⁴Since the first version of this paper, the connection between constraints and consumption concavity has been explored in more specific settings (see e.g. Park (2006) for CRRA utility, Seater (1997) for the case where time-discounting equals the interest rate, Nishiyama and Kato (2012) for quadratic utility, and Holm (2018) for the case with infinitely-lived households with HARA utility). The main contribution of the current paper is to derive the implications of liquidity constraints on consumption concavity in a life-cycle setting and to derive the implications of additional constraints at specific points in time on consumption concavity.