A necessary optimality condition in two-dimensional screening

This paper studies adverse selection problems with a one-dimensional principal instrument and a two-dimensional agent type. We provide an optimality condition that characterizes the bunching of continuum types. The approach is based on a reparameterization of the type space in terms of the endogenous optimal allocation level curves. The condition obtained is related with the optimality of two pooling types in the one-dimensional screening without the single-crossing. We illustrate the method by analyzing one example from the literature as well as a new example far from the linear-quadratic case