A note on the non-convexity problem in some shopping-time and human-capital models

Several works in the shopping-time and in the human-capital literature, due to the non-concavity of the underlying Hamiltonian, use first-order conditions in dynamic optimization to characterize necessity, but not sufficiency, in intertemporal problems. This note selects some works in these two areas and shows that optimality can be characterized, and some results quantitatively improved, by means of an application of Arrow's [Arrow, K. J., 1968. Applications of control theory to economic growth. In: Dantzig, G.B., Veinott Jr., A.F. (Eds.), Mathematics of the Decisions Sciences. American Mathematical Society, Providence, RI] sufficiency theorem.