Diversity and Quantity Choice in a Horizontally Differentiated Duopoly
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Diversity and Quantity Choice in a Horizontally Differentiated Duopoly Xiaokuai Shao1 Received: 26 August 2019 / Revised: 25 February 2020 / Accepted: 28 February 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The Hotelling model is extended where not only can consumers choose to buy from both sellers (multi-brand purchase), buying multiple units from one seller is also considered (within-brand multi-unit purchase). When an increase of the demand for within-brand multi-purchase exceeds a threshold: (i) firms’ strategies are switched from single-brand equilibrium with higher prices to multi-brand equilibrium with lower prices, if the incremental value from consuming an additional unit of the same product is independent of the preference for diversity; (ii) the direction of such equilibrium-switch is reversed if the two types of multi-purchase are substitutes. Keywords Hotelling duopoly · Multi-brand purchase · Within-brand multi-purchase · Complementarity JEL Classification L1 · D4
1 Introduction The spatial competition model, originally established by Hotelling (1929), is widely used in business analysis. Among the applications, a particular feature of the benchmark Hotelling model is that each consumer is assumed to buy one unit from one seller exclusively. As a result, the model implies that either an increase of the level of product differentiation or brand-loyalty brings about market power. The unit-demand restriction is relaxed by recent studies such as Kim and Serfes (2006) and Jeitschko et al. (2017) and Anderson et al. (2017), where consumers are allowed to buy from both sellers (multi-brand purchase). They show that the governing force on pricing is the degree of multi-brand complementarity relative to product differentiation—a new equilibrium emerges when the incremental value for product diversity exceeds a threshold, where duopolists offer lower prices in exchange for quantities, and profits are decreasing in consumer heterogeneities.
Xiaokuai Shao
[email protected]; [email protected] 1
School of Economics and Management, Tsinghua University, Beijing, 100084, China
Journal of Industry, Competition & Trade
In their pioneer works, each consumer is allowed to buy at most one unit from each seller—this might be perfectly applicable to the examples such as newspapers, iPad versus Kindle or software—but in some other markets, buying multiple units from the same seller is also pervasive (within-brand multi-purchase), e.g., food, credit cards, furniture, and services. Some customers may buy from both brands for enjoying the variety of brandspecific services (functionalities, styles, tastes), and meanwhile, some customers—e.g., loyal individuals or corporate clients—may buy multiple units of the same product for extra needs (e.g., additional capacities). Among the competing platforms, both multi-homing and repeated purchases are prevalent. In addition to multi-brand purchase, will the previous results still hold (or under what circumstances) when wit
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