The Converse Envelope Theorem
Econometrica · 2022 · Volume 90 · Issue 6
Abstract
I prove an envelope theorem with a converse: the envelope formula isequivalentto a first-order condition. Like Milgrom and Segal's (2002) envelope theorem, my result requires no structure on the choice set. I use the converse envelope theorem to extend to general outcomes and preferences the canonical result in mechanism design that any increasing allocation is implementable, and apply this to selling information.
Keywords
Envelope theorem, first-order condition, mechanism design
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