The role of inclination and part worth differences across segments in designing a price-discriminating product line

摘要

We consider a product line design problem with multiple quality-type attributes for a monopolist who serves multiple customer segments. We show that it is possible to get the first best solution (FBS) for this problem and develop a condition for it. We introduce the notion of inclination of a segment for a given bundle of attributes that measures the customer segment's overall preference for the bundle of attributes that are in the product category. We show that FBS implementability requires that the part worth between segments must be sufficiently separated. In fact, for a firm to price discriminate via a variety in the product line, this separation of parts worth between any pair of customer segments must be more than the separation in their inclinations. If inclination towards the product category varies vastly across segments, it will be harder to utilize the differences in part worth to offer separating products. We provide an elegant characterization of this condition in terms of divergence index between pairs of customers, which states that the divergence index must be less than one for FBS to be implementable. If inclination is equal across segments, then one can always design a differentiating product line no matter how many segments there are. We also provide a geometric interpretation of the FBS condition that is helpful in generating insights.