Naked exclusion by a dominant input supplier: Exclusive contracting and loyalty discounts

Recent literature has shown that an incumbent can use exclusive contracts to maintain supra-competitive prices when buyers of the good are also competitors. Most of the models require the incumbent to completely prevent a more efficient potential entrant from entering, and assume that the entrant is exogenously prevented from making exclusive offers. Such models cannot explain how exclusive arrangements can lower welfare when they do not completely foreclose a small rival, when the rival can make exclusive offers, nor can they identify rudimentary relationships such as how a dominant supplier's size affects his incentive and ability to exclude and lower welfare. I extend the intuition of the literature by formally modeling competition between a dominant input supplier and a small rival selling to competing downstream firms. I show that a dominant supplier can pay downstream firms for exclusivity, allowing him to maintain supra-competitive input prices, even when a small rival that is more efficient at serving some portion of the market can make exclusive offers. I also show that exclusives need not completely exclude the small rival to cause competitive harm. The payment the dominant supplier makes for exclusivity equals the incremental rents that the rival's input could generate if exactly one downstream firm sold final goods using it.