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Product differentiation under imperfect information: When does offering a lower quality pay?

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Abstract

In this paper, we extend the Varian (1980) model to examine endogenous quality differentiation by firms, with a particular emphasis on the interplay between the firms’ product quality decisions and the ensuing price rivalry. Specifically, we assume that the price-sensitive (or informed) consumers hold a lower valuation for product quality than the brand-loyal (or uninformed) consumers. It is shown that the firms will choose differentiated qualities for a broad class of consumer utility functions and production technologies. We obtain two results. First, the equilibrium quality choices are efficient as they are also the welfare-maximizing qualities chosen by a social planner. The equilibrium qualities are as if one firm serves only its loyal consumers and the other serves only the price-sensitive consumers, even though they each serve both types of consumers (at least for some fraction of time). Second, the firm choosing the lower quality makes greater profits and also prices more aggressively, in the sense that it maintains a lower maximum price and offers discounts more often. The lower-quality product is more profitable because it yields higher social surplus when consumed by the price-sensitive consumers.

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Notes

  1. We thank an anonymous referee (Referee 1) for providing the second interpretation.

  2. For empirical evidence on price dispersion, see, for example, Villas-Boas (1995), Brynjofsson and Smith (2000), Chevalier and Goolsbee (2003).

  3. In models of advertising consumers may also differ in the number of ads received (e.g., Butters, 1977; Robert and Stahl, 1993; McAfee, 1994; McGahan and Ghamawat, 1994).

  4. Just like (Raju et al., 1990; Rao, 1991) also considers a duopoly with asymmetric consumer loyalty, but with the magnitude of loyalty following a continuous, rather than discrete, distribution.

  5. In the price equilibrium below, the probability of such a tie is zero.

  6. We thank an anonymous referee (Referee 2) for noting this point.

  7. The firms’ quality choices according to the profit functions in case (2) of Proposition 1 are given by \(c^{\prime}(s_{H}^{\ast})=u_{2}( \theta_{1},s_{H}^{\ast})\) and \(c^{\prime}(s_{L}^{\ast})=u_{2}( \theta_{2},s_{L}^{\ast})\). Because \(\theta _{1}<\theta_{2}\) and \(u_{12}>0\) by assumption, we have \(s_{H}^{\ast}<s_{L}^{\ast}\), contradicting the presumption of Proposition 1 that firm 1's quality is equal to or higher than that of firm 2. The quality choices according to the profit functions in case (3) of Proposition 1 are given by \(c^{\prime}(s_{H}^{\ast})=u_{2}( \theta_{2},s_{H}^{\ast})\) and \(c^{\prime }(s_{L}^{\ast})=u_{2}(\theta_{2},s_{L}^{\ast})\). Hence, \(s_{H}^{ \ast}=s_{L}^{\ast}\). However, either firm benefits by deviating to a lower quality \(s_{L}^{{}}\) characterized by \(c^{\prime}(s_{L}^{{}})=u_{2}( \theta_{1},s_{L}^{{}})\). Therefore, cases (2) and (3) of Proposition 1 can never arise in the subgame perfect equilibrium.

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Acknowledgments

I wish to thank two referees for their insightful comments and the Editor, Rajiv Lal, for his encouraging remarks. Useful feedback was also received from the participants in a seminar at New York University and the 2006 Midwest Economic Theory conference, especially Jay P. Choi. Any remaining errors are my own.

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  1. Stern School of Business, New York University, 44 West 4th Street, KMC 8-79, New York, NY, 10012, USA

    Bing Jing

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JEL classifications D83 · L13 · M31

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Jing, B. Product differentiation under imperfect information: When does offering a lower quality pay?. Quant Market Econ 5, 35–61 (2007). https://doi.org/10.1007/s11129-006-9014-0

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