A Tale of Two Monopolies

TL;DR

This paper characterizes revenue-maximizing mechanisms for multiproduct monopolies using marginal analysis, providing a comprehensive framework that covers various demand structures and distribution assumptions.

Contribution

It introduces a novel application of marginal analysis to fully characterize optimal selling mechanisms across different demand and distribution scenarios.

Findings

Optimal mechanisms have no revenue-increasing perturbations for positive-demand bundles.

Pure bundling or separate selling can be suboptimal under certain conditions.

The analysis applies to symmetric two-dimensional type distributions with mild regularity.

Abstract

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.