On pricing of multiple bundles of products and services

This paper considers the pricing decision faced by a seller of bundles composed of a service and an associated product offered to customers on a subscription basis using a two-part tariff scheme. An optimal pricing policy that maximizes the profit of a firm is obtained using a dynamic programming approach and it is found that, in the long run, there is an optimal number of customers associated to each bundle. Due to managerial purposes, two suboptimal fixed-price policies are derived and compared to the optimal pricing policy. The conditions under which it is profitable for the firm to expand its offer from one to two bundles is studied. Finally, it is concluded that introducing a fee for subscribed customers to deter the switching from one bundle to the other, increases the profitability of the firm.