Envelopes for economists: an intellectual history

All economists know that a long-run average cost curve is the envelope of a family of short-run average cost curves, but many economists do not realise that envelope mathematics can be applied to many other topics. This paper reviews envelope mathematics and describes its intellectual history on several topics, including housing hedonics. The envelope derivations in this paper shed light on the key distinction in many envelopes between movement along a function in the family and equilibrium shifting from one family member to the next and ensure that the functional forms of the family of curves and their envelope are consistent with each other.