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

Pre-print, Working paper: 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.

Author(s)

Stefano Bosi, Carmen Camacho, Thai Ha-Huy

Date of publication
  • 2023
Keywords JEL
C61 D50 O40
Keywords
  • Human capital
  • Balanced growth path
Internal reference
  • PSE Working Papers n°2023-03
Pages
  • 9 p.
Version
  • 1