Optimal Pricing of New Subscription Services: Analysis of a Market Experiment

Abstract

There are now available a number of new subscription services that comprise a dual pricing system of a monthly access fee (rental) and a per-minute usage charge. Examples include cellular phones, the Internet, and pay TV. The usage and retention of such services depend on the absolute and relative prices of this dual system. For instance, a moderate access fee but a low-usage charge might initially appeal to customers, but later a low-usage customer might find the monthly fee unjustified and thereby relinquish the service. Providers of such services, therefore, usually offer several pricing packages to cater to differing customer needs. The purpose of this study is to derive a revenue-maximizing strategy for subscription services, that is, the combination of access and usage price that maximizes revenue over a specified time period. An additional objective is to determine access and usage price elasticities because they have historically played an important role in theoretical pricing models. The application area is the cellular phone market, but for a new rather than an existing product. To help gauge the likely usage rates and customer retention, a field experiment is conducted in which several alternative price combinations are used. Specifically, a sample of potential residential customers (most of whom did not have an existing cell phone) were divided into four treatment groups. The first group were not charged an access fee but did have to pay a small per-minute usage charge. The second group also paid a small usage charge but in addition had three access price increases over the duration of the trial. The third group paid no access fee but had usage charge increases, while the fourth group had both access fee and usage charge increases. Usage levels for each respondent are recorded, as is their month of dropout if they discontinue the service. An initial examination of the data shows that higher access fees result in higher customer attrition, and higher usage cost results in lower usage. Furthermore, usage and retention are related in that declining usage levels over time often signal impending customer attrition. Hence, two phenomena need to be modeled: usage of the service and customer retention conditional on usage. Some seasonal effects are also observed and are allowed for in the model. Modeling customer attrition simultaneously with usage is important because ignoring customer attrition will likely result in an underestimate of price sensitivity. This results from a censoring effect, whereby respondents who remain in the trial tend to be wealthier, and hence, less price sensitive. Given the known problems of ignoring customer attrition, we develop a theoretical model of usage, which explicitly incorporates attrition by extending a time-series model introduced by Hausman and Wise (1979). We make two extensions of the Hausman and Wise model. The first is to generalize it from two to many time periods and the second is to allow for respondent heterogeneity by incorporating latent classes. We fit the model by maximum likelihood and find that a two-segment model is best. In addition, we examine the predictive validity of our model and find it to be reasonably good. In general, the results show that access and usage prices have different relative effects on demand and retention. There are five key results. First, access price has some effect on usage but a much stronger effect on retention. Second, usage price has a strong effect on usage and a moderate effect on retention, in that if usage price increases so much that usage declines, then lower usage levels results in higher attrition. Third, access price elasticity is about half that of usage price, with both elasticities generally being much smaller than 1, indicating relative inelasticity for this particular service. Fourth, customer attrition rate (churn) is much more sensitive to access than usage price and, last, if just observed usage is examined and customer attrition is ignored, then price sensitivity is very likely to be substantially underestimated (on the order of 45% in our case). Finally, when developing the revenue-maximizing price combination we allow for the cost of customer acquisition by using some typical advertising-to-sales ratios for the telecommunications industry. We find that the revenue maximizing price is $27.70 per month for the access fee and $0.81 per minute for the airtime charge. These values are in line with current access fees and usage costs in the given market.