Nonlinear Pricing with Competition

This paper studies how increased competition affects nonlinear pricing, in particular the number of contracts offered by firms. We present a model with both horizontally and vertically differentiated products, with the set of consumers served in the market being endogenously determined. Though firms are only able to sort consumers in the vertical dimension, horizontal differentiation affects screening in the vertical dimension. Using a two-phase optimal control technique, we characterize the symmetric equilibrium menu of contracts under different market structures. When the market structure moves from monopoly to duopoly, we show that each firm offers more contracts (serving more types of consumers) and quality distortions decrease. As the market structure becomes more competitive (when the number of firms increases further), the effect of increasing competition exhibits some non-monotonic features: when the initial competition is not too weak, a further increase in the number of firms will lead to more contracts being offered and a reduction in quality distortions; when the initial competition is weak, an increase in the number of firms will lead to fewer contracts being offered, though the effect on quality distortions is not uniform. Our predictions are largely consistent with some empirical studies.

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