Quantity Discount or Small Quantity Premium? Violating the Single-Crossing Condition.
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| Title: | Quantity Discount or Small Quantity Premium? Violating the Single-Crossing Condition. |
|---|---|
| Authors: | Orzach, Ram1 (AUTHOR) orzach@oakland.edu, Stano, Miron1 (AUTHOR) stano@oakland.edu |
| Source: | Review of Industrial Organization. Jun2025, Vol. 67 Issue 1, p55-67. 13p. |
| Subjects: | Demand function, Direct costing, Inverse functions, Monopolies, Prices |
| 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Review of Industrial Organization is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 185595766 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Quantity Discount or Small Quantity Premium? Violating the Single-Crossing Condition. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Orzach%2C+Ram%22">Orzach, Ram</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> orzach@oakland.edu</i><br /><searchLink fieldCode="AR" term="%22Stano%2C+Miron%22">Stano, Miron</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> stano@oakland.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Review+of+Industrial+Organization%22">Review of Industrial Organization</searchLink>. Jun2025, Vol. 67 Issue 1, p55-67. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Demand+function%22">Demand function</searchLink><br /><searchLink fieldCode="DE" term="%22Direct+costing%22">Direct costing</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+functions%22">Inverse functions</searchLink><br /><searchLink fieldCode="DE" term="%22Monopolies%22">Monopolies</searchLink><br /><searchLink fieldCode="DE" term="%22Prices%22">Prices</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Review of Industrial Organization is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s11151-024-10007-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 55 Subjects: – SubjectFull: Demand function Type: general – SubjectFull: Direct costing Type: general – SubjectFull: Inverse functions Type: general – SubjectFull: Monopolies Type: general – SubjectFull: Prices Type: general Titles: – TitleFull: Quantity Discount or Small Quantity Premium? Violating the Single-Crossing Condition. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Orzach, Ram – PersonEntity: Name: NameFull: Stano, Miron IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 0889938X Numbering: – Type: volume Value: 67 – Type: issue Value: 1 Titles: – TitleFull: Review of Industrial Organization Type: main |
| ResultId | 1 |
