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On the Profitability of Firms in a Differentiated Industry

Stern School of Business, New York University, 40 West 4th Street, New York, New York 10012
bjing{at}stern.nyu.edu

In a model of vertical differentiation, the principal concern of this paper is to identify sufficient conditions for producing a higher- or lower-quality good to be more profitable (in terms of profits and profit margin). Our basic model considers a short-run scenario where the firms’ quality levels are fixed and they engage in price competition. Here, our results are three. First, we develop the notion of relative cost efficiency and show that its (increasing or decreasing) monotonicity in product quality implies that of firm profitability in equilibrium. A firm’s relative cost efficiency refers to its quality-adjusted cost (dis)advantage relative to its immediate competitors, for a given distribution of consumer tastes. Second, selling a higher-quality good is more profitable when absolute cost efficiency (defined as the ratio between a firm’s quality and unit cost) is increasing in quality. Third, we also establish a set of lower and upper bounds on each firm’s profitability.

The basic model is then extended in two directions. We examine unit cost functions that demonstrate monotone profitability, even when both quality and price are endogenous variables. We also show that the spirit of relative cost efficiency and its associated sufficient condition hold valid for a logconcave consumer distribution.

Key Words: vertical differentiation; profitability; Bertrand competition; game theory
History: Received: March 7, 2005;

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