All-units Discounts and Double Moral Hazard

An all-units discount is a price reduction applied to all units purchased if the customer's total purchases equal or exceed a given quantity threshold. Since the discount is paid on all units rather than marginal units, the tariff is discontinuous and exhibits a negative marginal price at the threshold that triggers the discount. Why would suppliers offer such tariffs? This paper shows that all-units discounts can arise in optimal contracts between upstream and downstream firms with market power who make non-contractible investments that enhance demand. I present conditions under which all-units discounts dominate two-part tariffs and other continuous tariffs. I also examine these tariffs when the upstream market faces a threat of entry. In the cases considered, continuous tariffs are a more profitable device for managing entry than all-units discounts. These findings begin filling the gap in economists' understanding of the equilibrium effects of all-units discounts in intermediate markets in which contract design affects incentives for pricing, investment, and competitive entry.