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Pré-Publication, Document De Travail (Working Paper) Année : 2023

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

Résumé

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.
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Dates et versions

halshs-03920386 , version 1 (03-01-2023)

Identifiants

  • HAL Id : halshs-03920386 , version 1

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Stefano Bosi, Carmen Camacho, Thai Ha-Huy. On the uniqueness of the optimal path in a discrete-time model à la Lucas (1988). 2023. ⟨halshs-03920386⟩
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