Competitive cross‐subsidization

• DOI: http://doi.org/10.1111/1756-2171.12293
• Published date: 01 September 2019
• Author: Zhijun Chen,Patrick Rey
• Date: 01 September 2019

RAND Journal of Economics

Vol.50, No. 3, Fall 2019

pp. 645–665

Competitive cross-subsidization

Zhijun Chen∗

and

Patri ck Rey∗∗

Cross-subsidization arises naturally when firms with different comparative advantages compete

for consumers with heterogeneous shopping patterns. Firms then face a form of co-opetition,

as they offer substitutes for one-stop shoppers and complements for multi-stop shoppers. When

intense competition for one-stop shoppers drives total prices down to cost, firms subsidize weak

products with the profits made on strong products. Moreover, firms have incentives to seek

comparative advantages on different products. Finally, banning below-cost pricing increases

firms’ profits at the expense of one-stop shoppers, which calls for a cautious use of below-cost

pricing regulations in competitive markets.

1. Introduction

Multiproduct firms compete using a variety of pricing strategies. One commonly observed

strategy is cross-subsidization, in which firms price some products below cost and compensate

the resulting loss with profits from other products. Competition between Apple and Amazon

in e-book and tablet computer markets offers an illustration. In 2010, Amazon was selling the

“Kindle Fire” below cost,1while Apple preloaded 30,000 books free of charge on the iBooks

store.2It was commonly recognized that Apple’s iPad offered more functions than the Kindle

Fire, whereas Amazon—with more than two million e-books—provided more variety and thus a

higher match value than the iBooks store. Hence, each firm had a comparatively stronger product

in relation to its rival. Furthermore, both firms were selling their comparatively weaker products

∗Monash University; chenzj1219@gmail.com.

∗∗University of Toulouse Capitole; patrick.rey@tse-fr.eu.

Weare g rateful to Luis Cabral, Arthur Cazaubiel, Stephen Hamilton, Alessandro Iara, and Paul Klemperer,as well as to

participants at the EARIE conference, the IIOC conference, the conference of the German Economic Association, the ACE

conference, and the seminars at the University of Aukland, the Universityof Melbour ne, the NHH, Monash University,

Singapore Management University, the Toulouse School of Economics, the Paris School of Economics, and CREST

for helpful comments. Financial support from the European Research Council (ERC) under the European Community’s

Seventh FrameworkProgramme (FP7/2007–2013) Grant Agreement N 340903, is also g ratefullyacknowledged.

1The Kindle Fire, which offered access to the Amazon Appstore, streaming movies, and TV shows, was

sold in the United States. at a retail price of $199. Amazon’s hardware cost for a Kindle Fire was estimated

at $201.70, not including “additional expenses such as software, licensing, royalties, or other expenditures.” See:

technology.ihs.com/389433/amazon-kindle-fire-costs-20170-to-manufacture.

2See AppleInsider’s report, available at: appleinsider.com/articles/10/03/25/apple_loads_up_new_ibooks_store_

with_free_public_domain_ipad_titles.

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646 / THE RAND JOURNAL OF ECONOMICS

below cost, and deriving profits from their strong products.3Moreover, consumers could combine

the two firms’ strong products, but not the weak ones: iPad users could download a free Kindle

Application to access Amazon’s e-books, whereas Kindle Fire users had no option to access the

iBooks store.

This strategy in competitive markets, such as tablets and e-books, is somewhat at odds with

the existing theory. According to this theory, cross-subsidization arises in the context of regulated

or monopolistic markets,4or in markets characterized by friction, such as consumers’ limited

information or bounded rationality (see the literature review below). Here, we develop a new

approach, based on the diversity of purchasing patterns.

The literature on competitive multiproduct pricing often assumes that customers engage in

“one-stop shopping” and purchase all products from the same supplier. Yet, in practice, many

customers engage in multi-stop shopping and rely on several suppliers to fulfill their needs. The

choice between these purchasing patterns is driven not onlyby the diversity and the relative merits

of suppliers’ offerings, but also by the transaction costs that buyers must bear in order to enjoy

the products. As mentioned by Klemperer (1992), these transaction costs include physical costs,

such as transportation costs, and nonphysical costs, such as the opportunity cost of time and the

adoption cost of using a new electronic device. Following the terminology of the literature, we

will refer to these costs as “shopping costs.” Obviously, these costs vary across customers. For

example, some consumers may face tighter time constraints and/or dislike shopping, whereas

others may be less time-constrained and/or enjoy shopping. Indeed, some users, already familiar

with the Kindle system, may be reluctant to switch to the iPad because of the associated learning

costs,5whereas others may enjoy the adoption of a new device. All other things being equal,

customers with high transaction costs tend to favor “one-stop shopping,” whereas others prefer

“multi-stop shopping.”

We first note that the diversity of purchasing patterns gives rise to a form of “co-opetition”:

on the one hand, firms offer substitutes for one-stop shoppers, who look for the best basket

of products; on the other hand, firms offer complements for multi-stop shoppers, who seek to

combine suppliers’ best products. We show that this duality drastically affects firms’ pricing

strategies and can lead to cross-subsidization, even in competitive markets.

Specifically, we consider a setting in which two firms offer the same product line (which

consists of two products, for simplicity). Consumers are perfectly informed about prices, as

is indeed the case for e-books and tablets. To discard price-discrimination motives, we further

assume that consumers have inelastic demands. Altogether,these assumptions allow us to abstract

from the motivations already highlighted in the literature on cross-subsidization (see the literature

review below). Our key ingredients are instead that: (i) consumers have heterogeneous shopping

costs; and (ii) through lower costs and/or higher consumer value, each firm enjoysa comparative

advantage overone product. For the sake of exposition, we initially assume that firms have similar

comparative advantages; that is, each firm has a stronger product than its rival, but overall, their

baskets generate the same surplus. In equilibrium, consumers with high shopping costs engage

in one-stop shopping, and competition for these consumers drives firms’ aggregate prices down

to cost. By contrast, consumers with low shopping costs engage in multi-stop shopping and buy

each firm’s strong product; thus, the firms make a profit. Cross-subsidization therefore arises

naturally, with each firm pricing its weak product below cost and subsidizing the resulting loss

with the profit from its strong product.

3Before 2010, Amazon wasalso selling newly released e-books below cost. However,prices were raised after Apple

proposed the controversial “agency model” for e-books. More recently, Amazon has introduced a more sophisticated

version of its reader (e.g., the Oasis), which offers additional features. Still, the pattern of cross-subsidizing weaker

products with stronger ones appears to have persisted from 2010 to 2016.

4For instance, Faulhaber(2005) asser ts that “under competitiveconditions, the issue of cross-subsidy simply does

not arise.”

5Before the launch of the iPad and the Kindle Fire, readers of Amazon’s e-books were mainly using the original

Kindle device.

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The RAND Corporation 2019.