In this note, we reconsider Arrow–Enthoven’s (1961) Sufficiency Theorem 1 onquasi-concave programming [Econometrica, 29(4), p. 783]. One example illustrates thefact that condition (c) of their Theorem 1 should include the twice continuous differen-tiability of the quasi-concave objective function so that the conditions of the theoremare sufficient to identify global optima.