The classical Pfaff-Darboux Theorem, which provides local ‘normal forms’ for 1-forms on manifolds, has applications in the theory of certain economic models [3]. However, the normal forms needed in these models come with an additional requirement of convexity, which is not provided by the classical proofs of the Pfaff-Darboux Theorem. (The appropriate notion of ‘convexity’ is a feature of the e...