A Tale of Two Monopolies

We apply marginal analysis \`a la Bulow and Roberts (1989) to characterize revenue-maximizing selling mechanisms for a multiproduct monopoly. We derive marginal revenue from price perturbations over arbitrary sets of bundles and show that optimal mechanisms admit no revenue-increasing perturbation for bundles with positive demand, nor revenue-decreasing perturbations for zero-demand bundles. For any symmetric two-dimensional type distribution under mild regularity, this analysis fully characterizes the optimal mechanism across independence, substitutability, and complementarity. For general type distributions and allocation spaces, our approach identifies bundles that must carry positive demand and provides conditions under which pure bundling or separate selling is suboptimal.