The Optimality of Upgrade Pricing

TL;DR

This paper identifies conditions under which a multiproduct monopoly can implement optimal pricing through nested upgrade menus, simplifying complex pricing strategies under certain consumer preference assumptions.

Contribution

It provides new sufficient conditions for upgrade pricing optimality using duality methods, including monotone MRS and regularity assumptions, and characterizes optimal menus.

Findings

Upgrade pricing is optimal under monotone MRS conditions.

Two sets of sufficient conditions for upgrade pricing optimality are established.

Upgrade pricing and separate pricing are equivalent when consumer types are monotone.

Abstract

We consider a multiproduct monopoly pricing model. We provide sufficient conditions under which the optimal mechanism can be implemented via upgrade pricing -- a menu of product bundles that are nested in the strong set order. Our approach exploits duality methods to identify conditions on the distribution of consumer types under which (a) each product is purchased by the same set of buyers as under separate monopoly pricing (though the transfers can be different), and (b) these sets are nested. We exhibit two distinct sets of sufficient conditions. The first set of conditions is given by a weak version of monotonicity of types and virtual values, while maintaining a regularity assumption, i.e., that the product-by-product revenue curves are single-peaked. The second set of conditions establishes the optimality of upgrade pricing for type spaces with monotone marginal rates of substitution (MRS) -- the relative preference ratios for any two products are monotone across types. The monotone MRS condition allows us to relax the earlier regularity assumption. Under both sets of conditions, we fully characterize the product bundles and prices that form the optimal upgrade pricing menu. Finally, we show that, if the consumer's types are monotone, the seller can equivalently post a vector of single-item prices: upgrade pricing and separate pricing are equivalent.