We generalize the usual screening approach and conditions for efficiency-at-the-top and acyclic property from linear to fixed-plus-separable or concave costs and multidimensional commodities. But under non-concave costs, like capacity constraints, an example shows a cycle in the solution graph....

In screening with non-concave costs: (i) cycles of active IC constraints can make all packages distorted; (ii) standard screening can be less profitable than price discrimination within a consumer type using first-come-first-served rationing.

Using linear demands for two types of consumers, this note shows why discounts are ubiquitous and premia are rare. By observing premia, one can infer that the package sold at premium is undistorted and the single-crossing condition must hold.