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sustainability
Article
Cloud Services and Pricing Strategies for
Sustainable Business Models: Analytical and
Numerical Approaches
Se-Hak Chun
Department of Business Administration, Seoul National University of Science and Technology,
232 Gongreung-Ro, Nowon-Gu, Seoul 01811, Korea; shchun@seoultech.ac.kr; Tel.: +82-2-970-6487
Received: 9 November 2019; Accepted: 30 November 2019; Published: 19 December 2019
Abstract:
Previous studies have introduced different potential pricing strategies for cloud services.
However, not much research has been done comparing subscription pricing and pay-per-use pricing,
which are commonly used pricing schemes. Also, there are very few studies which analyze a two-part
tariffpricing scheme for cloud services, even though this option may increasingly attract service
providers as the cloud market becomes more competitive and the profit margin grows narrower.
Previous research has focused on firms’ profitability rather than social welfare due to the limitations
of free services. This study uses theoretical and numerical analysis to compare the social welfare and
profitability of three pricing schemes commonly used by firms: subscription pricing, pay-per-use
pricing, and two-part tariffpricing. It shows that the pay-per-use pricing is the best solution from the
perspective of social welfare, which contrasts with the conclusion of a previous study stating that
social welfare is maximized under a two-part tariff. This paper also shows that the two-part tariffis
the most profitable pricing scheme for firms.
Keywords:
sustainable business model; cloud computing; service models; two-part tariffpricing;
subscription pricing; pay-per-use pricing
1. Introduction
With the development of information technology and Internet services, consumers are benefiting
from many digital services free of charge. Many digital content companies provide a large number of free
services to consumers in the form of common goods by relying on advertising revenues based on users’
visits and some personal information such as web surfing and purchasing behavior. In particular, cloud
computing has changed the traditional computing business environment by enabling customers to access
data and use software without the need to install it and providers to offer numerous online services.
Cloud services can be regarded as utility computing services, which are delivered in a manner similar
to traditional utilities, such as water, electricity, gas, and telecommunications [1]. However, due to the
limitations of free services, some companies are paying for digital goods and services to sustain their
business models. Therefore, as in other utility services, the implementation of adequate service models
and pricing schemes for cloud services is critical. Pricing enables the regulation of the supply and
demand of computing services and, along with variations in service models, affects providers’ profits
and social welfare [2,3].
Many studies have introduced different potential pricing strategies for cloud services, such
as pay-as-you-go pricing, subscription pricing, pay-for-resources pricing, value-based pricing,
cost-based pricing, customer-based pricing, competition-based pricing, and other dynamic pricing
strategies [4,5]
. In reality, the most popular pricing strategies are subscription, pay-as-you-use, and
two-part tariffmodels. Some dynamic pricing strategies have been studied by many researchers [
4
,
6
],
Sustainability 2020,12, 49; doi:10.3390/su12010049 www.mdpi.com/journal/sustainability
Sustainability 2020,12, 49 2 of 15
but a comparative
analysis of subscription pricing and pay-per-use pricing has not been done, although
these pricing methods are commonly used in cloud service systems. Also, an analytical study is
required for the two-part tariffpricing scheme, since the concept of a two-part tariffis nowadays
adopted as a cloud services’ pricing strategy and could gain in popularity among service providers as
the cloud market becomes more competitive and the profit margin grows narrower. Previous research
has focused on firms’ profitability with respect to the limitations of free services. Chun and Choi [
7
]
analyzed the two pricing schemes of subscription and pay-per-use pricing models from a provider’s
standpoint and discussed their implications for consumer surplus and social welfare. Chun et al. [
8
]
compared the three pricing schemes of subscription pricing, pay-per-use pricing, and two-part tariff
from the perspectives of a provider’s profit, consumer surplus, and social welfare.
This study differentiates itself from previous ones in several aspects. Firstly, I applied two-part
tariffpricing to cloud services by considering subscription pricing and pay-per-use pricing and
extended the previous two-part tariffto a more generalized customer heterogeneous model, in order to
utilize it for a cloud service pricing strategy. Secondly, I clarified the previous two-part tariffmodel and
compared the results from subscription, pay-per-use, and two-part tariffpricing with those obtained
from analytical and numerical approaches and recent real-world examples. In particular, I show how
two-part tariffpricing can include the other two pricing schemes of subscription and pay-per-use
pricing, through theoretical and numerical analysis. Thirdly, I discuss some possible conflicting issues
between customers and providers, in terms of consumer and producer surpluses.
This paper shows that the pay-per-use pricing is the best option from the perspective of social
welfare when there is no additional metering cost. This conclusion contrasts with that of a previous
study [
9
] stating that social welfare is maximized under a two-part tariff. This paper also shows that
the two-part tariffis the most profitable pricing scheme for the firm. This paper is organized as follows:
Section 2discusses service models and pricing models in cloud computing; Section 3investigates right
pricing schemes for cloud services using a theoretical analysis; Section 4compares the three pricing
schemes of subscription pricing, pay-per-use pricing, and two-part tarifffrom the perspectives of a
provider’s profit, consumer surplus, and social welfare, using theoretical and numerical analysis and
discusses some implications; Section 5concludes and discusses future research directions.
2. Research Background: Cloud Service Models and Pricing Models
2.1. Cloud Services and Practical Pricing Cases
Cloud computing is defined as a model for enabling ubiquitous, convenient, on-demand
network access to a shared pool of configurable computing resources (e.g., networks, servers, storage,
applications, and services) that can be rapidly provisioned and released with minimal management
effort or service provider interaction [
10
]. Cloud service providers offer their services to users
through three layers, i.e., software as a service (SaaS), platform as a service (PaaS), and infrastructure
as a service (IaaS) [
11
]. In IaaS, users are provided with processing capability, storage, networks,
and other fundamental computing resources and are able to deploy and run arbitrary software,
including operating systems and applications [
10
]. For example, Amazon offers services based on
its infrastructure, such as computing services (EC2) or storage services (S3). Amazon S3 provides
online storage, data request, and data transfer services. Table 1shows several Amazon S3 services
and price plans. Also, there are other examples of IaaS, such as those offered by AppNexus, Dropbox,
EU Reservoir project, FlexiScale, Joyent, and Rackspace. Most IaaS providers offer hourly services,
whose costs are based on usage-dependent and component-based rates. They provide users with
services at a low price per GB of storage, charge hidden costs for inbound and/or outbound data
transfer, and offer basic packages at a fixed price which can be extended according to the user’s needs,
similar to a two-part tariffscheme mixing subscription plus pay-per-use pricing. Also, users can pay a
fixed price in order to get discounts on usage-dependent prices [5].
Sustainability 2020,12, 49 3 of 15
Table 1. Amazon storage services (S3)0price plans (US East (Ohio), 2019).
Usage Storage Usage Data Transfer
S3 Standard Storage
Data Transfer out from Amazon S3 to Internet
First 50 TB/month $0.023 per GB Up to 1 GB/month $0.000 per GB
Next 450 TB/month $0.022 per GB Next 9.999 TB/month $0.09 per GB
Over 500 TB/month
$0.021 per GB Next 40 TB/month $0.085 per GB
S3 Standard-Infrequent Access Next 100 TB/month $0.07 per GB
All storage/month $0.0125 per GB Over 150 TB/month $0.05 per GB
Source: https://aws.amazon.com/s3/pricing.
PaaS allows users to deploy applications acquired or created using programming languages
and tools supported by the provider. A platform as a service provides users with a convenient
environment for developing applications [
12
]. In PaaS, cloud services are provided according to
three different pricing schemes: free of charge, as complete packages, and usage-dependent pricing.
An example of PaaS is Google App Engine, which is a platform for developing and hosting web
applications in data centers. Table 2shows Google App Engine’s price plans for its services per month
or hour. Other examples of PaaS are LongJump, Microsoft Azure, Zoho Creator, and SalesForce.com
Lightning Platform.
Table 2. Google App Engine’s price plans (2019).
Resource Unit Unit Cost
Standard environment instances Cost per hour per instance (Instance Class B1) $0.05
Flexible environment instances
vCPU per core hour $0.0526
Memory per GB per hour $0.0071
Persistent disk per GB per month $0.0400
Google Cloud Datastore calls
Stored data (1 GB free quota per day) per GB per month $0.18
Search
Total storage (documents and indexes) per GB per month $0.18
Other resources
Outgoing Network Traffic Gigabytes $0.12
Incoming Network Traffic Gigabytes Free
Blobstore, Logs, and Task Queue Stored Data Gigabytes per month $0.026
Dedicated Memcache Gigabytes per hour $0.06
Logs API Gigabytes $0.12
SSL Virtual IPs (VIPs) Virtual IP per month $39.00
Sending Email, Shared Memcache, Cron, APIs No additional charge
vCPU: virtual central processing unit, API: application programming interface, SSL: Secure Sockets Layer, Source:
https://cloud.google.com/appengine/pricing.
In SaaS, users can access providers’ applications running on a cloud infrastructure using various
devices through a thin client interface, such as a web browser. The SaaS pricing schemes include
free-of-charge services and complete packages at a fixed monthly charge [
13
]. NetSuite, SalesForce.com,
and SAP are examples of companies offering SaaS. For instance, the Sales Cloud of SalesForce.com
provides features such a sales representatives service with a complete customer profile and account
history for managing marketing campaigns and increasing sales [
5
]. The pricing plans for Sales Cloud
are shown in the Table 3.
Sustainability 2020,12, 49 4 of 15
Table 3. Sales Cloud’s price plans.
Product Description Price (Per User Per Month)
Out-of-the-box CRM for up to 5 users Basic sales and marketing for up to 5 users $25
Lightning Professional Complete CRM for any size team $75
Lightning Enterprise
Deeply customizable sales CRM for your business
$150
Unlimited Unlimited CRM power and support $300
CRM: customer relationship management, Source: http://www.salesforce.com/crm/editions-pricing.jsp.
2.2. Cloud Pricing Models
Recently, some studies have analyzed pricing strategies for cloud computing environments.
Two common types of pricing models are static pricing and dynamic pricing [
14
,
15
]. In static or fixed
pricing, the price charge does not change, and the cloud provider determines the price according to the
resource type in advance [
16
]. A fixed pricing model is more straightforward and easier to understand
for users, as compared to dynamic pricing models [
2
]. Fixed pricing includes pay-per-use, subscription,
and list prices or menu pricing [17].
In subscription pricing, users pay on a recurring basis to access software as an online service [
2
].
The user subscribes to use a preselected combination of service units for a fixed price and a longer
time frame, usually monthly or yearly [
6
]. With subscription-based pricing, a cloud service provider
offers fixed recurring pricing on a monthly basis for a service or product, and customers pay upfront,
prior to receiving access to the cloud services. A heavy user may choose a longer subscription to get
a lower price. However, a subscription-based model can result in customers overpaying for services.
Examples of the subscription pricing model can be found in Dropbox, Google, and other cloud storage
services, as shown in the Table 4.
Table 4. Pricing schemes for the subscription pricing model.
Company and Its Service Pricing Schemes
Google Drive 15 GB–Free, 100 GB–$1.99, 1 TB–$9.99 per month
Dropbox 2 GB–Free, 1 TB–$9.99 per month
Apple’s iCloud 5 GB–Free, 20 GB–$0.99, 200 GB–$3.99, 1 TB–$9.99 per month
Microsoft’s OneDrive
15 GB–Free, 100 GB–$1.99, 200 GB–$3.99, 1 TB–$6.99 per month
In pay-per-use pricing, users only have to pay for what they use and are aware of the cost of doing
business and consuming a resource. With a pay-per-use pricing model, a provider charges a price
based on the usage and consumption of a service. The major benefit of the pay-per-use pricing model
is that there are no wasted resources [
18
]. In the pay-per-use pricing model, customers are charged on
the basis of how much they consume a product or service. Examples are Amazon EC2 and S3 and
Google App Engine, shown in the Table 5[19,20].
Table 5. Pricing schemes for the pay-per-use pricing model.
Company and Its Service Pricing Schemes
Amazon Web Services (EC2) t3.nano: $0.0098 per hour
Amazon Web Service (S3) Storage: after 50 TB $0.023 USD/GB
Data transferred in GB: after 1 GB $0.09 per GB
Google App Engine
Standard runtime instances (Class B1): $0.05 per hour
For example, as shown in Table 5, Amazon’s pay-per-use price after the first 50 TB is $0.023 per
GB/month of storage. This approach is commonly used in PaaS and IaaS. Different providers use
different pricing schemes for the provisioning of services to the end user.
In dynamic pricing, the price charges change dynamically, according to supply and demand,
for example, by means of auctions. Amazon runs customer’s instances as long as the bid price is
Sustainability 2020,12, 49 5 of 15
higher than the spot price, which is set by Amazon based on their data center utilization [
17
], whilst
dynamic pricing policies could achieve more economically efficient allocations and prices for high-value
services [
2
,
6
,
21
]. Other examples of dynamic pricing strategies are a novel financial economic model
providing a high level of QoS (Quality of service) to customers [
22
], a genetic model for pricing in cloud
computing [
23
], a dynamic pricing scheme for federated clouds [
24
], and a hybrid pricing strategy,
mixing fixed-price reserved services with spot-price on-demand services [
25
]. However, in reality,
dynamic pricing is not common, and fixed prices such as subscription pricing and pay-per-use pricing
are typical [4,26].
3. The Model
3.1. Model Setting
This paper extends the study of pricing models by Chun et al. [
7
,
8
] and investigates subscription
pricing, pay-per-use pricing, and two-part tariffpricing from the perspectives of a provider’s profit,
consumer surplus, and social welfare. Chun and Choi [
7
] analyzed the two pricing schemes of
subscription and pay-per-use pricing models from a provider’s standpoint and discussed their
implications for consumer surplus and social welfare. Chun et al. [
8
] compared the three pricing
schemes of subscription pricing, pay-per-use pricing, and two-part tarifffrom the perspective of a
provider’s profit.
For simplicity, I assume that there is a monopoly provider of cloud services. The cost of providing
services depends on both fixed and variable elements and is expressed as
cq +f
, where
c
and
f
are the
marginal cost and fixed cost, respectively, and
q
is the quantity of service consumed. I assume that
f=
0 without loss of generality. The provider chooses the pricing scheme,
T(q) = A+pq
, where
A
is the lump-sum price, and
p
is the unit price. Thus, the pricing scheme can represent subscription
pricing when
p=
0 and
A>
0, pay-per-use pricing when
p>
0 and
A=
0, and two-part tariffwhen
p>0 and A>0. The provider profit can be expressed as
π= (AN +pQ)−cQ
where Nis the total number of consumers who are actually participating in the market and buy services,
and Qis the total amount of services all consumers purchased.
Let us turn to the demand side. I assume that consumers’ reservation prices are uniformly
distributed along [0, U] with unit height, i.e., u
∈
[0, U]. Thus, Ucan also represent the potential market
share of the product. Given the provider’s unit price (p), a consumer of type u
∈
[0, U] will obtain the
following surplus by consuming one unit of the product:
V(u) = u−p.
An individual consumer’s demand function is downward sloping and is expressed as
q=u−p
,
where
u
is the maximum willingness to pay for the services. Thus, a consumer
u
purchases the services
when
u≥p
. The consumer
u
has the net utility or surplus
Su(q
,
p) = Vu(q)−T(q
,
p)
when he or she
purchases
q
units of services, where
Vu(q)
is the total value when a consumer buys
q
units of services,
and
T(q
,
p)
is the payment. Since uis uniformly distributed along [0, U] with unit height, the total
number of consumers (or the potential market share of the product) is U. I consider a heterogeneous
customer distribution case where each different consumer
u
can purchase a different amount of services
according to his or her valuation of the services. For simplicity of analysis, when a representative
consumer
u
buys qunits of services, I assume that
Vu(q)
has the specific form of a concave utility
function [26–28]:
Vu(q) = nu2−(u−q)2o/2
where Vu(0) = 0, V0u(q)>0, and V00 u(q)<0.
Sustainability 2020,12, 49 6 of 15
A consumer uhas a downward sloping linear demand and maximizes his or her net utility,
max
qSu=max
q[Vu(q)−T(q,p)]
=max
qhnu2−(u−q)2o/2−(A+pq)i
and
q(p) = u−p. (1)
As explained, uis a representative consumer distributed along the length between 0 and U
according to maximum willingness to pay for the services and will buy an amount of services
corresponding to
qu(p) = u−p
. Also, a consumer U, who has the maximum willingness to pay, will
buy the amount of services
qU(p) = U−p
. Figure 1shows the amount of services each consumer buys
when the price is zero. The y-axis in Figure 1represents the amount of services a specific consumer
will buy. For example, a consumer
ˆ
u
will buy
qˆ
u(
0
) = ˆ
u−
0
=ˆ
u
when a price is zero but a consumer
ˆ
u
will buy qˆ
u(p) = ˆ
u−pwhen a price amounts to the positive value p.
Sustainability 2019, 11, x FOR PEER REVIEW 6 of 15
[]
{}
[]
)(2/)(max
),()(maxmax
22
pqAquu
pqTqVS
q
u
q
u
q
+−−−=
−=
and
.)( pupq −= (1)
As explained, u is a representative consumer distributed along the length between 0 and U
according to maximum willingness to pay for the services and will buy an amount of services
corresponding to .)( pupq
u
−= Also, a consumer U, who has the maximum willingness to pay,
will buy the amount of services .)( pUpq
U
−=
Figure 1 shows the amount of services each
consumer buys when the price is zero. The y-axis in Figure 1 represents the amount of services a
specific consumer will buy. For example, a consumer
u
ˆ
will buy uuq
u
ˆ
0
ˆ
)0(
ˆ
=−= when a price
is zero but a consumer
u
ˆ
will buy pupq
u
−= ˆ
)(
ˆ
when a price amounts to the positive value
p
.
Figure 1. Consumers’ valuation distribution and amount of purchased services.
Figure 2a depicts the total value or utility of a consumer u, and Figure 2b shows demand function
of the consumer u and net utility (shade area) from the amount of services.
(a)
)(qV
u
(b)
)( pq
Figure 2. Total value and demand function of consumer u.
By inserting (1) into the expression of )(qS
u
, the net utility for the consumer u is obtained.
ApuApS
u
−−= 2/)(),(
2. (2)
The first term on the right-hand side of (2) is the shaded area of Figure 2b.
Figure 1. Consumers’ valuation distribution and amount of purchased services.
Figure 2a depicts the total value or utility of a consumer u, and Figure 2b shows demand function
of the consumer uand net utility (shade area) from the amount of services.
Sustainability 2019, 11, x FOR PEER REVIEW 6 of 15
[]
{}
[]
)(2/)(max
),()(maxmax
22
pqAquu
pqTqVS
q
u
q
u
q
+−−−=
−=
and
.)( pupq −= (1)
As explained, u is a representative consumer distributed along the length between 0 and U
according to maximum willingness to pay for the services and will buy an amount of services
corresponding to .)( pupq
u
−= Also, a consumer U, who has the maximum willingness to pay,
will buy the amount of services .)( pUpq
U
−=
Figure 1 shows the amount of services each
consumer buys when the price is zero. The y-axis in Figure 1 represents the amount of services a
specific consumer will buy. For example, a consumer
u
ˆ
will buy uuq
u
ˆ
0
ˆ
)0(
ˆ
=−= when a price
is zero but a consumer
u
ˆ
will buy pupq
u
−= ˆ
)(
ˆ
when a price amounts to the positive value
p
.
Figure 1. Consumers’ valuation distribution and amount of purchased services.
Figure 2a depicts the total value or utility of a consumer u, and Figure 2b shows demand function
of the consumer u and net utility (shade area) from the amount of services.
(a)
)(qV
u
(b)
)( pq
Figure 2. Total value and demand function of consumer u.
By inserting (1) into the expression of )(qS
u
, the net utility for the consumer u is obtained.
ApuApS
u
−−= 2/)(),(
2. (2)
The first term on the right-hand side of (2) is the shaded area of Figure 2b.
Figure 2. Total value and demand function of consumer u.
By inserting (1) into the expression of Su(q), the net utility for the consumer uis obtained.
Su(p,A) = (u−p)2/2−A. (2)
The first term on the right-hand side of (2) is the shaded area of Figure 2b.
Sustainability 2020,12, 49 7 of 15
3.2. Subscription Pricing
Cloud service providers such as Dropbox, Google, and others charge a price based on time (monthly
or yearly), irrespective of the amount of consumption. Thus,
p=
0 and
A>
0. Thus, a consumer’s
decision to buy services depends on the lump-sum price of Aand his or her valuation of service
consumption. The customer compares his or her valuation of a service with the lump-sum price of A
and buys the service when his or her net utility is greater than zero. From (1) and (2), the net utility
when the customer buys uunits of a service is given by
Su=u2/2−A
where q=u, and p=0.
Then, a marginal consumer ˆ
uis defined as follows:
u2/2−A≥0 or ˆ
u≥(2A)1/2.
Since uis uniformly distributed along [0, U], the number of consumers (N) who purchase services is
N=U−ˆ
u=U−(2A)1/2.
For example, a consumer U, whose willingness to pay is the maximum, would buy the amount of
services
U−A
. A marginal consumer
ˆ
u
would purchase a zero amount of services when the lump-sum
price is A. Therefore, the total amount of services (Q) that are bought can be obtained by summing up
all the amounts of services that consumers purchase, as follows:
Q=ZU
ˆ
u=(2A)1/2udu =U2/2−A.
Then, the profits of the provider are:
π=AN −cQ
=AnU−(2A)1/2o−c(U2/2−A).
The provider finds an optimal price considering the total number of consumers who buy services
and the costs of providing the total amount of services requested. The literature about the two-part
tariffmodel assumes that there are one or two types of consumers and the costs depend on the number
of consumers. In this model, a provider’s total amount of sales is calculated from the number of
consumers who buy services, and the total costs are calculated from the total amount of services all
consumers buy. I here extend the two-part tariffmodel by considering that each consumer buys a
different amount of services, according to her/his purchasing decision based on net utility maximization.
From the first order condition, the optimal subscription price can be determined as follows:
AS=2(U+c)2/9. (3)
Note that the superscript Sis used to denote ‘subscription pricing’. The marginal consumer who
is indifferent to buying or not buying is described by
uS= (2AS)1/2=2(U+c)/3.
Using Eqation (3), the number of consumers, the quantity of services used, the profits of the
provider, and consumer surplus at the equilibrium can be easily calculated:
NS= (U−2c)/3, QS= (5U+2c)(U−2c)/18, πS= (4U+c)(U−2c)2/54.
Sustainability 2020,12, 49 8 of 15
The consumer surplus and social welfare can be obtained accordingly:
CSS=ZU
2(U+c)/3
Sudu = (7U+4c)(U−2c)2/162,
SWS=CSS+πS= (19U+7c)(U−2c)2/162.
Equilibrium exists when the maximum willingness to pay is sufficiently larger than the marginal
cost of providing services, and the number of consumers is not negative:
U≥2c. (4)
Equation (4) assumes the condition of
NS= (U−
2
c)/
3
≥
0. I assume that Equation (4) holds
throughout this paper.
3.3. Pay-Per-Use Pricing
Cloud service providers such as Amazon and Google charge prices based on the usage and
consumption of their services offered in EC2, S3, and Google App Engine. When a price is p, a consumer
uwill buy u−pquantity of services, and his or her surplus will be
Su= (u−p)2/2.
Then, the number of consumers purchasing services, the total quantity of services provided, and
the profits of the provider can be calculated similarly to the case of subscription pricing:
N=U−p,Q=ZU
p
(u−p)du = (U−p)2/2, π=pQ −cQ = (p−c)n(U−p)2/2o.
The first order condition (dπ/dp =0) generates the optimal pay-per-use price:
pP= (U+2c)/3.
The superscript Pis used to denote ‘pay-per-use pricing’. The marginal consumer who is
indifferent to buying or not buying is
uP−(U+2c)/3≥0, thus ˆ
uP= (U+2c)/3.
Then, the number of consumers purchasing services, the quantity of services consumed, the profits
of the provider, the consumer surplus, and social welfare at equilibrium can be obtained as follows:
NP=2(U−c)/3, QP=2(U−c)2/9, πP=2(U−c)3/27,
CSP=ZU
(U+2c)/3
Sudu =4(U−c)3/81, SWP=10(U−c)3/81.
3.4. Two-Part TariffPricing
Many providers use a hybrid pricing mechanism (or two-part tariffpricing) by mixing subscription
and pay-per-use pricing, which in fact is not much little different from the original two-part tariff[
4
].
For example, Google App Engine and Joynet Smart Machine’s prices are assigned on a monthly basis
and, if the usage exceeds a set limit, prices are charged as per GB [5].
In this section, I will focus on analyzing two-part tariffpricing, subscription pricing, and
pay-per-use pricing, because they are practically used for cloud service pricing. The purpose of a
Sustainability 2020,12, 49 9 of 15
two-part tariffis to extract more of the consumer surplus by using a pricing scheme consisting of a
fixed or one-time fee charged to each user and a price per each unit purchased [
27
,
28
]. Examples of
two-part tariffs are found in the rental of computers and copying machines, country club fees, and the
rate structures of some public utilities. A two-part tariffpricing model can be considered as a quantity
discounting scheme [26].
I consider the case when a provider charges pon usage and Afor a fixed fee, so that
p>
0, and
A>0. Then, it follows that
q=u−pand Su= (u−p)2/2−A.
The condition that a consumer upurchases services is given by
(u−p)2/2−A≥0 or u≥p+ (2A)1/2.
The number of consumers’ purchasing services, the total quantity of services provided, and the
profits of the provider are obtained as follows:
N=U−p−(2A)1/2,Q=ZU
p+(2A)1/2(u−p)du = (U−p)2/2−A,
π= (AN +pQ)−cQ
=AnU−p−(2A)1/2o+ (p−c)n(U−p)2/2−Ao.
By simultaneously solving the first-order conditions (
dπ/dA =
0,
dπ/dp =
0), optimal two-part
tariffprices are obtained,
AT=2(U−c)2/25 and pT= (U+4c)/5.
To denote ‘two-part tariff’, I used the superscript T. The marginal consumer who is indifferent to
buying or not buying is
uT=pT+ (2AT)1/2= (3U+2c)/5.
Then, the number of consumers, the quantity of services provided, the profits of the provider, the
consumer surplus, and social welfare at equilibrium can be calculated as follows:
NT=2(U−c)/5, QT=6(U−c)2/25, πT=2(U−c)3/25,
CST=ZU
(3U+2c)/5
Sudu =16(U−c)3/375, SWT=46(U−c)3/375.
4. Results of the Study
Comparisons and Discussion
Table 6shows equilibrium prices, the number of consumers, the total quantity of services, the
consumer surplus, the profits of the provider, and social welfare for each pricing scheme. As expected,
optimal prices calculated for the two-part tariffare lower than optimal prices under the subscription
and pay-per-use pricing schemes; therefore,
AT<AS
and
pT<pP
. When comparing the price of
two-part tariffto the price of subscription, heavy users prefer subscription pricing to pay-per-use
pricing, which leads to a higher total number of consumers under the two-part tariffthan under
pay-per-use pricing (
NS<NT
) and decreases the price of the two-part tariff(
AT<AS
). Also, when
comparing the price of two-part tariffto pay-per-use pricing, light users prefer pay-per-use pricing to
subscription pricing, which leads to a lower number of consumers under the two-part tariffthan under
pay-per-use pricing (
NT<NP
). However, the total amount of services under the two-part tariffscheme
is larger than under pay-per-use pricing (
QP<QT
), which decreases the price of the two-part tariffwith
Sustainability 2020,12, 49 10 of 15
respect to pay-per-use pricing (
pT<pP
). The number of consumers is the highest under pay-per-use
pricing, and the total amount of purchased services is the highest under subscription pricing.
Table 6. Comparison of the results.
Subscription (A) Pay-Per-Use (p) Two-Part Tariff(A,p)
Price AS=2(U+c)2/9pP= (U+2c)/3AT=2(U−c)2/25
pT= (U+4c)/5
Number of
consumers
NS= (U−2c)/3NP=2(U−c)/3NT=2(U−c)/5
NS<NT<NP
Total services (5U+2c)(U−2c)/18 2(U−c)2/9 6(U−c)2/25
QP<QT<QS
Consumer surplus (7U+4c)(U−2c)2/162 4(U−c)3/81 16(U−c)3/375
CST<CSS<CSPwhen c is very low, CSS<CST<CSPwhen c is not low
Profits
(producer surplus)
(4U+c)(U−2c)2/54 2(U−c)3/27 2(U−c)3/25
πS≤πP< πT
Social welfare (19U+7c)(U−2c)2/162 10(U−c)3/81 46(U−c)3/375
SWS<SWT<SWP
Figure 3shows consumers’ total payments according to each pricing scheme. As shown in
Figure 3, light users prefer pay-per-use pricing to subscription pricing, because pay-per-use pricing
better reflects their actual amount of consumption. On the other hand, heavy users prefer subscription
pricing to pay-per-use pricing, because subscription pricing fixes the consumer’s payment, regardless
of the actual amount of consumption. Preference for the two-part tariffs is typical of consumers
whose service consumption is intermediate. The consumers’ preference is indicated by the solid line
in Figure 3.
Sustainability 2019, 11, x FOR PEER REVIEW 10 of 15
Table 6. Comparison of the results.
Subscription (A) Pay-Pe
r
-Use (p) Two-Part Tariff (A, p)
Price
9/)(2
2
cUA
S
+=
3/)2( cUp
P
+=
25/)(2
2
cUA
T
−=
5/)4( cUp
T
+=
Number of
consumers
3/)2( cUN
S
−=
3/)(2 cUN
P
−=
5/)(2 cUN
T
−=
PTS
NNN <<
Total services
18/)2)(25( cUcU −+
9/)(2
2
cU −
25/)(6
2
cU −
STP
QQQ <<
Consumer
surplus
162/)2)(47(
2
cUcU −+
81/)(4
3
cU −
375/)(16
3
cU −
PST
CSCSCS <<
when c is very low, PTS
CSCSCS <<
when c is not low
Profits
(producer
surplus)
54/)2)(4(
2
cUcU −+
27/)(2
3
cU −
25/)(2
3
cU −
TPS
πππ
<≤
Social welfare
162/)2)(719(
2
cUcU −+
81/)(10
3
cU −
375/)(46
3
cU −
PTS
SWSWSW <<
Figure 3 shows consumers’ total payments according to each pricing scheme. As shown in Figure
3, light users prefer pay-per-use pricing to subscription pricing, because pay-per-use pricing better
reflects their actual amount of consumption. On the other hand, heavy users prefer subscription
pricing to pay-per-use pricing, because subscription pricing fixes the consumer’s payment, regardless
of the actual amount of consumption. Preference for the two-part tariffs is typical of consumers whose
service consumption is intermediate. The consumers’ preference is indicated by the solid line in
Figure 3.
Figure 3. Comparison of consumers’ payments.
The marginal consumer who is indifferent to buying or not buying under pay-per-use pricing
(
P
u) does not purchase services under a two-part tariff. Similarly, the marginal consumer who is
indifferent to buying or not buying under a two-part tariff (
T
u) does not purchase services under
subscription pricing. It follows that
STP
uuu << and
PTS
NNN << . Under subscription
pricing, consumers with a low willingness to pay will not purchase services due to the high initial
Figure 3. Comparison of consumers’ payments.
The marginal consumer who is indifferent to buying or not buying under pay-per-use pricing (
uP
)
does not purchase services under a two-part tariff. Similarly, the marginal consumer who is indifferent
to buying or not buying under a two-part tariff(
uT
) does not purchase services under subscription
Sustainability 2020,12, 49 11 of 15
pricing. It follows that
uP<uT<uS
and
NS<NT<NP
. Under subscription pricing, consumers
with a low willingness to pay will not purchase services due to the high initial payment (
AS
). Under
pay-per-use pricing, the largest number of consumers purchase services at the lowest price, which
implies that consumer surplus can be higher than for any other pricing schemes.
Considering the information provided in Table 1and Figure 3, the following proposition is
obtained, by comparing the values of consumer surplus (CSi, i =S, P, T).
Proposition 1.
Consumer surplus is always the highest under the pay-per-use pricing and the lowest under
subscription pricing, that is,
when c is not very low: CSS<CST<CSPand when c is 0: CSS>CST
Proof:
If cis not lower than
ˆ
c
(or
c>ˆ
c
, where
ˆ
c
is satisfying
CSS=CST
), then
CSS<CST<CSP
. Also if
c=0, CSS>CST.
Proposition 1 implies that the number of consumers in the cloud market is an important factor from
the perspective of consumer surplus. Under pay-per-use pricing, low-end consumers can participate
in the market with the lowest amount of payment, which leads to a high consumer surplus. Figure 4
shows how consumer surplus changes for each pricing model. For a graphical view, I show the case in
which costs change from zero to the maximum value (
c≤U/
2
=
10) for U=20. As shown in Figure 4,
pay-per-use pricing is the best from the perspective of consumer surplus. This figure also shows that
a two-part tariffgenerally produces better results for consumer surplus than subscription pricing,
although subscription pricing is better than two-part tariffpricing when the costs are very low.
Sustainability 2019, 11, x FOR PEER REVIEW 11 of 15
payment ( S
A
). Under pay-per-use pricing, the largest number of consumers purchase services at the
lowest price, which implies that consumer surplus can be higher than for any other pricing schemes.
Considering the information provided in Table 1 and Figure 3, the following proposition is
obtained, by comparing the values of consumer surplus ( i
CS , i = S, P, T).
Proposition 1. Consumer surplus is always the highest under the pay-per-use pricing and the lowest under
subscription pricing, that is,
when c is not very low: PTS CSCSCS << and when c is 0: TS CSCS >
Proof: If c is not lower than c
ˆ(or cc ˆ
>, where c
ˆ is satisfying TS CSCS =), then .
PTS CSCSCS <<
Also if 0=c,.
TS CSCS > □
Proposition 1 implies that the number of consumers in the cloud market is an important factor
from the perspective of consumer surplus. Under pay-per-use pricing, low-end consumers can
participate in the market with the lowest amount of payment, which leads to a high consumer surplus.
Figure 4 shows how consumer surplus changes for each pricing model. For a graphical view, I show
the case in which costs change from zero to the maximum value ( 102/ =≤ Uc ) for U = 20. As shown
in Figure 4, pay-per-use pricing is the best from the perspective of consumer surplus. This figure also
shows that a two-part tariff generally produces better results for consumer surplus than subscription
pricing, although subscription pricing is better than two-part tariff pricing when the costs are very
low.
Figure 4. Consumer surplus variation with service costs.
By comparing the values of i
π
(i = S, P, T), the following proposition is obtained:
Proposition 2. The profits of the monopoly provider are maximized under two-part tariff and minimized under
subscription pricing, that is,
TPS
πππ
<≤
This holds only when the marginal cost of providing services is zero.
Proof: from eq. (4), 054/)83( 22 ≥−=− cUc
SP
ππ
and 0675/)(4 3>−=− cU
PT
ππ
, it holds
that SP
ππ
=when 0=c. □
0
50
100
150
200
250
300
350
400
450
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
4.25
4.5
4.75
5
5.25
5.5
5.75
6
6.25
6.5
6.75
7
7.25
7.5
7.75
8
8.25
8.5
8.75
9
9.25
9.5
9.75
10
CS
cost
Consumer Surplus
subscription
pay-per-use
two part tariff
Figure 4. Consumer surplus variation with service costs.
By comparing the values of πi(i=S,P,T), the following proposition is obtained:
Proposition 2.
The profits of the monopoly provider are maximized under two-part tariffand minimized under
subscription pricing, that is,
πS≤πP< πT
This holds only when the marginal cost of providing services is zero.
Proof:
From Eqation (4),
πP−πS=c(
3
U2−
8
c2)/
54
≥
0 and
πT−πP=
4
(U−c)3/
675
>
0, it holds
that πP=πSwhen c=0.
Sustainability 2020,12, 49 12 of 15
The merit of subscription pricing from the provider’s perspective is to receive revenue from
consumers with a lower willingness to pay (or light users). On the contrary, the provider can
obtain a large revenue from the consumers with a higher willingness to pay (or heavy users) under
pay-per-use pricing. As shown by the fact that
πP=πS
when
c=
0, the provider can make equal
revenue from either pricing scheme by optimizing the lump-sum and unit prices. A two-part tariff
balances the revenue from high-end and low-end consumers and maximizes the profit of the provider.
Considering the examples of Google App Engine and Joynet Smart Machine, two-part tariffpricing is
motivated by customer segmentation. Therefore, subscription pricing targets light users, pay-per-use
pricing targets heavy users, and two-part tariffs targets users with light-to-heavy service consumption.
Taking these two propositions into account, the following proposition ensues:
Proposition 3.
Social welfare is the highest under pay-per-use pricing and the lowest under subscription
pricing, that is,
SWS<SWT<SWP
Proof: SWP−SWT=8(U−c)3/10125 >0. We know SWT−SWS>0 with simple calculation.
Proposition 3 states that social welfare is the best under pay-per-use pricing although profits
are the best under a two-part tariffpricing scheme. This is because profits gained under a two-part
tariffscheme are lower than consumer surplus loss, as shown in Table 6and Figure 4. These results
contrast with those of a previous study [
9
] stating that social welfare is the best under a two-part tariff.
Proposition 3 implies that a regulatory regime and consumers prefer a pay-per-use pricing scheme,
but firms prefer a two-part tariffto pay-per-use pricing. From the perspective of social welfare, a
regulatory regime can require firms to charge a lump-sum payment at least on basic service packages
or to use a pay-per-use pricing scheme. The proposition also shows that subscription pricing is the
lowest from the perspectives of the provider’s profits and social welfare.
Table 7summarizes the results of this study using a numerical example when U=20 and c=
0. The results show that the two-part tariffincludes the other two pricing schemes. As we expected,
consumer demand (or the total number of customers who buy services) is the lowest, and the total
consumption of services by all customers is the highest under subscription pricing, which implies that
subscription pricing cannot be efficiently utilized by consumers and leads to some losses in consumer
surplus, compared with other pricing schemes.
Table 7. Comparison of the results using a numerical example (when U=20 and c=0).
Subscription (A) Pay-Per-Use (p) Two-Part Tariff(A, p)
Price AS=88.88 pP=6.66 AT=32 pT=4
Number of
consumers
NS=6.66 NP=13.33 NT=8
NS<NT<NP
Total Services (Q) QS=111.11 QP=88.88 QT=96
QS>QT>QP
Consumer surplus CSS=345.67 CSP=395.00 CST=341.33
CST<CSS<CSPwhen cis very low
Profits
producer surplus
πS=592.59 πP=592.59 πT=640
πS≤πP< πT(equal is holds when c=0)
Social welfare SWS=938.27 SWP=987.00 SWT=981.33
SWS<SWT<SWP
For a more graphical explanation, Figure 5depicts a provider’s profits, consumer surplus, and
social welfare, according to the price bundles of pand Aunder two-part tariff. It shows how a two-part
Sustainability 2020,12, 49 13 of 15
tariffis related to the two other pricing schemes and summarizes the results of this study graphically.
The optimal price bundle of (p,A) under two-part tariffis (4, 32), and the highest profit amounts to 640
at (p,A)=(4, 32). The left points in Figure 5represent optimal solutions under subscription pricing,
which is a special instance of the two-part tariffwhen a price bundle is (p,A)=(0, 88). The points on
the right peaks represent the instance of pay-per-use pricing when a price bundle is (p,A)=(6.66, 0),
which corresponds to the highest values of social welfare and consumer surplus.
Sustainability 2019, 11, x FOR PEER REVIEW 13 of 15
Figure 5. Graphical view of the results in the case of two-part tariff.
For a more graphical explanation, Figure 5 depicts a provider’s profits, consumer surplus, and
social welfare, according to the price bundles of p and A under two-part tariff. It shows how a two-
part tariff is related to the two other pricing schemes and summarizes the results of this study
graphically. The optimal price bundle of (p, A) under two-part tariff is (4, 32), and the highest profit
amounts to 640 at (p, A) = (4, 32). The left points in Figure 5 represent optimal solutions under
subscription pricing, which is a special instance of the two-part tariff when a price bundle is (p, A) =
(0, 88). The points on the right peaks represent the instance of pay-per-use pricing when a price
bundle is (p, A) = (6.66, 0), which corresponds to the highest values of social welfare and consumer
surplus.
5. Conclusions
Although many cloud service providers offer numerous online services, pricing schemes are
different depending on service types and service levels. Previous research has focused on firms’
profitability with respect to the limitations of free services. This paper analyzed and compared three
commonly used pricing schemes, i.e., subscription pricing, pay-per-use pricing, and two-part tariff
pricing from the perspectives of a provider’s profit, consumer surplus, and social welfare. In
particular, this paper showed how two-part tariff pricing can include the two other pricing schemes
of subscription and pay-per-use pricing, that two-part tariff is the most profitable pricing scheme
compared with the other two pricing schemes, and that pay-per-use pricing is the best pricing scheme
from the perspective of consumer surplus and social welfare, which contrasts with the results of a
previous study [9] stating that social welfare is maximized under a two-part tariff. Other results and
implications of this study are summarized below.
Firstly, both the provider and consumers prefer pay-per-use pricing to subscription pricing. If
the marginal cost of providing services is negligible, pay-per-use pricing and subscription pricing are
the same for the provider. In reality, there are additional considerations, besides user benefits and
cost structure. For example, metering service usage entails additional costs in the case of pay-per-use
pricing. Therefore, if the additional metering cost is large, subscription pricing can be preferred to
pay-per-use pricing in service models. Secondly, from the perspective of profit, firms prefer two-part
tariffs to pay-per-use pricing. Thirdly, pay-per-use pricing is the most convenient for consumer
surplus and social welfare if there is no additional metering cost, which implies that profit gains from
a two-part tariff do not make up for the loss in consumer surplus when a provider changes his/her
pricing scheme from pay-per-use pricing to two-part tariff. However, the government or consumers
are concerned about social welfare or consumer surplus. Therefore, a regulatory regime may have
100
200
300
400
500
600
700
800
900
1000
1100
(0, 88)
(0.25, 84)
(0.5, 80)
(0.75, 76)
(1, 72)
(1.25, 68)
(1.5, 64)
(1.75, 60)
(2, 56)
(2.25, 53)
(2.5, 53)
(2.75, 46)
(3, 43)
(3.25, 40)
(3.5, 37.5)
(3.75, 34)
(4, 32)
(4.25, 29)
(4.5, 26)
(4.75, 24)
(5, 22)
(5.25, 20)
(5.5, 18)
(5.75, 16)
(6, 14.2)
(6.25, 12.5)
(6.5, 10.8)
(6.66, 0)
(7, 8)
(7.25, 6.7)
(7.5, 5.5)
(7.75, 4.5)
(8, 3.5)
(8.25, 2.7)
(8.5, 2)
(8.75, 1.3)
(9, 0.8)
(9.25, 0.5)
(9.5, 0.2)
(9.75, 0.1)
(10, 0)
Profit, CS, SW
Price bundle (p, A)
Comparision of three pricing schemes ( when U=20, c=0)
Profit
CS
SW
Figure 5. Graphical view of the results in the case of two-part tariff.
5. Conclusions
Although many cloud service providers offer numerous online services, pricing schemes are
different depending on service types and service levels. Previous research has focused on firms’
profitability with respect to the limitations of free services. This paper analyzed and compared three
commonly used pricing schemes, i.e., subscription pricing, pay-per-use pricing, and two-part tariff
pricing from the perspectives of a provider’s profit, consumer surplus, and social welfare. In particular,
this paper showed how two-part tariffpricing can include the two other pricing schemes of subscription
and pay-per-use pricing, that two-part tariffis the most profitable pricing scheme compared with the
other two pricing schemes, and that pay-per-use pricing is the best pricing scheme from the perspective
of consumer surplus and social welfare, which contrasts with the results of a previous study [
9
] stating
that social welfare is maximized under a two-part tariff. Other results and implications of this study
are summarized below.
Firstly, both the provider and consumers prefer pay-per-use pricing to subscription pricing.
If the marginal cost of providing services is negligible, pay-per-use pricing and subscription pricing
are the same for the provider. In reality, there are additional considerations, besides user benefits
and cost structure. For example, metering service usage entails additional costs in the case of
pay-per-use pricing. Therefore, if the additional metering cost is large, subscription pricing can be
preferred to pay-per-use pricing in service models. Secondly, from the perspective of profit, firms
prefer two-part tariffs to pay-per-use pricing. Thirdly, pay-per-use pricing is the most convenient
for consumer surplus and social welfare if there is no additional metering cost, which implies that
profit gains from a two-part tariffdo not make up for the loss in consumer surplus when a provider
changes his/her pricing scheme from pay-per-use pricing to two-part tariff. However, the government
or consumers are concerned about social welfare or consumer surplus. Therefore, a regulatory regime
Sustainability 2020,12, 49 14 of 15
may have the incentive to lead providers to use pay-per-use pricing or two-part tariffpricing with a
minimum lump-sum fee for basic services and a unit price for usage.
This paper has a number of limitations with respect to customers’ contracts for pricing schemes.
Thus, in future work, the choice of contract by customers and pricing differentiation for heterogeneous
customers groups need to be analyzed.
Funding:
This work was supported by the Ministry of Education of the Republic of Korea and the National
Research Foundation of Korea (NRF-2019S1A5A2A01046398).
Conflicts of Interest: The author declares no conflicts of interest.
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©
2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
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