Family Plans: Market Segmentation with Nonlinear Pricing

In the telecommunications market, firms often give consumers the option of purchasing an individual plan or a family plan. An individual plan gives a certain allowance of usage (e.g., minutes, data) for a single consumer, whereas a family plan allows multiple consumers to share a specific level of usage. The theoretical challenge is to understand how the firm stands to benefit from allowing family plans. In this paper, we use a game-theoretic framework to explore the role of family plans. An obvious way that family plans can be profitable is if it draws in very low-valuation consumers whom the firm would choose not to serve in the absence of a family plan. Interestingly, we find that even when a family plan does not draw any new consumers into the market, a firm can still benefit from offering it. This finding occurs primarily because of the strategic impact of the family plan on the firm's entire product line. By allowing high- and low-valuation consumers to share joint allowance in the family plan, the firm is able to raise the price to extract more surplus from the individual high-valuation consumers by reducing the cannibalization problem. Furthermore, a family obtains a higher allowance compared to the purchase of several individual plans and therefore contributes more profits to the firm. We also observe different types of quantity discounts in the firm's product line. Finally, we identify conditions under which the firm offers a pay-as-you-go plan.