Kyoto University,
Graduate School of Economics
Discussion Paper Series

Delineating zero-price markets with network effects:
An analysis of free messenger services

Akihiro Nakamura, Takanori Ida

Discussion Paper No. E-21-002

Graduate School of Economics
Kyoto University
Yoshida-Hommachi, Sakyo-ku
Kyoto City, 606-8501, Japan

July, 2021

Delineating zero-price markets with network effects:
An analysis of free messenger services
Akihiro Nakamura1
Takanori Ida2
Abstract: Billions of users worldwide use digital zero-price services every day.
This study proposes a market definition method for digital zero-price services,using the messenger service as an example. We employ the small but significant
non-transitory increase in cost (SSNIC) test, which is an improved version of thesmall but significant non-transitory increase in price (SSNIP) test, and conduct
conjoint analysis while considering the network effect, a characteristic of digital
services. Our results show that the price elasticity of demand is 0.628 and the criticalmarkup ratio is 1.492–1.542 when only the price effect is considered. When the
direct network effect is considered, the price elasticity of demand is 1.728 and thecritical markup ratio is 0.479–0.529. Furthermore, when considering a two-sided
market with indirect network effects, the price elasticity of demand is 2.162 and thecritical markup ratio is 0.363–0.413. Thus, the price elasticity of demand for freemessenger services is higher when the network effects and two-sided markets are
considered.
Keywords: Freemium services, Market definition, Competitive policy, Conjoint
analysis
JEL Classification: L13, L52, L41, L86, and L96

1

Faculty of Economics, Chuo University, 742-1 Higashinakano, Hachioji, Tokyo, 1920393,
Japan, akihiro.00x@g.chuo-u.ac.jp
2
Graduate School of Economics, Kyoto University, Yoshida, Sakyo, Kyoto 606-8501, Japan,
ida@econ.kyoto-u.ac.jp1

1.

Introduction

In the digital marketplace, free or zero-price services frequently use the business model
called "freemium," in which basic services are provided for free and premium services areoffered for a fee (Anderson, 2009). Google has been dominating the digital advertising market
by offering its search engine and applications for free, with Facebook following its lead inproviding social networking services. The rationale for offering free services is that themarginal cost of providing digital services is close to zero. However, because of fixed costs
such as R&D and management, these companies will incur losses if the service is provided forfree.
Why do companies offer zero-price services in the digital marketplace? First, humans havea behavioral tendency known as the "free bias" (Gal and Rubinfeld, 2015), meaning that
consumers find special utility in free services. In return, companies offering zero-price services
collect consumers' personal information. Second, the accumulating number of consumers who
use a free service creates a network effect in which consumer utility increases with the size ofthe market. Platforms that provide a place for transactions in the digital marketplace utilize the
network effect on the free-market side to charge the other market.3 In addition, mega-platforms,
such as Google and Facebook, have been acquiring new tech companies to strengthen their
dominant position in the market. These mergers, often referred to as "killer acquisitions," havebecome a competition policy consideration.
Zero-price services represent a difficult problem for competition authorities. The traditional
antitrust policy uses the small but significant non-transitory increase in price (SSNIP) test to
define the market.4 The SSNIP test assumes a 5% increase in price over a year; however, a 5%
increase in price at zero is still zero. Therefore, we cannot use the SSNIP test to define a market
for digital services that are provided for free.5
To define a zero-price market, several alternatives to the SSNIP test have been proposed.
One approach is the small but significant non-transitory decrease in quality (SSNDQ) test,
which uses a decrease in quality instead of an increase in price. Hartman et al. (1993) use small
price substitutability but large quality substitutability between different types of diagnostic
imaging equipment industries for market definition. However, the SSNDQ test has some
limitations. For instance, it is difficult to conduct SSNDQ tests for all the different types ofquality. Another option is the small but significant non-transitory increase in cost (SSNIC) test,
which uses an objective or subjective increase in the cost borne by the consumer. Newman(2015, 2016) argues that consumers are willing to provide private data to platforms for free,
and thus zero-price services are not truly free, given their real cost burden. Evans (2008) points
3

Rochet and Tirole (2003) and others have theorized such business models as "two-sided
markets." For market delineation in a two-sided market, see Evans (2003), Filistrucchi et al.
(2014), and Kawahama and Takeda (2017).
4
The SSNIP test defines the narrowest market as one in which a single firm can sustainably
raise prices or otherwise exercise market power (Werden, 2003).
5
Not all economists are in favor of SSNIP testing. Among them is Kaplow (2010, 2015) who
says that market definition is not based on economic theory and does not make sense forcompetition policy.
2

out that personal information, collected by such platforms, contains substantial value because
it exposes the "attention" and "privacy" of consumers. If we regard the provision of such
personal information and the risk of personal information leakage as the hidden cost burden ofzero-price services, market definition by SSNIC test can be considered operationally feasible.6
In this study, we apply the SSNIC test to define a "messenger service" usually provided freeof charge. Additionally, conjoint analysis, a stated preference method (SPM), is used tomeasure the price elasticity of demand for zero-price services. 7 For the analysis of priceelasticity of demand, it is necessary to measure the change in the quantity demanded in response
to a 5% increase in price, which requires current price information as reference. Here, we use
the hidden cost that consumers pay for zero-price services as the reference price, and focus on
the fact that consumers must provide personal information to use the services for free. Many
zero-price services, including messenger services, bundle basic components such as messenger
applications with ancillary services such as digital advertising and payment services to recover
the overall cost. In summary, as the provision of personal information entails a substantial
burden cost for users, we conduct a conjoint analysis to evaluate this cost in monetary terms.
As Hensher et al. (2005) explain, a conjoint analysis is a method of analyzing statedpreference, and unlike revealed preference data obtained from market transactions, datacollection is conducted by asking respondents to express their subjective evaluation of services
that are not directly traded in the market, such as new products not yet released. Using statedpreference data has many advantages over revealed preference data. In a virtual experimentbased on the SPM, the analyst can ensure the diversity of attributes, including price, in theexperimental design. In addition, multicollinearity between each attribute variable can be
avoided by adopting an orthogonal experimental design. Thus, as suggested by Newman (2016),
SPMs have become a powerful tool as a thought experiment for zero-price market delineation.
This study uses web survey data collected in February 2019. The survey results are obtainedusing conjoint analysis, where users of free messenger services are asked whether they willcontinue to use the service if it is to be paid for. As mentioned earlier, the SSNIC approach isapplied to measure the price elasticity of demand for free messenger services. Since messenger
services are affected by network effects, we first estimate the direct network effect, whichmeans that if the number of users decreases due to pricing of service, the utility users receivefrom the service will also decrease. Furthermore, free messenger services are viable as abusiness model because they represent a two-sided market. The profitability of the paired
services of the messenger service, such as advertising and payment services, depends on thenumber of users. In a two-sided market, if the number of users decreases due to price increasein one market, the value of the other market will decrease through indirect network effects.
6

Kawaguchi et al.’s (2021) pioneering study uses the SSNIC test to propose a new model ofimperfect competition for ad-sponsored media that can sell "free" products for merger analysis
applicable to the mobile app industry.
7
Prior studies dealing with market definition and mergers in two-sided markets include card
payments (Emch and Thompson, 2006) the Google/DoubleClick case (Evans and Noel, 2008)
newspapers (Filistrucchi et al., 2012; Affeldt et al., 2013; Cayseele and Vanormelingen, 2019)the radio (Jeziorski, 2014) and mobile apps (Kawaguchi et al., 2021).
3

Under certain assumptions, this study also attempts to simulate the repercussion on the freemarket caused by the decrease in revenues from the other market.
Evaluating the subjective cost of providing personal information to a free messenger service,
we find that the real cost burden is JPY 706.7 (USD 7.07, assuming JPY 100 = USD 1). Using
this amount as a starting point, we calculate the extent to which a 5% surcharge would reduce
the probability of choice. First, we perform a one-sided market demand substitutability analysis,
focusing only on the messenger service market. We obtain a price elasticity of demand of 0.628.
Using this estimate, we calculate the critical markup ratio, which ranges from 1.492 (for profit
maximization) to 1.542 (for constant revenue). Next, when calculating the price elasticity ofdemand, we take into account the direct network effect, where the value of a service increases
as the number of users increases. As a result, the price elasticity of demand considering thedirect network effect is 1.728. The critical markup ratio ranges from 0.479 (for the profit
maximization case) to 0.529 (for the constant revenue case). Finally, in the case of a two-sided
market, as we consider paired services on opposite sides, the calculation of price elasticity takes
into account indirect network effects in addition to direct network effects. As a result, the priceelasticity of demand considering the indirect network effect is 2.162. The critical markup ratio
ranges from 0.363 (for profit maximization) to 0.413 (for constant revenue). Thus, in this study,
we calculate the price elasticity of demand, owing to the actual cost borne by the user of a zeroprice service and the 5% surcharge, by adding the direct and indirect network effects. Usingzero-price messenger services as an example, this study is a pioneering attempt to define themarket for digital zero-price services considering direct and indirect network effects and twosided markets.

2. Data
2.1 Online survey
The survey was conducted in late February 2019. Before conducting the conjoint analysis,
respondents were asked if they were using messenger services, and the subsequent conjoint
analysis was limited to messenger users. The total number of respondents to the online survey
was 1,225. The number of valid responses was 908 because respondents who did not use themessenger service daily, such as those who had installed the messenger service but notregistered any friends, were excluded. For analysis, we focused on the 908 respondents who
used the messenger service.
The survey was outsourced to an internet research company, and the respondents wererandomly selected from among the company's respondent monitors. A summary of the sample
is presented in Table 1. The survey questionnaire was developed to reflect the distribution of
the population by gender and age in Japan. While respondents were selected based on theirlevel of use of messenger services, there was enough variation for analysis by gender and age
within the valid sample. However, while we were able to obtain a certain number of responses
for both males and females up to the age of 59, there were fewer responses from the older age
groups. Therefore, the model estimation that follows is weighted based on population
4

distribution in Japan and messenger service usage rate by gender and age. 8 We also
investigated usage trends in messenger services, with LINE being the most popular application,used by approximately 86% of respondents, followed by Facebook Messenger, used by only
4%. LINE is also the most popular application in terms of number of active users in a month,used by approximately 93% of the respondents, followed by Twitter DM, used byapproximately 18%.
Table 1 shows the descriptive statistics of the variables used in the subsequent analysis. In
terms of personal information provided by the respondents, e-mail address and phone number
were the most common, at approximately 76% and 71%, respectively. More than 60% of the
respondents provided their real names and ages. When asked about the subjective probability
that their information would be leaked by their messenger service provider within a year,
approximately 23% of respondents believed that there was a 50% chance, 46% believed thatthe probability was less than 10%, 19% believed that it was less than 1%, and 12% believed
there would be no information leakage. Regarding the number of friends registered withmessenger services, approximately 17% of the respondents had five or fewer friends, 34% had
10 or fewer friends, and 22% had between 10 and 25 friends. This means that more than halfof the respondents had fewer than 25 friends.
Table 1 near here
The attributes of registered friends were considered next. Eight categories of friend attributes
were selected: "family members living together," "family members or relatives living apart,""private friends currently in a relationship," "private friends who were in a relationship in thepast but are not in a relationship now," "friends or acquaintances from work or school who are
currently in a relationship," "friends or acquaintances from work or school who were in a
relationship in the past but are not in a relationship now," "lovers," and "others." As seen from
Table 1, the largest number of respondents (about 88%) registered "private friends currently ina relationship," followed by "family members living together" (about 70%). By examining the
average social distance (the extreme right column of Table 1), we consider that the smaller thevalue, the more important is the friend attribute in each category to the respondent (closer social
distance). The social distance to "family members living together," the second-largest share ofregistrants, is the smallest, and the social distance to "family members or relatives living apart,"
the fourth largest share of registrants, is the second smallest. The details of the definition ofsocial distance are explained in subsection 3.1.

2.2 Conjoint analysis

8

The weights used in the estimation were calculated from the population distribution data forJapan in FY2019 (Ministry of Internal Affairs and Communications, Statistics Bureau HP,
http://www.stat.go.jp/data/jinsui/2019np/index.html). Messenger services’ usage rates bygender and age were obtained from the screening of this survey.
5

The definition of a market requires information on the price elasticity of demand and themarginal cost of a hypothetical monopolist. As mentioned earlier, this study uses conjoint
analysis to measure the price elasticity of demand for zero-price services. We consider the
personal information that users provide to use a free messenger service as the real burden costthat they pay. Therefore, in our conjoint analysis, the provision of personal information and therisk of leakage are included as attributes.
In the conjoint analysis, we set a hypothetical question on whether the respondents will stopusing the messenger service if a fixed monthly fee is imposed on the messenger service whosebasic service is currently free. As shown in Figure 1, we present the respondents with two usage
plans and ask them to choose either to continue using the messenger service under one of theplans or to stop using the messenger service altogether.
Figure 1 near here
The conjoint card has the attributes of "monthly fee," "need for personal information input,"and "risk of information leakage within one year," as well as "circumstances under which otherusers stop using the service." The attributes of the necessity of personal information input andinformation leakage risk are set to determine the cost of the SSNIC test. The monetaryevaluation of these two attributes represents the actual burden cost paid by the free messenger
service users. The SSNIC test adopts the attribute of people who stop using the hypotheticalmessenger service for free or at a fee, after considering the direct network effect. In addition,
we insert the monthly usage fee as an attribute to evaluate the inconvenience of entering
personal information and the risk of information leakage as the numéraire in terms of monetary
value.
The attributes and their levels are listed in Table 2. To ensure that the combination of
attributes and their levels is appropriate for this study, two pre-test surveys were conducted:
the first was conducted on 200 respondents in mid-January 2019, and the second on 150
respondents in mid-February 2019. Consequently, the attributes and levels employed in thissurvey were determined based on the results of the pre-test.
Table 2 near here
We pre-tested several conjoint questions on the fee level, including as high as JPY 3,000.
The results of the pre-test showed that most respondents stopped using the service when theprice exceeded JPY 1,000, yet they hardly responded to small price increases of approximately
JPY 100. Therefore, for this survey, we decided to set the lower limit of the fee level at zeroyen, which implies free service, the lower limit of the priced service at JPY 100, with an upper
limit at JPY 1,000, and a level of JPY 500 in between.
Regarding the probability of information leakage, the following arrangements were made.
In the pre-tests, respondents were asked to estimate the likelihood that their information would
be leaked within one year, including the provision of information to third parties without theirconsent. In response to this question, more than 30% of the respondents thought that there was6

a 50% or greater probability that some kind of information leakage would occur. There werealso four options below 50%: 0%, 1%, 10%, and 30%, and a certain number of respondents
were distributed across each option. Based on these pre-test results, the conjoint analysis was
set to four levels of 0%, 1%, 10%, and 30%, as shown in Table 2.
Next, we conducted a pre-test survey on personal information provided to application
providers for service use, such as account information of social networking services (SNS) andpersonal information that may cause trouble if leaked. The same questions were used in thissurvey (see Table 1). Although there is a wide range of personal information provided, thevariation in attribute levels for conjoint analysis should be considered so that respondents caneasily recognize the differences. Therefore, in this analysis, we used three categories of
personal information as attribute levels on the conjoint card, taking into account the pre-test
responses. Specifically, we set "real name and address" as basic personal information, "e-mailaddress and phone number" as secondary personal information, and "credit card and bankaccount information" as personal information related to finance. Furthermore, assuming thatthe provision of "real name and address" information is included in personal information
provision, we created the following four levels: "real name and address" only, "real name andaddress" + "e-mail address and phone number," "real name and address" + "credit card andbank account information," and “all three types of personal information.” The fifth level was"none" (ID and password settings only), or not requiring the provision of any other personal
information.
The analysis considers the importance of the social relationship between those who stopusing the service after it becomes fee-based and the respondents. On the one hand, even if those
who rarely exchange messages stop using the service, the decrease in the utility of the service
user is small. On the other hand, if those who frequently exchange messages with the
respondents stop using the service, the decline in the users' utility will be large. Specifically,as shown in Table 1, there is a significant decrease in the utility of the service for "family
members living together," "family members or relatives living apart," "private friends whocurrently exchange messages," "private friends who exchanged messages in the past, but not
so much at present,” “friends or acquaintances at work or school who exchange messages atpresent,” and “friends at work or school who exchanged messages in the past, but not so muchat present.” In addition to the seven categories in which users in each category stop using themessaging service, we added a category where no one stops using messaging, generating a totalof eight levels. By specifying the attributes of the recipients of the messages, we measured themarginal decline in users' utility according to the corresponding categories.
Consequently, using the results of the pre-test as a reference, 20 cards were prepared by theorthogonal experimental design method, with each conjoint card considering only the main
effect of each attribute. These 20 cards were randomly combined to prepare 10 multiple-choicequestions as shown in Figure 1. All respondents answered the same 10 questions.

3. Estimation model and results
3.1 Model
7

Since the preferences of each consumer are considered to be heterogeneous, the randomparameter logit (RPL) model is used to analyze the data.9 Additionally, since the distributionof the parameters is unknown at the time of the RPL model estimation, certain parametricprobability distributions are assumed for the estimation.
The stochastic utility function in this study is defined as a linear model using the following
equation.
𝑈𝑖𝑗𝑡 = 𝛼𝑈𝑆𝐸,𝑖 + 𝛽𝐿𝑒𝑎𝑘,𝑖 𝐿𝐸𝐴𝐾𝑗𝑡 + 𝛽𝑁𝑎𝑚𝑒,𝑖 𝑁𝐴𝑀𝐸𝑗𝑡 + 𝛽𝑀𝑎𝑖𝑙,𝑖 𝑀𝐴𝐼𝐿𝑗𝑡 + 𝛽𝐹𝑖𝑛,𝑖 𝐹𝐼𝑁𝑗𝑡+ 𝛽𝐷𝑟𝑜𝑝,𝑖 𝐷𝑅𝑂𝑃𝑗𝑡 +𝛽𝑃𝑟𝑖𝑐𝑒 𝑃𝑅𝐼𝐶𝐸𝑗𝑡 + 𝜀𝑖𝑗𝑡.
In terms of the parameters of the stochastic utility function, αi represents the utility of using
the messenger services if consumer i chooses option j in question t. As for the other parameters
βi, all are expected to be negative, but the signs of the variables are transformed such that theparameters βi become positive.
Each variable on the right side of the above equation corresponds to each attribute of theconjoint card shown in Table 2, where LEAK represents the risk of information leakage within
one year (in 10% increments). NAME is a dummy variable that takes a value of 1 if the userneeds to provide the app companies with the "real name and address" information and 0
otherwise; MAIL is a dummy variable that takes the value 1 if the "email address and phone
number" is provided to the app companies and 0 otherwise; FIN is a dummy variable that takes
the value of 1 if the user needs to provide credit card or bank account information to the app
companies and 0 otherwise; and PRICE represents the monthly fee paid for using themessenger services.
A more detailed explanation is required for the variable DROP, which corresponds to thecommunication partner who has stopped using the service due to fees charged, one of theattributes of the conjoint card. The value of DROP relates to the subjective social distanceassumed by the respondent for those who stop using the service. In our online survey, in
addition to the conjoint-type questions, the subjective social distance of respondents
corresponding to those who stopped using the service in each category was ascertained fromtheir answers to the following question:"It may not be a reality, but suppose you have 100 correspondents registered in yourmessenger app. If the person you want to communicate with the most in those apps is number
1, and the person who is registered but whose name and face do not match (and with whom
you do not need to communicate) is number 100, please fill in the number of people whocorrespond to the following attributes."
The method of ascertaining the social distance between oneself and others was adopted from
Rankin (2006). "People who stop using the service” cover seven categories, including privateand business acquaintances, family members, and lovers, which appear in the conjoint cards.

9

For more details on the RPL model, see, for example, Train (2009).
8

In the above question, the respondents were asked to identify the social distance of each ofthese categories. In addition, we define DROP corresponding to the category that appears in
the attribute "people who will stop using messenger services" in option j in question t as (100SOC), where SOC is the social distance for each category that respondents are asked to quantify
by a number between 1 and 100. The average SOC for each category is shown in Table 1,
where the smaller the SOC or the larger the DROP, the closer the person is to that respondent.10

3.2 Estimation results
For the estimation of the RPL model, a multivariate normal distribution is assumed for allparameters except PRICE, and 300 Halton draws are used to find the optimal value of the
maximum simulated likelihood (MSL). The parameter βi in the RPL model is assumed to be
distributed as a population reflecting the preference heterogeneity among respondents. Since
the respondents answered 10 conjoint-type questions at a time, the respondent's βi is considered
to be fixed for the data generated by the 10 questions answered by the same respondent.
Therefore, the estimation is treated as for panel data.
The coefficient of PRICE is assumed to be fixed without assuming any probability
distribution to avoid including zero or infinity in the definition of the PRICE coefficient, whichis the denominator. This is because the coefficients of PRICE are used to divide the coefficientsof other variables when converting the actual burden cost of inputting personal information
into monetary terms, given that the monthly usage fee is the numéraire (Train, 2009).
Table 3 shows that all the parameters are statistically significant and different from zero atthe 1% level with the expected sign. The standard deviations of all parameters, assuming anormal distribution, are also statistically significant and different from zero at the 1% level.
The constant term αi represents the benefit of using the messenger services, and the value
obtained by dividing the parameter estimate by the parameter for the monthly usage fee, PRICE,
which represents the willingness-to-pay (WTP) for the messenger service use. In Table 3, theWTP for the use of messenger services is estimated to be about JPY 781 (US$ 7.81) per monthbased on the average population distribution. As for the probability of information leakage, forevery 10% increase in the probability of information leakage, the monthly WTP is estimatedto decrease by JPY 167 per month. Similarly, the monthly benefit of using the messenger
services is reduced by JPY 76, JPY 109, and JPY 323 per month, when providing real names
and addresses (NAME), phone numbers and email addresses (MAIL), and financial-related
personal information (FIN), respectively. In addition, the marginal utility loss is estimated to
be JPY 38/month for each additional unit of social distance for those who have stopped using
the messenger service.
Table 3 near here10

If no one stops using the service, the SOC is set to 100. In other words, the change in utility
when the 100th partner stops using the service is equivalent to when no one stops using theservice.
94. Demand elasticity analysis for a one-sided market
4.1 Change in choice probability with an additional 5% charge
We measured the price elasticity of demand for a 5% price increase based on the estimation
results obtained using the RPL model. First, we estimated the price elasticity of demand in a
one-sided market where there are no direct network effects. The reference price is defined asfollows. To estimate the actual burden cost, we calculate a hypothetical price X such that Pr(use | price = 0, personal information provision rate = average provision rate of respondents,
information leakage risk = average subjective probability of respondents) = Pr (use | price = X,
personal information provision rate = none, information leakage risk = none). In other words,
X represents the magnitude of the real cost to be borne, such that using the free service given
the average personal information provision rate and information leakage risk (as obtained byanswers to questions of the online survey) and using the paid service in the absence of personal
information provision and information leakage risk are non-discriminatory.
The average values for the provision of personal information and the risk of information
leakage were as follows. As mentioned earlier, the survey examined the types of personal
information provided by respondents. The average values for the 908 respondents were 0.6784
for NAME (percentage of respondents who provided their names and addresses), 0.8447 for
MAIL (percentage of respondents who provided their email addresses and phone numbers),
0.1486 for FIN (the percentage of respondents who provided their credit card or bank accountinformation), and 0.3082 for LEAK (the average expected probability of information being
leaked within a year). These values were multiplied by the average value of each βi estimatedby the RPL model and summed to calculate the decrease in utility. By dividing this value by
the PRICE parameter, we calculated the actual burden cost for providing personal informationand the information leakage risk, finding the actual average cost for this to the respondents to
be JPY 706.7 (US$ 7.07) per month, which we employed as the hypothetical price X for themessenger service use.
We then calculated the price elasticity of demand. The actual cost burden of JPY 706.7 permonth was the initial value used to apply the SSNIC test. The probability of using the service
was 0.7151.11 Next, we simulated the SSNIC test. When calculating the probability of using
the service if we charge an additional JPY 35.34 per month, which is 5% of the subjective
monthly cost of JPY 706.7, the choice probability changes to 0.6927. Therefore, the rate ofdecrease from the initial choice probability of 0.7151 becomes -0.0314 (= [0.6927 0.7151]/0.7151), indicating that a 5% increase in price will reduce the choice probability by
about 3.1%. Therefore, the price elasticity of demand is calculated as -0.6280 (= -0.0314/0.05).
11

In our study, the respondents who actively used the messenger services were included in theanalysis. However, it should be noted that in the conjoint analysis, even if the variable is set tothe current level, the probability of using the service does not necessarily integrates to 1. It canbe interpreted that the ratio of respondents who have installed but intend to continue using theservice is only 0.7151.
10

4.2 Change in choice probability considering direct network effects
Next, we measured the demand elasticity of a one-sided market considering the direct
network effect. In the simulation described above, the decrease in the probability of choice due
to an additional 5% charge was 3.1%. However, there should be a direct network effect at workin the messenger service, such that the more the users, the higher the utility of using the service.
In this model, the DROP variable represents the extent to which the utility of using themessenger service decreases when others stop using it. As explained earlier, using the social
distance SOC, the DROP variable is defined as (100-SOC). In other words, the more important
a communication partner is, the smaller is the SOC when the partner stops using the application.
Here, we assume that 3.1% of in-app communicators with average social distance would stopusing the messenger service.
Note that the median number of people on the roster of correspondents in the application is74, and the average social distance of people on the roster is 66.4. Therefore, we calculated the"median number of people registered in the communication roster (74) × service outage rate
(0.0314) × social importance of dropouts (66.4/100)" and extrapolated that number to the
DROP variable as a decrease in network size. As a result of calculating the selection probability
using this method, its value changed to 0.6533. Therefore, the rate of change from the original
selection probability was -0.08642 (= [0.6533 - 0.7151]/0.7151). Considering the above direct
network effect, a 5% change in price decreases the choice probability by 8.6%, resulting inprice elasticity of demand of -1.728 (= -0.08642/0.05).

5. Simulation analysis for a two-sided market
Here, we consider the indirect network effects to measure the price elasticity of demand ina two-sided market. The intuition behind the free business model is that companies can use
free-service customers as a base to generate billing revenue on the other side of the market. In
other words, as the number of users of a free service increases, the revenue gained from users
in the paid market also increases due to the indirect network effects, and vice versa. In otherwords, if the number of free service users decreases, the revenue from the paid market shrinks.
Considering messenger services as a two-sided market, the number of communicators
exchanging messages is a variable that represents the size of the network. In the case of freemessenger services, the advertising market and other application services form the other (paid)side of the market to monetize the two-sided market business. Naturally, the revenue generated
by the paid market depends on the network size of the free market. Thus, if both the size of thefree market and the profitability of the paid market decrease, the quality of the free service
must be reduced or the free business must be abandoned.
Here, we attempt to simulate market delineation under simple assumptions that include both
direct and indirect network effects. First, as when measuring the impact of direct network
effects, we assume an initial monthly price increase of JPY 35.3 (5% of JPY 706.7) for personal
information collection and information leakage risk. In this case, the price level after the11increase is JPY 742.0 per month, and the decrease in the probability of choice due to the 5%
price increase is the value measured in the case of the direct network effect (-8.6%).
Furthermore, considering the indirect network effect, a decrease in the size of the network in
one (free) market results in a decrease in revenue in the other (paid) market, which in turnrebounds to the original market. Here, if a decrease in network size due to a 5% price increasein the original market causes a decrease in revenue in the other market, the decrease in revenue
must be compensated by increasing the real cost incurred in the original market. For example,
assuming that the network size of a messenger service decreases by 10% due to a 5% priceincrease. In this case, due to the indirect network effect from the other market, the hypotheticalprice of the messenger service will additionally increase by JPY 74.20 (or, 10% of JPY 742.0)
per month to compensate for the decrease in revenue. In this simulation, we need to incorporate
this additional JPY 74.20 monthly price increase into the calculation of the price elasticity ofdemand.
In our previous calculations, we obtained the result that the first 5% price rise decreases the
network size by 8.6% via the direct network effect. Therefore, we now simulate the indirect
network effect by considering an additional monthly price increase of JPY 63.82, equivalent to8.6% of the actual burden cost of the messenger service market. This additional fee reduces theuser's utility, which further reduces the choice probability, resulting in a change in the choiceprobability by -0.6378 and a rate of change of 0.1081 (= [0.6378 - 0.7151]/0.7151). Therefore,
when the simulation is performed considering the direct and indirect network effects, theprobability of choice decreases by 10.8% for the first 5% price increase.

6. Market delineation for zero-price services
Based on the estimated price elasticity of demand, we now delineate one-sided markets
without direct network effects, one-sided markets with direct network effects, and two-sided
markets with indirect network effects. To delineate markets, the critical price elasticity ofdemand must be calculated (Werden, 1998; Werden, 2003). If the marginal price elasticity ofdemand is greater than the price elasticity of demand measured at the current price level, theincrease in the maximum profit price will be greater than the SSNIC level. Therefore, thishypothetical monopolist will be able to increase its profit margin through SSNIC, and thecompetition authority will define this service as a relevant market. Conversely, if the criticalprice elasticity is less than the elasticity of demand measured at the current price level, thecompetition authority would not be able to define such a product as a relevant market.
Now, we briefly explain the critical price elasticity of demand in the case of linear demand.
Let the linear demand curve for service i be 𝑝 = 𝑎 − 𝑏𝑞, where p is price, q is demand, and a
𝜕𝑝0

and b are the parameters. Let 𝑝0 be the current price. Since 𝜕𝑞0 = −𝑏, we calculate the priceelasticity of demand at the current price of the linear demand line and obtain 𝜀𝑖 (𝑝0 ) =𝑝0 /(𝑎 − 𝑝0 ). Next, let the profit maximization price be 𝑝𝑚 and the marginal cost be c to
calculate the profit maximization price of the hypothetical monopolist. Since the profit function12

is 𝜋(𝑝𝑚 ) = (𝑝𝑚 − 𝑐)𝑞(𝑝𝑚 ), we obtain 𝑝𝑚 = (𝑎 + 𝑐)/2 by𝜕𝜋(𝑝𝑚 )
𝜕𝑝𝑚

= 0. By transforming

this profit maximization condition, we obtain 𝑎 = 2𝑝𝑚 − 𝑐 , and by substituting it in thedefinition equation of price elasticity of demand, we obtain 𝜀̅(𝑝0 ) = 𝑝0 /(2𝑝𝑚 − 𝑐 − 𝑝0 ).
This is the expression of the price elasticity of demand at the current price level 𝑝0 using the
profit maximization price 𝑝𝑚 . Here, the current price-cost markup ratio is 𝑚 = (𝑝0 − 𝑐)/𝑝0 .
In addition, since the rate of increase from the current level to the maximum profit price is 𝑡 =(𝑝𝑚 − 𝑝0 )/𝑝0 , we can rewrite the price elasticity of demand using m and t to obtain 𝜀̅𝑖 (𝑝0 ) =1
𝑚+2𝑡. Furthermore, if we consider constant revenue instead of profit maximization, the critical1

elasticity is 𝜀̅𝑖 (𝑝0 ) = 𝑚+𝑡. Here, we do not make any specific assumptions about corporate
behavior; thus, we calculate the critical elasticity values for both profit maximization andconstant revenue.
We converted the zero price of the messenger service into JPY 706.7 (US$ 7.07) per month,which is the actual cost of providing personal information. Using this amount as a starting point,
we calculated how much a 5% price increase would reduce the probability of choice. First, we
conducted a demand substitutability analysis of the one-sided market, focusing only on themessenger service market, finding that the price elasticity of demand, defined as the decreasein the probability of choice due to a 5% surcharge, to be 0.628. Since we do not know themarkup ratio of the hypothetical monopolist, if the actual markup ratio is less than this level,
we calculate the critical markup ratio at which the relevant market can be defined as a relevantmarket. The critical markup ratio ranges from 1.492 (for profit maximization) to 1.542 (forconstant revenues). Since the range of possible markup ratio is between 0 and 1, this service
can always be defined as a relevant market.
Next, when calculating the price elasticity of demand, we considered the direct network
effect, in which the value of a service increases when more people use it. Considering the direct
network effects, we found the price elasticity of demand to be 1.728. Additionally, the criticalmarkup ratio was found to range from 0.479 (for profit maximization) to 0.529 (for constantrevenue). Therefore, if the markup ratio is smaller than 0.479 or 0.529, the service can be
defined as a relevant market.
Finally, to calculate the price elasticity of demand, one service is considered a counterpartof the other service, and both indirect and direct network effects are considered, resulting inprice elasticity of demand of 2.162. The critical markup ratio was computed to range from
0.363 (for profit maximization) to 0.413 (for constant sales). Therefore, if the markup ratio issmaller than 0.363 or 0.413, the service can be defined as a relevant market. Table 4summarizes the results of this market definition for zero-price services.1212

In this study, we assume that the repercussions of indirect network effects between the twomarkets are short-term and one time only as the market delineation of the SSNIC test is basedon a short-term assumption of one year. However, in the long term, there could be a catastrophic
scenario where multiple repercussions between the two markets will constantly reduce the
network size in both markets.
13

Table 4 near here

7. Conclusions
Using messenger services as an example, this study proposes a market definition method forzero-price services. We employ the SSNIC test, which is an improved version of the SSNIP
test, and conjoint analysis, while considering network effects, an important characteristic ofdigital services. In summary, in the case of a 5% price increase, we find a 3.1% change in theprobability of choice, and the price elasticity of demand to be 0.628 when only the price effectis considered, while the decrease in the probability of choice is 8.6% when the direct network
effect is considered. Additionally, the price elasticity of demand is1.728. Furthermore, when
considering a two-sided market with indirect network effects, a decrease in the probability ofchoice of 10.8% is observed for a 5% price increase, resulting in price elasticity of demand of
2.162.
Thus, the results of the SSNIC-type market delineation test show that the price elasticity ofdemand for free messenger services is higher when network effects and two-sided markets are
considered; thus, it is difficult to say that a free messenger service is a relevant market that is
independent of the nearest other communication services. A free service is a typical businessmodel of digital service provision, and the two-sided nature of the market makes it difficult for
applying competition policy. Although it is difficult to directly apply the SSNIP-type market
definition method, which uses the price elasticity of demand, to zero-price markets, it ispossible to perform SSNIC-type market definition tests by calculating the actual burden costs
and considering the effects of network effects. The method proposed in this study shows that amarket definition for free markets is eminently possible.
Nevertheless, there are several limitations to this study. First, we only used the hypotheticalstated preference method; future work should conduct analysis using the revealed preference
method. Second, our model does not assume specific corporate behavior. Future studies canaddress this issue by conducting structural estimations assuming certain corporate behaviors.
Third, this analysis was conducted for a short term, of approximately one year, and future
research should conduct a long-term analysis to model the repercussions between markets.

14

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16

Table 1. Descriptive statistics

Most
used
apps

Activeuser

Personal information
actually provided

Age

Male

FemaleName of
app

10s

5.2%

12.0%

LINE

86.5%

93.3%

Real name

65.7%

20s

5.0%

10.5%

Facebook
Messenger

3.7%

16.4%

Age

60.0%

30s

6.7%

10.7%

Google Allo

0.2%

0.9%

Occupation

33.0%

40s

8.1%

7.2%

Skype

2.6%

9.0%

Mailing address

33.9%

50s

6.3%

5.9%

Twitter DM

3.5%

17.8%

Phone number

70.9%

60’s

10.6%

6.3%

Instagram
DM

1.5%

14.3%

E-mail

75.8%

13.8%

70s

4.3%

1.3%

Snapchat

0.0%

0.6%

Account
information forsocialnetworking sites
other than that
app

Over
80

0.0%

0.0%

WhatsApp
Messenger

0.1%

1.3%

Credit card
information

13.1%

Others

1.8%

7.4%

Bank accountinformation

8.0%

Other
information

11.8%

Nothing

7.7%

Note：N=908

17

(continued)

Subjective
probability that
information will be
leaked within a year

Number ofcommunication
partners registeredin the apps

Averagevalue ofsocialdistance

Attributes of registeredcommunication partners

0%

12.2%

Less than5

17.3%

Family members living
together

70.0
%

7.56

1%

6.4%

5 to 9

16.9%

Family members or
relatives living apart

55.0
%

11.06

5%

10.0%

10 to 24

21.6%

Lovers

16.2
%

22.71

16.4%

Private friends with whom
one has a current
relationship

87.8
%

13.76

13.2%

Private friends with whom
one had a relationship in
the past but not anymore

41.3
%

33.23

9.8%

Friends or acquaintancesfrom work or school withwhom one has a current
relationship

59.1
%

26.69

4.8%

Friends or acquaintancesfrom work or school withwhom one had arelationship in the past
but not anymore

21.4
%

54.51

Others

2.1%

51.24

10%

30%

50%

17.1%

17.5%

23.0%

70%

5.5%

90%

3.3%

100%

5.0%

25 to 49

50 to 99

100 to299

Over 300

Note：N=908

18

Table 2. Attributes and levels of the conjoint questions
Attributes

LevelsPrice: 4 levels.

JPY 1,000/month
JPY 500/month
JPY 100/month
JPY 0/month

Probability of information leaking fromthe app provider, including the content of
messages exchanged, within one year: 4levels.

0%
1%
10%
30%

Type of information you need to give tothe app provider (information you enter
when creating an account): 5 levels
including 0.
*: When entering information, it isassumed that "real name and address" arerequired, or "e-mail address and phone
number" or "credit card or bank accountinformation" are required in addition to"real name and address.”

None (ID and password only)“Real name and address” only
“Real name and address” + “E-mail address and phone
number”“Real name and address” + “Credit card or bank accountinformation”“Real name and address” + “E-mail address and phone
number” + “Credit card or bank account information”

People who are expected to stop using
the service due to changes in plansettings: 8 levels including 0.
*: assuming that there is only one
category for each card that will no longer
be used.

“Nobody”"Family members living together""Family members or relatives living apart""Private friends with whom one has a current
relationship""Private friends with whom one had a relationship in thepast but not so much anymore""Friends or acquaintances from work or school withwhom one has a current relationship""Friends or acquaintances from work or school withwhom one had a relationship in the past but not so muchanymore""Lovers"

19

Table 3. Estimation results

Mean

S.E.

S.D.

S.E.

USE (α)2.38030.02202.78450.0241LEAK

0.50940.00470.43490.0058NAME

0.23110.010900.31190.0191MAIL

0.33150.01020.23010.0203FIN

0.98440.01000.14880.0254DROP

0.11640.0104

0.09660.0225PRICE

0.30470.0014--

McFadden Pseudo R2

WTP

JPY
781.30JPY
167.20
JPY
75.84
JPY
108.80JPY
323.10JPY
38.21-

0.3037

Note: All parameter estimates are significantly different from zero at the 1% significance level.

20

Table 4. Market delineation for zero-price services
Critical Markup Ratio
Price elasticity
of demand

Profit maximization

Constant revenue

One-sided market
without direct network effects

0.628

1.492

1.542

One-sided market
with direct network effects

1.728

0.479

0.529

Two-sided market
with indirect network effects

2.162

0.363

0.413

21

Figure 1. Examples of conjoint questions









Please read the following instructions carefully and answer the questions.
Assume that all messenger services have made changes, including fee-based services, and that allapps will collect fees and register personal information in one place.
Suppose that from the next month, all the messenger services will be managed collectively, andyou will be able to use only "Plan 1" or "Plan 2."
Assume that the following changes will occur as a result of the plan change: Setting a usage price (including the case of "free/0 yen") Some people will stop using the app (assuming you know who will stop using it).
 You will have to provide additional personal information.
In addition, let us assume that the probability that personal information, including messages
exchanged, will be leaked from one of the apps within the next year is the same for all app
companies, and this probability is known.
Please choose the more convenient of the following two plans, or the "stop using all messenger
services" option.

Type of information you need togive to the app provider

Plan 2

1%

0%(It will never leakwithin a year).

Real name andaddress

People who are expected to stopusing the service due to changes inplan settings

Real name andaddress,
credit card or bankaccount information
Family members
living together

Monthly charge

Free (0 yen/month)

JPY 1,000/month

Please select one

〇

〇

22

Stop using all messenger apps.

Probability of information leaking
from the app provider, including
the content of messages exchanged,
within one year

Plan 1〇