Hamiltonian approach to multi-dimensional screening

In this paper, I consider a problem of multi-dimensional screening in the case when the number of consumer's characteristics, m, differs from n, the number of goods produced by a monopolist. I show that, in the case when n > m, the qualitative features of solution are similar to those obtained by Rochet and Chone (1998) for the case n = m. When the monopolist has too few instruments (n < m), new qualitative features arise. In particular, there are distortions in the outward direction at the top, discontinuity in the bundle of goods consumed on the lower boundary of participation region, and full separation of types is impossible over any open subset of type space. (C) 2001 Elsevier Science B.V. All rights reserved.