All‐units discounts as a partial foreclosure device

• Author: Guofu Tan,Adam Chi Leung Wong,Yong Chao
• Published date: 01 March 2018
• Date: 01 March 2018
• DOI: http://doi.org/10.1111/1756-2171.12220

RAND Journal of Economics

Vol.49, No. 1, Spring 2018

pp. 155–180

All-units discounts as a partial foreclosure

device

Yong Chao∗

Guofu Tan∗∗

and

Adam Chi Leung Wong∗∗∗

We investigate the strategic effects of all-units discounts (AUDs) used by a dominant firm in the

presence of a capacity-constrained rival. Due to the limited capacity of the rival, the dominant

firm has a captive portion of the buyer’s demand for the single product. As compared to linear

pricing, the dominant firm can use AUDs to go beyond its captive portion by tying its captive

demand with part of the competitive demand and partially foreclose its small rival. When the

rival’s capacity level is well below relevant demand, AUDs reduce the buyer’s surplus.

1. Introduction

A common form of pricing is all-units discounts (AUDs), in which the price per unit

is cut on all units once the buyer’s order crosses a threshold. AUDs and related conditional

rebate schemes are frequently observed in intermediate-goods markets, and their adoption by

∗University of Louisville; yong.chao@louisville.edu.

∗∗University of Southern California; guofutan@usc.edu.

∗∗∗Lingnan University; adamwong@ln.edu.hk.

Wethank the Editor, Benjamin Hermalin, and two anonymous referees for manyinsightful comments and suggestions, and

weare grateful to many people for helpful discussions, especially Marcel Boyer, Luis Cabral, Juan Carrillo, YongminChen,

Zhijun Chen, Zhiqi Chen, Harrison Cheng, Joseph Farrell, Liliane Giardino-Karlinger, KenHendricks, Dmitr y Lubensky,

Massimo Motta, Daniel O’Brien, Cheng-Zhong Qin, TomRoss, Michael Williams, Ralph Winter,and seminar par ticipants

at the University of Southern California, the University of Louisville, Koc¸ University, Zhejiang University, Shandong

University, the 2012 Southern California Symposium on Network Economics and Game Theory, the 9th Workshop

on Industrial Organization and Management Strategy, the Annual Conference of Mannheim Centre for Competition

and Innovation, the 11th Annual International Industrial Organization Conference, the 2013 North American Summer

Meeting of the Econometric Society, the Workshop in Industrial Economics, Academia Sinica, Tsinghua University,

CIRANO-PHELPS Session at the CEA 2014 Meetings, the 28th Summer Conference on Industrial Organization, Fall

2014 Midwest Economic Theory Conference, the 42nd EARIE Annual Meeting, 2016 Next Generation of Antitrust

Scholars Conference, and Pennsylvania State University. The usual caveat applies.

C2018, The RAND Corporation. 155

156 / THE RAND JOURNAL OF ECONOMICS

dominant firms has become a prominent antitrust issue. For instance, in the Tom ra 1and Michelin

II2cases, “individualised retroactive rebate schemes” used by Tomra, and quantity rebates used

by Michelin, were found to be exclusionary. Additionally, the European Commission has found

loyalty discounts adopted by dominant firms to be anticompetitive in several cases.3

All these cases are Section 2/Abuse of Dominance cases. By the very nature of dominance,

part of the buyer’s demand is captive to the dominant firm. In reality, such captive demand could

arise from various sources: small rivals often have capacity constraints, as in the cases of Tetra

Pak ,4Tom ra ,Michelin II, and Intel5; the dominant firm usually offers a must-carry brand to

customers, as in the cases of Post DanmarkII6and Intel. Regardless of where the captive demand

comes from, the important fact is that the small rival can only compete for a portion of the buyer’s

demand. The major concern about an AUD scheme and its variations is their potential foreclosure

effects on the competitivepor tion of the market. Intuitively, a dominant firm can take advantageof

its captive portion of the demand to induce a buyer to purchase a significant portion of her require-

ments from it. Hence, AUDs can mean reduced sales for smaller rivals. Such reasoning has been

employed in some of the cases discussed,as well as by the European Commission (see European

Commission DG COMP Discussion Paper, 2005, and Guidance Paper, 2009). However, to the

best of our knowledge, there has been no formal analysis of this claim in the economic literature.

In this article, we propose a model to formalize the idea that AUDs permit foreclosure when

a dominant firm competes against a small rival. The dominant firm enjoys a captive demand

due to the capacity constraints of its smaller rival. In particular, we consider a three-stage game

with complete information, in which the dominant firm and its rival produce identical products

with zero costs and make sequential price offers to a buyer before the buyer makes her purchase

decision. We find that AUDs always increase the dominant firm’s profits, sales, and market share

over linear pricing (LP). At the same time, AUDs adopted by the dominant firm lead to partial

foreclosure of the rival, in the sense that the rival’s profits, sales, and market share are strictly

reduced relative to what they would be under LP. These results hold for any capacity level of the

small rival. When the rival’s capacity level is especially low relativeto demand, AUDs reduce the

buyer’s surplus but increase total surplus.7

The intuition for our findings is that, due to the limited capacity of the rival, the dominant

firm is able to use AUDs to tie part of the competitive portion (as the tied good) to its captive

portion (as the tying good) of a single product, leveraging its market power from the captive to

the competitive demand. Under AUDs, the list price is set so high that it coerces the buyer into

meeting the threshold if she buys anything from the dominant firm. The dominant firm always

sets its quantity threshold above the captive demand size, together with a per-unit discount as an

incentive. The discontinuity of AUDs forces the buyer to contemplate taking a “chunk” from the

dominant firm, consisting of its captive portion and part of the competitive portion, rather than

making a purchase decision on the marginal principle, as under LP. This effectuates a tie: the

1Case COMP/E-1/38.113, C(2006)73, Prokent-Tomra, Commission Decision of 29 March 2006. Case T-155/06,

TomraSystems and Others v.Commission, Judgment of the General Court of 9 September 2010. Case C-549/10 P,To mra

Systems and Others v. Commission, Judgment of the Court (Third Chamber) of 19 April 2012.

2Case COMP/E-2/36.041/PO-Michelin, Commission Decision of 20 June 2001. Case T-203/01, Manufacture

Franc¸aise des Pneumatiques Michelin v. Commission of the EuropeanCommunities supported by Bandag Inc., Judgment

of the Court of First Instance of 30 September 2003. See Motta (2009) for discussions of this case.

3To name a few, British Airways (Case C-95/04, British Airwaysplc v. Commission of the European Communities

supported by Virgin Atlantic Airways Ltd., Judgment of the European Court of Justice, March 2007), and Intel (Case

COMP/C-3/37.990—Intel (2009); Docket No. 9341, In the Matter of Intel Corporation (2010)).

4On November 16, 2016, the State Administration of Industry and Commerce (SAIC) of China announced that,

between 2009–2013, TetraPak abused its dominance in relevant product markets in China. One of the abusive practices

cited in the SAIC’sdecision was a collection of discount policies conditional on volume thresholds.

5Intel (Case COMP/C-3/37.990—Intel (2009); Docket No. 9341, In the Matter of Intel Corporation (2010)).

6Case C-23/14, Post DanmarkII.

7Chao and Tan (2013) haveshown that even when the rival has a lower marginal cost than the dominant firm, the

partial foreclosure results still hold, and AUDsmay reduce total surplus.

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