Multiproduct Duopoly with Vertical Differentiation

Abstract

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.

Deterministic Versus Random Utility: Implied Patterns of Vertical Product Differentiation in a Multi-Product Monopoly

“…Champsaur and Rochet (1989) and Bonnisseau and Lahmandi-Ayed (2006) find that the profit-optimising duopolist supplies just a single product variant. Cheng et al (2011) argue that the assumption of perfectly inelastic demand may explain the results found by Champsaur and Rochet (1989) and Bonnisseau and Lahmandi-Ayed (2006). In our model the demand for products conditional on buying a product is perfectly inelastic, however, the unconditional demand is elastic because consumers can choose not to buy and obtain their base utility, y, as shown in the last line of both Eq (1) and Eq (3).…”

“…The desire to understand the economic motives of multi-product firms applying vertical product differentiation resulted into a number of studies in which these firms are assumed to maximise profits using two decision variables, typically prices and qualities (see e.g. Mussa and Rosen (1978), Champsaur and Rochet (1989), Bonnisseau and Lahmandi-Ayed (2006), and Cheng et al (2011)). …”

“…2 A key question regarding vertical product differentiation is whether the predicted equilibrium patterns are symmetric, in the sense that prices and qualities of all product variants supplied by a single firm are equal, or not. Mussa and Rosen (1978) and Cheng et al (2011) show that for deterministic models fully differentiated equilibrium patterns exist in case of a monopoly and duopoly. In sharp contrast, Anderson et al (1992) mention the so-called constant mark-up property as a result from the random utility model, 2 Seminal empirical contributions are made by Berry (1994) and Berry et al (1995), see for a recent overview on this literature Crawford (2012).…”

“…applied throughout the literature by, amongst others, Mussa and Rosen (1978), Gabszewicz et al (1986), Bonnisseau andLahmandi-Ayed (2006), andCheng et al (2011).…”

“…By assuming a=0 and b=1/2 we arrive at the specification applied by Cheng et al (2011). Note that the supply of a product variant with infinite quality is ruled out to be profitable using these utility and cost functions.…”