All-Units Discounts and Double Moral Hazard

39 Pages Posted: 5 Mar 2013 Last revised: 25 Jul 2017

Date Written: March 2013


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 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 small scale entry. In the case considered, all-units discounts are a stronger entry deterrent than continuous tariffs, but can yield higher welfare by fostering demand-enhancing 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.

Keywords: All-units discounts, retroactive rebates, double marginalization, double moral hazard, principal-agent

JEL Classification: D42, D86, L12, L42

Suggested Citation

O'Brien, Daniel P., All-Units Discounts and Double Moral Hazard (March 2013). Available at SSRN: or

Daniel P. O'Brien (Contact Author)

Compass Lexecon ( email )

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Washington, DC 20004
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