Continuity without the additional distortion–rent condition

Establish whether the continuity theorem for optimal contracts remains valid without an additional primitive condition such as Assumption H, which requires the distortion–rent ratio to be strictly increasing above the relaxed allocation.

Background

The paper studies one-dimensional screening problems in which the Spence–Mirrlees condition fails along a monotone dividing curve. In the no-crossing configuration, the authors prove that any optimal implementable allocation is continuous when the relaxed allocation lies above the dividing curve and the distortion–rent ratio satisfies Assumption H.

This result repairs an incomplete continuity argument in Schottmuller (2015), identified in a subsequent corrigendum. The paper explicitly leaves unresolved whether a condition of the type imposed by Assumption H is genuinely necessary for continuity, or whether the continuity theorem can be proved under the paper’s baseline assumptions alone.