Equilibrium pricing structure in a differentiated duopoly: uniform vs. two-part pricing

Abstract

This paper investigates the effect of product substitutability on subgame perfect Nash equilibrium pricing structures (Uniform vs. Two-part Pricing) in a duopoly where each firm chooses its pricing policy first and then decides the level of the strategic variables (unit price and fixed fee) associated with the chosen pricing policy to maximize its own profit. Previous studies on two-part pricing in a monopoly situation showed that two-part pricing yields higher profits than uniform pricing, and we show that two-part pricing is also a subgame perfect Nash Equilibrium at all degrees of product substitutability even in a duopoly situation. However, this paper shows that if the degree of substitutability is quite high, uniform pricing can also become a subgame perfect Nash equilibrium strategy, although both firms can afford higher profits if both firms adopt two-part pricing. This paper also shows how the equilibrium unit price and fixed fee change as the product substitutability increases in each pricing structure and how the consumers in the market behave for these prices (purchase none, one of the products, or both). When both firms choose the two-part pricing policy, unit price and fixed fee show distinctive forms of U-shape and inverted U-shape as the substitutability increases, for which we explore the rationale.