Tastes and technology: curvature is not sufficient for regularity

In specifications of tastes and technology, econometricians often impose curvature globally, but monotonicity only locally or not at all. In fact monotonicity rarely is even mentioned in that literature. But without satisfaction of both curvature and monotonicity, the second-order conditions for optimizing behavior fail, and duality theory fails. The resulting first-order conditions, demand functions, and supply functions become invalid. Although unconstrained specifications of technology are more likely to produce violations of curvature than monotonicity, I believe that induced violations of monotonicity become common, when curvature alone is imposed. Hence the current common practice of equating regularity with curvature is not justified.