PRODUCT FUNCTIONALITY, COMPETITION, AND MULTIPURCHASING

• Published date: 01 February 2017
• Author: Hans Jarle Kind,Simon P. Anderson,Øystein Foros
• Date: 01 February 2017
• DOI: http://doi.org/10.1111/iere.12213

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 1, February 2017

PRODUCT FUNCTIONALITY, COMPETITION, AND MULTIPURCHASING∗

BYSIMON P. ANDERSON,ØYSTEIN FOROS,AND HANS JARLE KIND1

University of Virginia, U.S.A; NHH Norwegian School of Economics, Norway;

NHH Norwegian School of Economics, Norway

The more functionalities a good offers, the greater is its perceived quality. Equilibrium prices in standard spatial

competition models depend solely on quality differences. We assume that new functionalities are more appreciated

the closer a product is to a consumer’s ideal variety. Prices are then increasing in functionality levels. Furthermore, we

endogenize whether consumers buy only one of two varieties (single-purchase) or both (multipurchase). Under multi-

purchase, there might be a hump-shaped relationship between equilibrium prices and functionality levels. Therefore,

it could be optimal for each supplier to sacrifice sales and set prices so high that multipurchase is eliminated.

1. INTRODUCTION

Some consumers buy different variants of horizontally differentiated goods (multipurchasing)

like cars, newspapers, and software programs, whereas others buy only one (single-purchasing).

As an example, there are people who install Scientific Workplace as well as Mathematica on

their computers, but others are not willing to pay for both—and installing two copies of the

same software on a computer adds no benefit.

For hardware, compare smartphones (e.g., iPhone or HTC) and multipurpose computer

tablets (such as Windows Surface or Apple iPad). Most smartphones and multipurpose tablets

offer attributes like the ability to play games, make phone calls, read e-mails, watch videos,

and listen to music. One source of horizontal differentiation is the physical size. Compared to

a smartphone, a tablet-like surface is superior for watching videos when sitting in the armchair

at home, but a smartphone is significantly more convenient when traveling.2Many people thus

end up buying both a smartphone and a tablet.3Likewise, a lot of consumers buy both an iPad

and a Kindle.

In a press release (December 27, 2010) Amazon.com’s founder and CEO Jeff Bezos said that

“We’re seeing that many of the people who are buying Kindles also own an LCD tablet (e.g.

an iPad). Customers report using their LCD tablets for games, movies, and web browsing and

their Kindles for reading sessions. They report preferring Kindle for reading because it weighs

less, eliminates battery anxiety with its month-long battery life, and has the advanced paper-like

Pearl e-ink display that reduces eye-strain, doesn’t interfere with sleep patterns at bedtime, and

works outside in direct sunlight, an important consideration especially for vacation reading.”

These devices thus have different attributes, so multipurchasing provides incremental value

over buying just one. But what will happen in the market place in the future if both these goods

∗Manuscript received January 2014; revised June 2015.

1We thank Fang Guo and Yiyi Zhou for spirited research assistance. Furthermore, we thank participants at the 10th

World Congress of the Econometric Society, August 21, 2010, Shanghai, China; the Conference on Platform Markets:

Regulation and Competition Policy, June 1, 2010, Mannheim, Germany; the 8th IIOC, May 16, 2010, Vancouver,

Canada; and EARIE, September 2, 2011, Stockholm, Sweden, for helpful comments. Please address correspondence

to: Hans Jarle Kind, Department of Economics, NHH, Norwegian School of Economics, Helleveien 30, Bergen, Bergen

5045, Norway. Phone: +4795739837. E-mail: hans.kind@nhh.no.

2Due to their size, tablets are awkward for conventional voice telephony, but may be superior to smartphones for

video conferences.

3See the discussion by Mies, PCWorld April 4, 2010, “iPad Versus the iPhone.” URL: http://www.pcworld.com/

article/193420/ipad_versus_the_iphone_why_i_dont_need_bothyet.html

183

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(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

184 ANDERSON,FOROS,AND KIND

are improved and offer more attributes?4How might this affect prices and profits, and will

multipurchasing become more or less likely? How does competition play out if each good offers

exclusive attributes compared to if there is a substantial overlap in the attributes the goods offer

(shared attributes)? These are among the questions we address in this article.

Most economic analysis of discrete choice assumes that consumers buy one unit of at most one

variant (see Anderson et al., 1992). Yet the examples above suggest that there are many cases

of purchase of (one unit of) several variants. For each variant, its attractiveness is increasing

in its attributes: An attribute or function (we shall use these terms interchangeably) could be

a particular mathematical tool in a software program, a web browsing opportunity or an e-ink

display on a tablet. A consumer will buy several variants to the extent that this increases the

number of different attributes she can access.5Thus, for any given consumer we might observe

unit demand (at most) for any particular variant, but bringing both an iPad and a Kindle on a

journey might be useful.

The Hotelling model is the workhorse for analyzing unit demand when goods are horizontally

differentiated. We follow this line, but make two innovations. First, we assume that consumers

have a higher willingness to pay for a good the greater the set of attributes it offers. Specifically,

the more satisfied a consumer is with the horizontal characteristics of a good, the greater will be

her marginal utility of having access to more functions (vertical characteristics). On the tablet

market, for instance, it is likely that when Amazon introduced a Kindle with a color screen

opportunity, then the increased willingness to pay for that device was more pronounced for a

Kindle lover than for an iPad lover.6For comparison with more conventional models, it should

be noted that if the set of attributes increases, then also the perceived quality of the good

improves.

Our second innovation is to make single-purchase or multipurchase an endogenous outcome

that depends on consumer preferences, the functionalities of the goods, and the strategic choices

by the suppliers. We take into account that for a multipurchasing consumer, the incremental

value from exclusive attributes (not offered by the rival) is typically higher than for overlapping

(shared) attributes.

Our first innovation implies that the higher the functionality level of the goods, the higher their

prices under single-purchase. In standard symmetric Hotelling models, prices are independent

of the (vertical) quality level. In contrast, product functionality, in the present model, interacts

with the distance-based utility, so functionality is not a pure measure of vertical differentiation.

This feature is also germane to more traditional circumstances with a single discrete choice

between the variants offered.

Noting that prices increase in the functionality levels under single-purchase, it is appropriate

to ask whether there is reason to believe that the same holds under multipurchasing. At the

outset one might think so, but actually the opposite could be true. To see why, suppose that

Apple improves iPad’s e-book reading quality and that Kindle becomes more of a multipurpose

tablet. This will clearly increase the stand-alone value of each of the devices. However, it could

also reduce the incremental value of having an iPad in addition to a Kindle (and vice versa). Put

differently, although the attractiveness of the goods clearly increases in the functionality they

offer, more shared functionality may also make it less imperative for consumers to multipur-

chase. Consistent with this, we show that there might be a hump-shaped relationship between

equilibrium prices and functionality under multipurchase. One implication of this is that if a

sufficiently large number of the functionalities are shared (and the incremental value of shared

4With Kindle Fire, Amazon introduced a version of its e-book reader with more attributes. Kindle Fire is closer to

a multipurpose tablet-like iPad, thereby reducing the incremental value of having both.

5With due tribute to Lancaster (1966) for emphasizing the importance of the characteristics embodied in goods as

the fundamental objects of desire.

6To our knowledge, the only paper to use a similar formulation is Waterman (1989–90). He allows quality to

interact with transportation costs in an extension of his analysis of the trade-off between quality and variety in a circle

framework. However, he does not focus on the features of the formulation highlighted here. Another related paper is

Bonatti (2011), who analyzes nonlinear pricing when consumer quality valuation is brand specific.