Optimal multiproduct nonlinear pricing with correlated consumer types

We examine the design of nonlinear prices by a multiproduct monopolist who serves customers with multidimensional but correlated types. We show that the monopoly can exploit the correlations between consumers' types to design pricing mechanisms that fully extract the surplus from each consumer. Our main insight is that regardless of the dimensionality of the consumers types and the number of goods that the monopoly produces, the surplus that each consumer gets from buying is a scalar. Hence, it is possible to design a two step mechanism where in the first step the monopoly induces the consumers to make efficient purchasing decisions (given their private information), and in the second step the monopoly extracts the surplus from each consumer via a (random) fixed fee.