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This note analyzes a model of a monopolist selling multiple goods to a continuum of heterogeneous consumers. The implementation of Direct Revelation Mechanisms is analyzed in that setting, finding that it is possible for the monopolist to implement all Stochastic Incentive Compatible Mechanisms by committing to post a decreasing sequence of prices. The posted prices depend on time and have the desirable property of being step functions. When the optimal mechanisms are stochastic, it is optimal for the monopolist to price discriminate over time, contrary to the conventional wisdom that a single-good monopolist committed to an ex-ante price strategy will not price discriminate.

A Note on the Multidimensional Monopolist Problem and Intertemporal Price Discrimination