The Envelope Theorem in its Proper Perspective.

The Envelope Theorem is showm to involve comparisons between the performance of the optimal policy and that of alternative policies, which satisfy the constraints of the problem and may also have other features. The theorem is activated whenever parameter values are such that the extreme value function is reached by the value functions of such policies; it produces tangency and curvature results for variations in any parameter entering the objective ot the constraint fucntions of the problem. The proposed perspective frees the theorem from all problems besetting its presentation in the literature; more importantly, it offers possibilities for extending its scope well beyond its usual setting.