This paper investigates a two-stage competition in a vertically differentiated industry, where each firm produces an arbitrary number of similar qualities and sells them to heterogeneous consumers. The number of products, qualities, prices, and the extent of the market coverage are endogenously determined. We show that when unit costs of quality improvement are increasing and quadratic, each firm has an incentive to provide a disconnected set of similar qualities approximating a continuum. The finding contrasts sharply with the single-quality outcome when the market coverage is exogenously determined. We also show that allowing for multiple qualities intensifies the level of competition, lowers the profit of each firm, and raises the consumer surplus and the social welfare in comparison to the single-quality duopoly.
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