We solve a class of two-dimensional screening problems in which one
dimension has the standard features, while the other dimension is impossible to exaggerate and enters the agent's utility only through the message
but not the true type. Natural applications are procurement and regulation where the producer's ability to produce quality and his costs of
producing quantity are both unknown; or selling to a budget constrained
buyer. We show that under these assumptions, the orthogonal incentive constraints are necessary and sufficient for the full set of incentive
constraints. Provided that types are affiliated and all the conditional distributions of types have monotonic inverse hazard rates, the solution is
fully separating in both dimensions
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