced growth path (search for similar items in EconPapers)
Date: 2023-01
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03920386v1
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Working Paper: On the uniqueness of the optimal path in a discrete-time model à la Lucas (1988) (2023)
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