Non-negativity and capacity constraints on accumulation, and price floors, have particular relevance for water, oil, gas, electricity, and other energy commodities. Such constraints are empirically relevant; even if historical records do not include periods where the capacity constraint is binding or where marginal value is zero, a positive probability that such events might occur affects rational accumulation and consumption decisions. In this paper we provide sufficient conditions for non-convergence and sufficient conditions for convergence of a solution algorithm widely used to solve and characterize dynamic models, which is fast if it converges. Our results are useful for policy evaluation based on structural econometric estimation involving large numbers of solutions.