A new class of problems in the calculus of variations

Ivar Ekeland (1) , Yiming Long (2) , Qinglong Zhou (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 NKU - Nankai University
3 ECJU - East China Jiaotong University

We revisit the neo-classical model of optimal growth by introducing an additional term, due to Chichilnisky, which embodies society's concern for the long-term welfare of future generations. We show that the additional term causes time inconsistency, so there is no such thing as an optimal solution. However, we introduce a notion of equilibrium solution and we prove that there is a continuum of such solutions

Mots clés: Optimal growth model; time inconsistency; intergenerational justice

Domaines: Mathématiques générales [math.GM]

Ivar Ekeland, Yiming Long, Qinglong Zhou. A new class of problems in the calculus of variations. Regular and Chaotic Dynamics, 2013, 18 (6), pp.553-584. ⟨10.1134/S1560354713060014⟩. ⟨hal-01521463⟩