Quantity Discount or Small Quantity Premium? Violating the Single-Crossing Condition

Ram Orzach () and Miron Stano ()
Additional contact information
Ram Orzach: Oakland University
Miron Stano: Oakland University

Review of Industrial Organization, 2025, vol. 67, issue 1, No 3, 55-67

Abstract: Abstract This paper analyzes the rationale for a profit-maximizing firm with monopoly power that uses quantity discounts to a point where the additional quantity is sold below its marginal cost. Our model has two consumer types with linear demand functions. Unlike the standard assumption, we assume that their inverse demand functions cross. This will create a violation of the single-crossing condition so that Maskin and Riley’s characterization of nonlinear pricing cannot apply. Thus, we develop algorithms to circumvent the mathematical challenge of finding the optimal price-quantity bundles. We show that selling additional quantities below marginal cost can occur naturally in this framework. The solution indicates that it is the high price of the regular portion for one consumer type - - and not the discount on the additional quantities as commonly perceived - - that induces that consumer type to supersize. For our second result, we consider two consumer types and any linear inverse demand functions. We prove that crossing linear demands is a necessary condition to create the illusion of a great deal.

Keywords: Nonlinear pricing; Violating the single-crossing condition; Quantity discounts; Mechanism design; D82; L12 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11151-024-10007-9 Abstract (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:revind:v:67:y:2025:i:1:d:10.1007_s11151-024-10007-9

Ordering information: This journal article can be ordered from
http://www.springer. ... on/journal/11151/PS2

DOI: 10.1007/s11151-024-10007-9

Access Statistics for this article

Review of Industrial Organization is currently edited by L.J. White

More articles in Review of Industrial Organization from Springer, The Industrial Organization Society Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().