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 (“cliff”) at the threshold that triggers the discount. This paper shows that all-units discounts arise in optimal agency contracts between upstream and downstream firms that face double moral hazard. I present conditions under which allunits 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 case considered, all-units discounts deter entry by less efficient rivals without distorting price and investment, whereas continuous tariffs either accommodate such entry or deter it by distorting price and investment. 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.