Optimal Selling Mechanisms for Multiproduct Monopolists: Incentive Compatibility in the Presence of Budget Constraints.

We demonstrate the existence of an optimal, individually rational, and incentive compatible selling mechanism for a multiproduct monopolist facing a market populated by consumers with budget constraints. Our main contribution is to show via examples and our existence result that, in general, when facing consumers with budget constraints the monopolist is able to maximize profits over the set of individually rational and incentive compatible selling mechanisms only if other goods are available and only if the monopolist's goods are nonessential relative to other goods.