\textit{R. Shephard} [''Indirect production functions'' (1974; Zbl 0278.90036)] and \textit{S. E. Jacobsen} [J. Econ. Stud. 1972, 458-464 (1972)] have shown that the cost function is convex if and only if the production technology of a firm is convex. Convexity of technology is a strong assumption, however, and in fact many problems of firms can be solved using the quasi-convex cost function only. In this note, we introduce a weaker axiom sufficient to make the cost function quasi- convex. Examples of the usefulness of quasi-convexity may be found in the field of dual production theory.