In many industries the tariffs are not strictly proportional to the quantity purchased i. e
they are nonlinear. Examples of nonlinear tariffs include railroad and electricity schedules
and rental rates for durable goods and space. The major justification for the nonlinear pricing
is the existence of private information on the side of consumers. In the early papers on the
subject private information was captured either by assuming a finite number of types (e. g.
Adams and Yellen 1976) or by a unidimensional continuum of types (Mussa and Rosen 1978).
Economics of the unidimen sional problems is by now well understood. The unidimensional models
however do not cover all the situations of practical interest. Indeed often the nonlinear
tariffs specify the payment as a function of a variety of characteristics. For example
railroad tariffs spec ify charges based on weight volume and distance of each shipment. Dif
ferent customers may value each of these characteristics differently hence the customer's type
will not in general be captured by a unidimensional characteristic and a problem of
multidimensional screening arises. In such models the consumer's private information (her type)
is captured by an m-dimensional vector while the good produced by the monopolist has n quality
dimensions.
