Subscription Pricing for Free Delivery Services

Abstract

Many firms that offer home delivery of products purchased online now provide consumers the option of subscribing to a membership plan for free delivery of limited or unlimited number of orders instead of customers paying delivery charges for each order. This paper seeks to understand the benefits to firms and consumers of introducing such free-delivery subscription (FDS) plans to complement their traditional pay-for-delivery (PFD) option, characterize the firm's optimal FDS subscription pricing strategy, and study the effects of product, consumer, and market characteristics on the subscription fees and firm's profits. We develop and analyze an economic model that incorporates salient features of product delivery settings that prior models of subscription pricing do not fully capture. The features include simultaneous availability of PFD and FDS options, lift in a consumer's demand when she switches from PFD to FDS, the possibility of attracting new consumers when the firm introduces FDS, and order batching by customers due to per-order delivery charges and free-delivery order allowances. Our utility-based approach to model consumers’ purchasing choices incorporates consumer heterogeneity both in terms of their utility for the product and their shopping preference under the PFD option. For homogeneous consumers, we show that introducing a FDS plan raises the firm's profit, establish the optimality of offering unlimited free-delivery allowance, and analyze comparative statics. With multiple customer types, our analysis of two subscription pricing strategies for FDS plans—a single “Universal” plan and multiple “Tiered” plans with varying subscription fees and free-delivery limits—leads to several interesting insights on delivery pricing strategies, as well as drivers and sensitivity of the optimal policy, profits, and number of subscribers. We supplement this analysis with extensive computational experiments that reveal a substantial increase in profits when a firm adds one or more FDS plans to its PFD option even though the optimal subscription fee(s) only covers part of the firm's actual shipping costs. These results also permit us to gauge the influence and understand the trends in the profitability of the Universal and Tiered plans as various parameters change.