The Converse Envelope Theorem

Ludvig Sinander

Econometrica, 2022, vol. 90, issue 6, 2795-2819

Abstract: I prove an envelope theorem with a converse: the envelope formula is equivalent to 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.

Date: 2022
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