We prove strict concavity of the value function for liquidity constrained dynamic accumulation models without adopting at least one of the following restrictive assumptions: zero response of productive effort, bounded marginal value of accumulated balances, or strictly convex cost of holding accumulated balances. Thus we extend well known theoretical results to more general models of saving with liquidity constraints and of commodity storage with non-negativity constraints on stocks. Our results provide a foundation for estimation of a homogeneous markovian process for consumption in models of saving, or for price in commodity storage models, under more realistic assumptions.