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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 by Daniel O'Brien shows that all-units discounts arise in optimal agency contracts between upstream and downstream firms that face double moral hazard.