  A screening instrument is costly if it is socially wasteful and productive
otherwise. A principal screens an agent with multidimensional private
information and quasilinear preferences that are additively separable across
two components: a one-dimensional productive component and a multidimensional
costly component. Can the principal improve upon simple one-dimensional
mechanisms by also using the costly instruments? We show that if the agent has
preferences between the two components that are positively correlated in a
suitably defined sense, then simply screening the productive component is
optimal. The result holds for general type and allocation spaces, and allows
for nonlinear and interdependent valuations. We discuss applications to
multiproduct pricing (including bundling, quality discrimination, and upgrade
pricing), intertemporal price discrimination, and labor market screening.
