Optimizing Price Menus for Duration Discounts: A Subscription Selectivity Field Experiment

Abstract

Subscription services typically offer duration discounts , rewarding longer commitments with lower per-period costs. The “menu” of contract plan prices must be balanced to encourage potential customers to select into subscription overall and to nudge those that do to more profitable contracts. Because subscription menu prices change infrequently, they are difficult to optimize using historical pricing data alone. We propose that firms solve this problem via an experiment and a model that jointly accounts for whether to opt in and, conditionally, which plan to choose. To that end, we conduct a randomized online pricing experiment that orthogonalizes the “elevation” and “steepness” of price menus for a major dating pay site. Users’ opt-in and plan choice decisions are analyzed using a novel model for correlated binary selection and multinomial conditional choice, estimated via Hamiltonian Monte Carlo. Benchmark comparisons suggest that common models of consumer choice may systematically misestimate price substitution patterns, and that a key consideration is the distinctiveness of the opt-out (e.g., nonsubscription) option relative to others available. Our model confirms several anticipated pricing effects (e.g., on the margin, raising prices discourages both opt-in overall and choice of any higher-priced plans), but also some that alternative models fail to capture, most notably that across-the-board pricing increases have a far lower negative impact than standard random-utility models would imply. Joint optimization of the menu’s component prices suggests the firm has set them too low overall, particularly so for its longest-duration plan.