Competition, Product Proliferation and Welfare: A Study of the
U.S. Smartphone Market∗
Ying Fan†
Chenyu Yang‡
University of Michigan
University of Michigan
February 15, 2015
(Incomplete and preliminary. Please do not cite.)
Abstract
We consider a structural model of demand and supply where firms endogenously offer vertically differentiated products and exercise second-degree price discrimination. We apply this
model to the smartphone industry and quantify the welfare effects of price discrimination and
competition. We use counterfactual simulations to assess how the welfare changes when each
firm only offers its highest-quality product. We also study the market outcomes such as price,
product variety and welfare if later entrants in the market entered earlier.
Key words: endogenous product choice, second-degree price discrimination, smartphone industry
JEL Classifications: L11, L15, L13, L63
1
Introduction
Economists have long recognized firms’ incentives to lower the quality of part of their outputs
in order to provide differentiated products for the purpose of price discrimination. By offering a
menu of products with different qualities and different prices, firms can induce consumers with
different tastes for quality to sort themselves and hence extract more surplus. The welfare effect of
such a price discrimination practice, however, is ambiguous. On the one hand, price discrimination
may lead to a higher price for the higher-end products. On the other hand, it can result in a
larger product variety and presumably larger market coverage, which is welfare enhancing. In
∗
We thank the Michigan Institute for Teaching and Research in Economics and NET Institute for their generous
financial support.
†
Department of Economics, University of Michigan, 611 Tappan Street, Ann Arbor, MI 48109; [email protected].
‡
Department of Economics, University of Michigan, 611 Tappan Street, Ann Arbor, MI 48109;
[email protected].
1
other words, how second-degree price discrimination affects welfare is an empirical question. In
an imperfectly competitive setting, the theoretical predictions are even more ambiguous. The
results very often depend on market details such as consumer heterogeneity in tastes and firm
heterogeneity in technology. In this paper, we empirically study the welfare effect of second-degree
price discrimination and how competition affects the product variety and eventually the welfare in
the smartphone industry.
The smartphone industry has been one of the fastest growing and most innovative industries
in the world with billions of dollars at stake. Samsung shipped out over 80 million smartphones in
the third quarter of 2013 worldwide, and Apple more than 30 million. The industry has affected
the daily lives of millions of consumers. More importantly, the aforementioned second-degree
price discrimination practice is prominent in the smartphone industry. For example, although
the sales of Samsung’s Galaxy S series consist of 70% of its U.S. smartphone sales in the first
quarter of 2013, there were 16 other Samsung smartphones in the market at the same time. In
2012, a smartphone manufacturer on average has seven products in the market simultaneously.
The average price dispersion among models produced by the same manufacturer (measured in the
standard deviation of the subsidized price,1 averaged across manufacturers) is $47 while the average
price is $116. The average price difference between a manufacturer’s highest-priced product and
the second-highest priced product is $31. Such price dispersion is associated with dispersion on
product quality. Manufacturers offer a wide selection of smartphones. The standard deviation
of product characteristics such as camera resolution and processor speed is around 1/2 of their
respective mean. Manufacturers provide this variety typically by simultaneously offering a few
flagship products and several non-flagship products of lower qualities.
In this paper, we focus on how manufacturers choose the qualities of their non-flagship products
in the U.S. market. We choose to study this particular aspect of product variety for several
reasons. First, the flagship products are usually equipped with the cutting-edge technologies, which
capitalize on the innovation processes of the many upstream industries that are sometimes beyond
the control of the smartphone manufacturers. Secondly, our data are only on the U.S. market,
which accounts for about 10% of smartphone units sold in the global market.2 Most smartphone
manufacturers operate on a global scale. The large investment on developing their flagship products
is driven by the global market conditions. On the other hand, introducing a new smartphone below
the quality frontier is not likely to be a decision that entails heavy investment. More importantly,
these non-flagship products are tailored to the U.S. market rather than sold globally. Having data
on the U.S. market is enough to study the demand of such products, and hence to allow us to study
firms’ decisions on such products.
1
The subsidized price is the average retail price of a smartphone device for consumers who subscribe to a carrier’s
service plans.
2
http://www.gartner.com/newsroom/id/2335616
2
To address our research questions on welfare while capturing the key market characteristics,
we set up a static three-stage structural model. The manufacturers first observe the exogenous
qualities of the flagship products, and choose the number and qualities of the products below the
frontier. The manufacturers set the wholesale prices for all products and sell them to the carriers
in the second stage. We allow carriers to be heterogeneous in their service qualities and net service
profits. Based on the wholesale prices and their characteristics, in the third stage, carriers set the
retail prices and sell the products to the consumers.
Our data come from the Investment Technology Group (ITG) Market Research. This data set
provides information on the price and quantity for all smartphones in the U.S. market between the
first quarter of 2009 and the first quarter of 2013. We choose this particular period because the
carrier fee structure has been relatively stable until March 2013, when T-Mobile started changing
their fee structure, and other major carriers followed suit.3 For every carrier in the U.S. and every
quarter during our sample period, we observe the price and sales of each smartphone sold through
the carrier. We also observe the manufacturer and key specifications of each product, such as
battery talk time, camera resolution, display size, pixel density, processor speed and weight.
We have obtained preliminary estimation results of the demand side of the model (and are
yet to complete estimating the supply side of the model). Our demand estimation quantifies the
consumer preference for the processor speed, screen size, pixel density, camera resolution, weight,
talk time and brands. The quality index we recovered agrees with the general perception that
Apple is the quality leader in the industry. We also find sizable consumer heterogeneity in price
sensitivity. Such consumer heterogeneity motivates firms to offer products of different qualities in
order to extract more surplus through price discrimination, and also to differentiate themselves
from each other in order to soften price competition.
Overall, our demand estimation results seem sensible and consistent with intuitions. With the
constructed quality index, estimated price sensitivity and the distribution of consumers’ tastes for
quality, we estimate determinants of manufactures’ decisions on product proliferation and pricing.
Based on the estimated model, we plan to conduct two sets of counterfactual simulations to
address our research questions. First, to estimate how firms’ price discrimination incentives affect
market outcomes such as price, profit and welfare, we plan to simulate the outcomes corresponding
to a pricing equilibrium where each firm only produces one product, i.e., their highest-quality
product. Through the comparison of the counterfactual equilibrium and the data, we will show the
difference in the price of the highest-quality product of each firm, the difference in firm profits and
eventually the difference in consumer surplus and total surplus. Second, we plan to simulate market
outcomes if a later entrant in our data entered the market earlier. In this simulation, we allow firms
to choose their product profiles (the number of products and the quality of each product) as well
3
T-Mobile launched an “Uncarrier” campaign in April of 2013, which abandoned service contracts and subsidy
for the device. Consumers buy a device outright, or through a device installment plan.
3
as prices. This exercise will allow us to understand how competition affects product variety and
welfare.
This paper contributes to two strands of literature. First, by studying the welfare effect of
second-degree price discrimination, we contribute to a growing empirical literature on price discrimination. The papers that are most closely related to our focus of quality choice and welfare
effects in an oligopolistic competitive market include Leslie (2004), which studies the broadway
theatre ticket pricing, Busse and Rysman (2005), which analyze how the pricing policy varies with
the level of competition, McManus (2007), which considers the distortion of product characteristics induced by the incentive of price discrimination and Cohen (2008), which studies the welfare
effects of quantity discounts. In addition, Borzekowski, Thomadsen and Taragin (2009) show that
increased competition increases the propensity of producers to offer more products and exercise the
second-degree price discrimination. Among these, Cohen (2008) finds price discrimination modestly welfare-enhancing, and Leslie (2004) and McManus (2007) show that the practice has a small
welfare impact. There is also a large theoretical literature on price discrimination, and Stole (2007)
offers an excellent review.
By studying the endogenous product choices of firms and how competition affects these choices,
our paper is also related to the literature of endogenous product choice, examples of which include
Mazzeo (2002), Crawford, Shcherbakov and Shum (2011), Draganska, Mazzeo and Seim (2009),
Chu (2010) as well as Fan (2013).4 Among these papers, Crawford, Shcherbakov and Shum (2011)
is the most closely related to this paper as they also study the welfare effect of product choice due
to a firm’s price discrimination incentives. But different from their paper, which studies the cable
TV industry where markets can be reasonably assumed to be monopoly markets, we study the
oligopolistic smartphone market in the U.S. Our paper is also closely related to Eizenberg (2014).
Unlike Eizenberg (2014), we study the effect of competition, and especially how competition affects
the product variety when firms price discriminate.
The rest of the paper is organized as follows. Section 2 describes our data. Section 3 presents
the structure model of the smartphone market and derives estimating equations. Section 4 explains
the estimation approach and reports preliminary estimation results of demand.
2
Data
2.1
Data Source and Variable Definitions
In this section, we describe our data source and how key variables such as price and quantity are
measured. Our data come from the Investment Technology Group (ITG) Market Research. This
data set provides information on the price and quantity for all smartphones in the U.S. market
4
Other examples in this literature include Seim (2006), Watson (2009), Eizenberg (2014), Crawford and Yurukoglu
(2012) and Sweeting (2013). See Crawford (2012) for a survey of this literature.
4
between the first quarter of 2009 and the first quarter of 2013. For every carrier in the U.S.
and every quarter during our sample period, we observe the price and sales for each smartphone
sold through the given carrier in the given quarter. We also observe the manufacturer and key
specifications of each product such as camera resolution and processor speed.
The price information provided by the ITG for the four major national carriers (AT&T, Verizon,
Sprint and T-Mobile) is the average price for a smartphone device sold to consumers who subscribe
to a carrier’s service. In other words, the price reported for the four major national carriers is
the subsidized price that a carrier charges a consumer who subscribes to its service plan. The
price information for other carriers such as Boost or MetroPCS, however, is unsubsidized, as these
carriers very often only provide prepaid service plans. In addition, these carriers usually serve a
certain regional market only. Therefore, we drop observations of these fringe carriers.5
Our data are about the U.S. market only. While most products in the data are only available
in the U.S., a few products are globally sold. Such products, which we refer to as “hero products”,
are typically premium smartphones that are sold as the same model in multiple countries. For
example, all iPhone models are hero products. Table A.1 in Appendix A lists all hero products in
the industry. Given this data limitation, we focus on the firms’ product proliferation decisions in
this study and take the availability and quality of the hero products as given.
2.2
Summary Statistics and Evidence on Product Proliferation
Our sample consists of 1573 observations, each of which is a product/carrier/quarter combination between 2009Q1 and 2013Q1. There are 18 manufacturers and 282 products all together in
the sample. Table 1 presents the summary statistics on quantity, price and product characteristics.
From Table 1, we can see that the average quarterly sales is 166,000 while the standard deviation
of the quarterly sales is more than twice the mean, suggesting large dispersion in the popularity of
products. There is also a sizable variation of price across observations: the price is 116 dollars on
average, with a standard deviation of 81. Table 1 indicates that such dispersion in quantity and
price coincides with the dispersion in product characteristics. The standard deviations of product
characteristics are about 20% to 60% of the corresponding means. In summary, the market has a
wide variety of products with different prices and different quantities sold. As we will show later,
the variation of products and prices not only exists across products in the market but also exists
within the set of products produced by the same manufacturer.
Table 2 lists the top five manufacturers according to their average quarterly sales of their smart
phones. They are Apple, Samsung, BlackBerry, HTC and Motorola. Among them, Apple is the
undisputable leader in the industry, with an average quarterly sales of more than 6 million. It is
followed by Samsung, whose average sales in a quarter is around 2 million. From Table 2, we can
5
The total market share of these fringe carriers in terms of quantity sold is about 10%.
5
Table 1: Summary Statistics
Variable
Mean Std. Dev.
quantity (1,000)
166.08 360.39
price ($)
115.85 80.95
battery talk time (hours)
6.97
2.72
camera resolution (megapixel) 4.60
2.10
pixel density (pixels/inch2 )
221.12 51.97
processor speed (MHz)
959.96 552.43
2
screen size (inch )
3.44
0.72
weight (gram)
135.19 22.68
Obs
1573
a One product in our sample (BlackBerry 8830) does
Min
0.09
0.05
3
0a
127
200
2.2
89.5
Max
3915.90
404.89
22
13
441
3400
5.54
193
not have a camera.
see that all of these five manufacturers offer multiple products simultaneously. For example, on
average, Samsung has almost 20 products per quarter on average, followed by BlackBerry and HTC
who offer 17 products.
Table 2: List of Top Five Manufacturers
Manufacturer
Headquarters
Apple
Samsung
BlackBerry
HTC
Motorola
US
Korea
Canada
Taiwan
US
a
b
Avg. Number
of Productsa
4.88
19.53
17.29
17.00
12.00
Avg. Retail Priceb
($)
164.58
137.13
159.45
165.39
177.08
Avg. Quarterly Sales
(million)
6.04
2.39
1.94
1.88
1.43
Averaged across quarters.
Our data report the average retail price for each product/carrier/quarter combination. We compute the sales
weighted average of this price across all product/carrier/quarters related to a manufacturer, i.e., across all products
of the manufacturer and across all corresponding carriers and quarters that a product of this manufacturer is sold.
The multiple products offered by a manufacturer are of different qualities and are charged
different prices, as shown by Table 3. In Table 3, we report three dispersion measures for each
manufacturer/quarter combinations. Take price for example. For each manufacturer/quarter, we
compute the standard deviation of the prices of all products available in the given quarter produced
by the given manufacturer.6 We also compute the difference between the highest and the second
highest price as well as the difference between the highest and the lowest price among all products
of the same manufacturer/quarter. We then take the average across manufacturer/quarters, and
report the average value of these three dispersion measures in Table 3. We report the average
across all 199 manufacturer/quarters and across 149 manufacturer/quarters where a manufacturer
has multiple products in a quarter, respectively, in Table 3(a) and Table 3(b). Unsurprisingly, the
6
If a product is available on multiple carriers in a quarter, we take the average of price across carriers first.
6
average dispersion measures are larger when we condition on manufacturer/quarters with more
than one product. For example, on average, the standard deviation of prices among products
produced by the same manufacturer in the same quarter is 47 dollars or 63 dollars depending on
which sample we use, which is more than 1/3 of the average price in the data. In comparison,
the standard deviation of price across all observations is 81 dollars, implying that the within
manufacturer/quarter variation is larger than the across manufacturer/quarter variation. The
average range of the price (again within the same manufacturer/quarter) is as high as 128 dollars
(in Table 3(a)) or 172 (in Table 3(b)). The within manufacturer variation of product characteristics
is also significant. For example, a comparison of the standard deviation in Table 1 and the first
column of Table 3(a) shows that the within-manufacturer standard deviation is always more than
1/3 of the overall standard deviation. The within manufacturer/quarter standard variation in pixel
density consists of even more than 1/2 of the variation across all observations. Overall, while
the summary statistics in Table 1 show the product and price dispersion in the industry, Table 3
provides evidence on such dispersion within a manufacturer, consistent with firms’ incentives to
offer differentiated goods for price discrimination and for product differentiation. In Section 3, we
set up a model where consumers have heterogeneous willingness-to-pay for quality and describe
how firms choose the number of products, the qualities and the prices of their products.
Table 3: Summary Statistics on Quality and Price Dispersion within a Manufacturer/quarter
(a) All 199 manufacturer/quarters
Std. Dev. Highest - Lowest
price ($)
46.97
128.46
battery talk time (hours)
1.21
3.38
camera resolution (megapixel)
1.01
2.45
pixel density (pixels/inch2 )
26.91
68.42
processor speed (MHz)
207.89
523.23
screen size (inch2 )
0.25
0.68
weight (gram)
12.92
34.52
Highest - 2nd highest
30.72
0.91
0.69
16.74
92.67
0.15
8.31
We set the standard deviation to 0 for manufacturer/quarters with a single product.
(b) 149 manufacturer/quarters with multiple products
Std. Dev. Highest - Lowest Highest - 2nd highest
price ($)
62.73
171.56
41.02
battery talk time (hours)
1.62
4.52
1.21
camera resolution (megapixel)
1.35
3.27
0.93
2
pixel density (pixels/inch )
35.93
91.38
22.36
processor speed (MHz)
277.65
698.81
123.77
screen size (inch2 )
0.34
0.91
0.21
weight (gram)
17.26
46.1
11.1
7
3
Model
3.1
Demand
The demand is described by a discrete choice model. In the model, a consumer chooses a
carrier/product combination or an outside option of not buying a smartphone. Let Jct be the set
of products that carrier c offers in period t, and Jt be the union of them across carriers, i.e., the set
of products in the market in period t. The utility that consumer i gets from purchasing product j
from carrier c in period t is assumed to be
uicjt = qj − αi pcjt + fcj (Jt ) + κct + ξcjt + εicjt ,
(1)
where qj is a quality index of product j. It depends on a set of product characteristics xj such
as camera resolution and processor speed as well as a brand dummy. Specifically, we assume that
it is linear in the product characteristics xj : qj = xj β. The price of product j sold by carrier c
in period t is denoted by pcjt . The random price coefficient αi captures consumer heterogeneous
price sensitivity or, equivalently, willingness-to-pay for quality. It is assumed to follow a normal
distribution with mean α and variance σ 2 . In equation (1), fcj (Jt ) is an Ackerberg-Rysman
type term (Ackerberg and Rysman (2005)) that accounts for the crowding in the characteristic
space. Specifically, for any product of brand m (m stands for “manufacturer”), we assume that the
congestion factor fcj (Jt ) depends on three parts:
fcj (Jt ) = θ1 ln (Jcmt ) + θ2 ln (Jmt ) + θ3 ln (Jct ) ,
(2)
where Jcmt is the number of products of brand m that are simultaneously sold by carrier c in period
t, Jmt is the number of products that manufacturer m has in the market in period t, and Jct is the
number of product sold by carrier c in period t.
We include a carrier/year fixed effect in the utility function (1) captures carrier c’s service quality
and service price in period t as well as a general time trend in consumers’ tastes for smartphones.7
We also include a quarter fixed effect to capture seasonality in demand. For simplicity in notation,
we denote these two fixed effects by κct . The term ξcjt is a demand shock. Finally, the error term
εicjt captures consumer i’s idiosyncratic taste, which is assumed to be i.i.d. and follow a Type I
Extreme Value distribution. We normalize the mean utility of the outside option to be 0 so the
utility of the outside option is ui0t = εi0t .
Under the type-I extreme value distributional assumption of εicjt , the market share of the choice
7
In a reduced-form way, it also captures the average switching cost for consumers buying from carrier c. For
example, the term κct for Verizon is decreasing in its opponents’ market share last quarter as the proportion of
consumers who have to pay switching costs to use Verizon’s service is increasing.
8
cj is
Z
scj (q t , pt , ξ t , Jt ) =
1+
exp (qj − αi pcjt + fcj (Jt ) + κct + ξcjt )
dF (αi ) , (3)
P
c0 ∈C
j 0 ∈J 0 exp qj 0 − αi pc0 j 0 t + fcj (Jt ) + κc0 t + ξc0 j 0 t
P
c t
where C denotes the set of carriers, q t = (qj , j ∈ Jt ) is a vector of the quality indices of all
products in the market, and pt and ξ t are analogously defined as pt = (pcj , c ∈ C, j ∈ Jct ) and
ξ t = (ξcjt , c ∈ C, j ∈ Jct ), respectively.
3.2
Supply
On the supply side, we model firms’ decisions on the number of products, and the qualities and
the prices of their products. As mentioned, we take the availability and the quality of the hero
products as given. Thus, our model describes firms’ decisions on the number and the qualities of
their non-hero products. In our model, firms choose the prices of all products, hero products or not.
We make this modelling choice because the key feature of a hero product is that its specifications do
not vary across countries, but its price does. Therefore, modelling firms’ quality decisions on their
frontier hero products would require us to have data on the worldwide market. However, studying
the pricing decision in the U.S. does not impose such a data requirement. We also treat carriers’
service plans (their features and their prices) as exogenous. We do so for two reasons. First, we
do not have data on carriers’ service plans. It is also difficult to compare service plans provided
by different carriers as they differ in many dimensions. Second, and more importantly, a carrier
typically does not redesign its service plans when a new phone is introduced to the market. That
is, it is plausible to assume that carriers’ service plans are exogenous to firms’ product and price
choices.
The supply side of the model is described by a static three-stage game. In the first stage,
manufacturers choose the number and the qualities of their products. Next, manufacturers choose
the wholesale prices charged to the carriers. Finally, carriers chooses the retail prices. We describe
these three stages backwards.
3.2.1
Carrier Decision on the Retail Price
At this stage, carriers observe the set of products available on each carrier, the quality of them
and the wholesale prices. They also observe the demand shock and choose the retail prices pcjt
to maximize the total profits given the wholesale price wcjt charged by product j’s manufacturer.
Suppose that the profit that carrier c obtains through its service is bct per consumer, which is the
difference between the service fee and the marginal cost of serving one additional consumer on
carrier c’s network. As mentioned, we treat this profit margin as exogenous. Carrier c’s total profit
margin for each unit of a product sold is therefore pcjt + bct − wcjt . Let w̃cjt = wcjt − bct . Carrier
9
c’s profit maximizing problem is
max
X
pcjt ,j∈Jct
N scj (q t , pt , ξ t , Jt ) (pcjt − w̃cjt ) ,
(4)
j∈Jct
where N is the market size. The first-order conditions written in the vector form is as follows:
w̃ct = pct +
Dsct
Dpct
−1
sct ,
(5)
where w̃ct = (w̃cjt , j ∈ Jct ), pct = (pcjt , j ∈ Jct ) and sct = (scj , j ∈ Jct ). We denote the equilibrium
of this stage by p∗cjt (w̃t , q t , ξ t , Jt ), where w̃t = (w̃cjt , c ∈ C, j ∈ Jct ).
3.2.2
Manufacturer Decision on the Wholesale Price
We assume that the marginal cost of a product depends on the difference between the quality
and the quality frontier at the time (denoted by q̄t = maxj∈Jct qj ), and a carrier/product/timespecific shock. Marginal costs may vary across carriers because different radio technologies are
used for products sold by different carriers. Moreover, carriers sometimes require manufacturers
to preload different softwares on a smartphone, which may come with different costs. Specifically,
we assume that the marginal cost is mccjt = γ0 + γ1 (qj − q̄t ) + ωcjt . Let m̃ccjt = mccjt − bct , and
γ̃ct = γ0 − bct . With these notations, we re-write the marginal cost as
m̃ccjt = γ̃ct + γ1 (qj − q̄t ) + ωcjt .
(6)
The profit that manufacturer m gets for its product j sold on carrier c is therefore
II
πcj
(w̃t , q t , ξ t , ω t , Jt ) = (w̃cjt − m̃ccjt ) N scj (q t , p∗t (w̃t , q t , ξ t , Jt ) , ξ t , Jt ) ,
(7)
where the superscript II stands for “stage 2” of the game. At this stage, given its products
in the market (denoted by Jmt ), a manufacturer chooses the wholesale prices, or equivalently,
P
II (w̃ , q , ξ , ω , J ).
(w̃cjt , cj ∈ Jmt ) to maximize its profit cj∈Jmt πcj
t t t
t
t
The first-order condition is

scjt +
X
w̃c0 j 0 t − m̃cc0 j 0 t 
c0 j 0 ∈Jmt
X
c00 j 00 ∈Jt
∂p∗c00 j 00 t

∂sc0 j 0 t
 = 0,
∂pc00 j 00 t ∂ w̃cjt
(8)
which implies the following estimation equation
w̃cjt + ∆−1 smt cjt = γ̃ct + γ1 (qj − q̄t ) + ωcjt ,
10
(9)
where smt = (scj , cj ∈ Jmt ) and ∆ is a |Jmt | × |Jmt | matrix, a typical element of which is
∗
P
∂sc0 j 0 t ∂pc00 j 00 t
∗ (q , ξ , ω , J ) be the equilibrium wholesale price that the man. Let w̃cjt
t
t
t t
c00 j 00 ∈Jt ∂p 00 00 ∂ w̃cjt
c j t
ufacturer of product j charges carrier c in period t minus bct .
3.2.3
Manufacturer Decision on Products
We assume that the availability and qualities of the hero products are exogenously determined
before the manufacturers choose the qualities of other products. As explained earlier, the hero
products are sold worldwide, and their quality decisions are driven by many factors not related to
the U.S. market, for which we do not have data. Hero products are also the flagship products that
are typically at the technology frontier of a manufacturer. Their quality are therefore affected by the
innovation processes of the many upstream industries that are sometimes beyond the control of the
smartphone manufacturers, in addition to the economic tradeoffs studied in the paper. Therefore,
we focus on the manufacturers’ decisions on non-hero products for given availability and qualities
of the hero products.
At this stage of the model, manufacturers choose the number and qualities of (non-hero) smartphones for production in every period. Specifically, we discretize the quality of a product into
L bins and assume that manufacturers’ product proliferation decisions are in fact the number of
products in each quality bin. We restrict the number of products in each bin to be between 0 and
K. In estimation, we will choose a large L so that there is only one product in each quality bin in
the data. In other words, our discretization in the estimation is so fine that it does not affect the
estimate of the variable profit function.8
Since non-hero products are behind the technology frontier, we assume that there is no sunk
cost of introducing a new non-hero product. There is, however, a fixed cost of production for every
product. We assume that this fixed cost varies across manufacturers and depends on the quality
of a product. Let λml be the average fixed cost for manufacturer m producing a product in the
lth bin. Let νmlkt be the fixed cost shock for a product k (k = 1, ..., K) in the lth bin in period
t. Given the dependency of the fixed cost with respect to the product’s quality and the shock, we
denote the fixed cost of manufacture m producing product j by Fm (qj , νmjt ), which is the sum of
λml and the fixed cost shock. In other words, if the quality of a product is in the lth quality bin,
its fixed cost of production is
Fm (qj , νmjt ) = λml + νmjt ,
(10)
where νmjt takes one of the values of νml1t , ..., νmlKt . (With an abuse of notation, we denote the
shock by νmjt ).
In making the product proliferation decision, a manufacturer decides the set of existing products
8
This discretization is necessary so that we only need a finite number of fixed cost shocks (see below) in the model
to explain the data.
11
to keep in its product profile and a set of new products to add to its product profit. We assume
that a manufacturer makes the product proliferation decision after observing shocks to its fixed
cost,9 but before the demand shocks and marginal cost shocks are realized. In other words, the
manufacturer considers the tradeoff between the fixed cost of production and the expected variable
profit. The expectation is taken over the demand shocks and marginal cost shocks. To reduce the
dimension of the integral, we assume that manufacturers use the last-period demand shocks and
the last-period marginal cost shocks for the existing products to form the expectation. Under this
assumption, the expectation is taken only over the shocks of the new products. We denote the
realized demand shocks of the carried-over products in the last period by ξ old
t−1 and the demand
shocks to the new products by ξ new
. We also denote the respective marginal cost shocks by ω new
t
t
and ω old
t−1 . The relevant profit function is

I
old
πmt
q t , Jt , ξ old
t−1 , ω t−1 , ν t

= Eξnew
,ω new
t
t

X
II
new

πcj
w̃∗t , q t , ξ new
, ξ old
, ω old
t
t−1 , ω t
t−1 , Jt
cj∈Jmt
−
X
Fm (qj , νmjt ) .
(11)
j∈Jmt
Nash equilibrium implies that given competitors’ product portfolios at the equilibrium, any
deviation from manufacturer m’s equilibrium product portfolio would generate a lower profit for
m. For example, manufacturer m’s profit would be lower if an existing product is removed. Let
q t \qj be the qualities of all products except product j by manufacturer m. Then, such an inequality
is
I
old
I
old
old
πmt
q t , Jt , ξ old
for any j ∈ Jmt .10
t−1 , ω t−1 , ν t ≥ πmt q t \qj , Jt \j, ξ t−1 , ω t−1 , ν t
(12)
Similarly, we also consider manufacture m’s counterfactual product profile when a new product in
quality bin l is added to its profile, the resulting inequality identifies the lower bound for λml :
I
old
I
old
old
πmt
q t , Jt , ξ old
where j 0 is added to Jmt .
t−1 , ω t−1 , ν t ≥ πmt q t ∪ qj0 , Jt ∪ j0, ξ t−1 , ω t−1 , ν t ∪ νj0
(13)
To reduce the number of fixed cost parameters (λml ) to be estimated, we assume that the fixed
costs take on four values, depending whether the product is made by a major or minor manufacturer,
and of high or low quality with respect to the manufacturer’s frontier. To obtain a consistent set
estimate of the fixed costs, we follow Eizenberg (2014) and assume that the fixed cost of product
line j, Fm (qj , νmjt ) is bounded by the maximum difference in profit for the single product deviation
9
The manufacturers also observe the carrier-period specific fixed effects in demand (κ) and in the marginal cost
(γ̃).
10
old
old
Note that for expositional simplicity, we keep the last three arguments (ξt−1
, ωt−1
, µt ) in the right-hand side of
the inequality unchanged. But in fact µt should be µt \µj as µj is not needed to compute the profit when product j
old
old
old
old
is removed. Similarly, (ξt−1
, ωt−1
) should be (ξt−1
\ξj , ωt−1
\ωj ) if j is also in Jmt−1 .
12
in Equations (12) and (13) across all deviations and all manufacturers in the same period.
4
Estimation
4.1
Instruments and Estimation Procedure
We estimate the parameters on the demand side and the parameters in the marginal cost
function using the Generalized Method of Moments. The estimation of the random-coefficient
random model is rather standard. We use the typical instrumental variables used in the literature
such as the product characteristics of the products produced by the same manufacturer and other
manufacturers. We also include the characteristics of the products on the same and other carriers
as instruments because of the particular structure of the US smartphone market. The estimates of
the parameters in the marginal cost function are obtained using moment conditions based on the
first-order condition with respect to the wholesale price (equation (9)). We estimate the fixed cost
parameters using inequalities (12), (13).
4.2
Preliminary Estimation Results
We have obtained preliminary estimation results for the demand side of the model and are yet
to complete the estimation for the supply side of the model. The estimated demand parameter
values are reported in Table 4. The estimation results largely agree with the intuition. Consumers
on average favor smartphones with high camera resolution, long talk time and large screens. Specifically, for an average consumer, a decrease in camera resolution by 1 megapixel is equivalent to
an increase in price by 8 dollars. Similarly, a decrease in the talk time by one hour is equivalent
to an increase in price by 4 dollars. The estimates of congestion show evidence on crowding. Our
estimates also confirm sizable consumer heterogeneity in price sensitivity, or willingness to pay for
quality. The estimated standard deviation of the random coefficient is 2.02, while the estimated
mean is -4.31. Both are precisely estimated.
To see the own and cross-price elasticities implied by these estimates, we compute and report
the elasticities in July 2012 across the 5 best-selling models on AT&T in Table 5. These five models
are iPhone 3GS, iPhone 4, iPhone 4s, Vivid (by HTC) and Galaxy S III (by Samsung), sorted by
their availability dates. From Table 5, we can see that, unsurprisingly, the own price elasticities are
larger than the cross price elasticities. Among the three iPhone models, a price change in iPhone
3GS has almost no effect on the sales of competing products. A 10% price decrease by iPhone 4s,
however, can depress the sales of its major rival Galaxy S III by as much as 2.5%, or the sales of
the older model iPhone 4 by 1.9%.
The estimation of the coefficients of the quality characteristics allows us to construct the quality
index for each product. Table 6 reports the elasticities of quality for fixed prices, again for the top
13
Table 4: Preliminary Estimate Results: Demand
Parameter
Price ($100)
mean
std. dev.
Estimate
Std. Error
α
σ
4.31???
2.02???
1.20
0.57
Quality Characteristics
battery talk time (h)
camera resolution (megapixel)
pixel density (100 pixels/inch2 )
processor speed (1000MHz)
screen size (inch)
weight (100 grams)
manufacturer fixed effect
carrier fixed effect
year fixed effect
quarter fixed effect
β1
β2
β3
β4
β5
β6
yes
yes
yes
yes
0.18???
0.36???
1.24???
0.23
0.75??
-0.09
0.06
0.1
0.25
0.29
0.38
0.36
Congestion
log(products by same carrier)
log(products by same manufacturer)
log(products by same carrier/manufacturer)
θ1
θ2
θ1
-1.85???
0.45???
-1.22??
0.63
0.19
0.62
???
indicates 99% level of significance,
??
indicates 95% level of significance.
5 selling products on AT&T in July 2012, using the estimated quality index. Across all five models,
we see that a one percent increase in the quality index corresponds to around 12% of sales increase.
A 7.7 percent increase in quality index for iPhone 4, which brings its quality to iPhone 4s, would
roughly double the sales. We indeed see in the data that iPhone 4s’ sales in its quarter of launch
is about 2 times the sales of iPhone 4.
To see the evolution of smartphone quality over time, we plot the maximum quality and the
median quality of all products in a quarter over time in Figure 1. The quality frontier in the Figure
is driven by the iPhone products. The frontier experiences a discrete jump whenever a new iPhone
product is introduced. Other firms have managed to stay at a constant distance behind the frontier.
The overall quality as reflected in the median quality has risen over time.
Table 7 shows quality dispersion within products of the same manufacturer. We report the
difference between the highest and lowest qualities, the difference between the highest and the
second highest qualities, and the standard deviation in quality of products by a manufacturer,
all averaged across quarters. From the Table 7, we can see that while Samsung and LG sell many
different products, Apple also manages to cover a wide quality spectrum by selling the older models
alongside its latest model.
Overall, our demand estimation results seem sensible and in line with intuitions. With the
14
Table 5: Own and Cross Price Elasticities (%)a
iPhone 3GS
iPhone 4
iPhone 4s
Vivid
Galaxy S III
a
iPhone 3GS
-0.38
0.00
0.00
0.00
0.00
iPhone 4
0.06
-2.68
0.05
0.08
0.04
iPhone 4s
0.08
0.19
-3.43
0.15
0.25
Vivid
0.01
0.01
0.00
-2.21
0.00
Galaxy S III
0.02
0.05
0.07
0.04
-3.38
July 2012, top 5 selling models on AT&T
Table 6: Semi-elasticity of Quality (%)a
iPhone 3GS
iPhone 4
iPhone 4s
Vivid
Galaxy S III
a
iPhone 3GS
11.91
-0.04
-0.02
-0.05
-0.02
iPhone 4
-0.29
13.96
-0.39
-0.41
-0.35
iPhone 4s
-0.22
-0.63
14.10
-0.49
-1.51
Vivid
-0.04
-0.05
-0.04
11.33
-0.03
Galaxy S III
-0.04
-0.13
-0.34
-0.10
12.94
July 2012, top 5 selling models on AT&T
constructed quality index, estimated price sensitivity and the distribution of consumers’ taste for
quality, we study manufacturers’ decisions on product proliferation and pricing.
Table 7: Quality Dispersiona
Manufacturer
Apple
Samsung
LG
Motorola
HTC
BlackBerry
a
Highest - Lowest
Highest - 2nd Highest
Std.Dev
2.6
5.1
3.3
4.5
4.3
3.2
0.8
0.6
0.7
1.0
0.6
0.2
1.2
1.5
1.0
1.4
1.3
1.1
measured in constructed quality index and averaged across quarters
15
Figure 1: Smartphone Quality over Time
Quality Evolution
18
16
Industry Frontier
Median Quality
Quality Index
14
12
10
8
6
Q1 2009
Q1 2010
Q1 2011
Time
16
Q1 2012
Q1 2013
References
Ackerberg, Daniel A and Marc Rysman (2005), “Unobserved product differentiation in discretechoice models: estimating price elasticities and welfare effects.” RAND Journal of Economics, 36,
1–000.
Borzekowski, Ron, Raphael Thomadsen, and Charles Taragin (2009), “Competition and price
discrimination in the market for mailing lists.” QME, 7, 147–179.
Busse, Meghan and Marc Rysman (2005), “Competition and price discrimination in yellow pages
advertising.” RAND Journal of Economics, 378–390.
Chu, Chenghuan Sean (2010), “The effect of satellite entry on cable television prices and product
quality.” RAND Journal of Economics, 41, 730–764.
Cohen, Andrew (2008), “Package size and price discrimination in the paper towel market.” International Journal of Industrial Organization, 26, 502–516.
Crawford, Gregory (2012), “Accommodating endogenous product choices: A progress report.”
International Journal of Industrial Organization, 30, 315–320.
Crawford, Gregory S., Oleksandr Shcherbakov, and Matthew Shum (2011), “The welfare effects
of monopoly quality choice: Evidence from cable television markets.” working paper, University
of Warwick.
Crawford, Gregory S. and Ali Yurukoglu (2012), “The Welfare Effects of Bundling in Multichannel
Television Markets.” American Economic Review, 102, 643–85.
Draganska, Michaela, Michael Mazzeo, and Katja Seim (2009), “Beyond plain vanilla: Modeling
joint product assortment and pricing decisions.” Quantitative Marketing and Economics, 7, 105–
146.
Eizenberg, Alon (2014), “Upstream innovation and product variety in the U.S. home PC market.”
Review of Economic Studies, 81, 1003–1045.
Fan, Ying (2013), “Ownership Consolidation and Product Characteristics: A Study of the US
Daily Newspaper Market.” American Economic Review, 103, 1598–1628.
Leslie, Phillip (2004), “Price discrimination in broadway theater.” RAND Journal of Economics,
520–541.
Mazzeo, Michael (2002), “Product choice and oligopoly market structure.” The RAND Journal of
Economics, 33, 221–242.
17
McManus, Brian (2007), “Nonlinear pricing in an oligopoly market: The case of specialty coffee.”
The RAND Journal of Economics, 38, 512–532.
Seim, Katja (2006), “An empirical model of firm entry with endogenous product-type choices.”
RAND Journal of Economics, 37, 619–640.
Stole, Lars A (2007), “Price discrimination and competition.” Handbook of industrial organization,
3, 2221–2299.
Sweeting, Andrew (2013), “Dynamic product positioning in differentiated product markets: The
effect of fees for musical performance rights on the commercial radio industry.” Econometrica, 81,
1763–1803.
Watson, Randal (2009), “Product variety and competition in the retail market for eyeglasses.”
Journal of Industrial Economics, 57, 217–251.
A
Hero Products
Table A.1 lists all hero products in the industry by manufacturers.
Table A.1: Hero Products in the Industry
Manufacturer
Apple
Blackberry
HTC
LG
Motorola
Samsung
Model
all iPhone models
Z10, Q10, Z30
HTC One M8
G2
Moto X
all Galaxy S models
18