Optimal selling mechanisms for multiproduct monopolists: incentive compatibility in the presence of budget constraints

We analyze the nonlinear pricing problem faced by an incomplete information monopolist operating in a market populated by agents with budget constraints. We show that if other goods are available and if the monopolist's goods are nonessential relative to other goods, then there exists an optimal, individually rational, and incentive compatible selling mechanism for the monopolist (Theorem 1). Moreover, we show that a solution to all such nonlinear pricing problems exists if and only if the monopolist's goods are nonessential (Theorem 2). In the absence of nonessentiality, we show that if the monopolist's profit function is independent of quantity (e.g., if all costs are fixed), then an optimal selling mechanism exists (Theorem 3). Finally, we show that if there is reporting (of types by agents) and partial recognition of types (by the monopolist), then an optimal selling mechanism exists, even in the absence of nonessentiality, provided agents' utility functions are affine and continuous in goods (Theorem 4).