On the optimal fixed-up-to pricing for information services

Fixed-up-to (FUT) pricing allows consumers to purchase a fixed usage amount of an information service for a certain fixed price chosen from a set of options. In this study, we derive an optimal analytical solution for FUT pricing without imposing the strong single-crossing assumption. Further, we illustrate the analytical solution by leveraging mixed integer nonlinear programming to derive an optimal FUT pricing scheme for information services and also investigate when and by how much FUT pricing improves upon commonly used “flat rate” pricing. Our numerical results show that FUT pricing improves the service provider’s profits while enhancing social welfare when consumers face different maximum consumption-level bounds. Notably, in terms of optimal pricing, our numerical results show that the consumers’ maximum consumption-level bounds are more important than their utility functions. Most importantly, our results show that FUT pricing performs better than flat rate pricing under conditions of incomplete information. Finally, we empirically show that it is not necessary to treat over-the-limit rates as a decision variable in terms of optimal FUT pricing since both FUT pricing and three-part tariffs are reasonable approximations of nonlinear pricing in terms of both firm profits and social welfare. We conclude with a discussion of theoretical and practical implications for the design of optimal FUT pricing in terms of enhancing firm profits, consumer surplus, and social welfare.