Naked Exclusion and the Anticompetitive Accommodation of Entry: Two Examples

In this appendix, specific results for the linear demand specification and Hotelling specification are established, corresponding to the paper: “Naked Exclusion and the Anticompetitive Accommodation of Entry” 1 Representative consumer (linear demand) Consider the standard exogenous differentiation model with linear demands, with consumers’ utility from the two products defined as U (q1, q2) = α (q1 + q2)− β ( q 1 + q 2 2 + 2γq1q2 ) 2 , (1) where qi is the amount consumed of good i. This provides a convenient way to parameterize the degree of competition between manufacturers. Specifically, inverse demand functions are given by pi = α− β(qi + γqj), where 0 ≤ γ < 1 serves as a measure of the degree of differentiation, and α > cI . The higher γ is, the more homogenous are the two products. When the prices for the two goods are sufficiently close, both manufacturers will enjoy positive demands. However, when the prices for the two goods strongly diverge, the higher priced good will attract no demand, while the lower priced good will attract the entire market demand. Specifically, for any price pj , when pi ≥ α (1− γ)+γpj , manufacturer i receives no demand, while for 0 < pi ≤ (−α (1− γ) + pj) /γ, manufacturer i captures the entire market. Thus, firm i’s demand function is qi = α (1− γ)− pi + γpj β (1− γ2) if −α (1− γ) + pj γ < pi < α (1− γ) + γpj (2) = α− pi β if 0 < pi ≤ −α (1− γ) + pj γ (3) = 0 if pi ≥ α (1− γ) + γpj . (4) Now consider the equilibrium profits arising under the different subgames considered in the companion paper. • If the entrant E does not enter (for instance, since the incumbent I signs up all retailers), I will sell to retailers at the monopoly price, which also becomes the retail price pM = α+ c 2 , ∗National University of Singapore: email [email protected]