Multidimensional Screening with Complementary Activities: Regulating a Monopolist with Unknown Cost and Unknown Preference for Empire Building

We study the optimal regulation of a monopolist when intrinsic efficiency (intrinsic cost) and empire building tendency (marginal utility of output) are private information, but actual cost (the difference between intrinsic cost and effort level) is observable. This is a problem of multidimensional screening with complementary activities. Results are not only driven by the prior probabilities of the four possible types, but also by the relative magnitude of the uncertainty along the two dimensions of private information. If the marginal utility of output varies much more (less) across managers than the intrinsic marginal cost, there is empire building (efficiency) dominance. In that case, an inefficient empire builder produces more (less) and at lower (higher) marginal cost than an efficient money-seeker. It is only when variabilities are similar that there may be the natural ranking of activities (empire builders produce more, while efficient managers produce at a lower cost).