Product Variety and Competitive Discounts, Journal of Economic Theory
A market with free entry monopolistic competition is studied. Nonlinear pricing is shown to be the Bertrand-Nash equilibrium strategy for firms. Given small per capita fixed costs, the nonlinear pricing equilibrium approaches the perfectly competitive equilibrium with marginal cost pricing. Nonlinear pricing is associated with greater product variety than linear pricing. Increased variety leads to efficient pricing.
Spulber, Daniel. 1989. Product Variety and Competitive Discounts. Journal of Economic Theory. 48(2): 510-525.