On the concavity of consumption function with the time-varying discount rate - Liutang Gong; Ruquan Zhong; Heng-fu Zou (Economics Letters, 2012)
In this paper, we consider a finite-horizon model with the time-additive utility and the time varying discount rate. With the assumption of the concavity of absolute risk tolerance, the concavity of the consumption function has been proved. This result significantly broadens the conclusion of Carroll and Kimball (1996) for the case of the HARA utility function.