A Constructive Characterization of Optimal Bundling

This paper studies a monopolist selling multiple goods to a consumer with one-dimensional private types.

I provide a sufficient condition--single-crossing differences of virtual values together with monotonic differences of valuations--under which the monopolist's problem is equivalent to finding the upper envelope of the marginal revenue curves.

This approach guarantees that the optimal mechanism is deterministic and can be implemented via a menu of bundles.

I further characterize this upper envelope using a dominance notion.

This characterization yields a constructive algorithm that computes the unique optimal menu by iteratively eliminating dominated bundles.

As my main application, I use this framework to introduce and provide sufficient conditions for the optimality of tree bundling, a common but previously unmodeled sales strategy where the optimal menu contains a "root" bundle but features distinct upgrade paths.

This structure captures prevalent sales practices across industries, from automobile manufacturers offering base models with customizable upgrade packages to software companies allowing modular feature additions.