Comparison of Three Different Pricing Models for Cloud Computing Services
1Zhang Rui, 2Tang Bingyong
1, 2
Glorious Sun School of Business and Management, Donghua University, Shanghai, China, E-mail:[email protected]
Abstract
Based on the theory of two-sided markets, this paper discusses and compares the price strategies of cloud computing services from three different charging mode-charging a lump-sum fee, charging a per-transaction fee and two-part tariff. The result shows that prices for users or developers and the profits of cloud platforms are both directly proportional to the marketing differentiation strategy of cloud platforms and are inversely proportional to the dependence between users and developers and the scale effect of users; two-part tariff is the optimal pricing mode when users and developers are single-homing; Amazon, Google, Microsoft and other cloud computing service companies do not get maximum profits via charging a per-transaction fee.
Keywords
: Cloud Computing, Pricing, Two-Sided Markets, Lump-Sum Fee, Per-Transaction Fee, Two-Part Tariff1. Introduction
Cloud computing is the latest development trends in the field of information technology. Similar to other large-scale distributed systems, such as peer-to-peer networks, grid computing, cloud computing is shared and used via the Internet. It provides an immediate access to these resources, without up-front capital investments for consumers [1].Typically, cloud computing provides resources for consumers by infrastructure as a service (IaaS), platform as a service (PaaS) and software as a service (SaaS) [2].
In current market, the pricing strategies of cloud computing services follow a very simple method that all kinds of resources on cloud are charged at a fixed price by carriers. Pay per use, subscription and tiered pricing mechanism, are widely used in cloud services [3]. In particular pay per use mechanism is the most commonly way to price, which has been used by many companies, such as Amazon, to provide consumers with computing and storage services. This pricing method is easily acceptable by consumers. But using of cloud computing in width such as the quantity of resource types and services, as well as in depth such as the number of resource providers, are constantly increasing.
Therefore, with the rising number of consumers, the traditional pricing method of the fixed rate cannot accurately reflect the changes in the supply-demand relationship and the market conditions, and cannot meet the needs of consumers. It is necessary to find a suitable pricing method to solve these problems.
In this paper, an innovative way to use the theory of two-sided markets to analyze the economic attributes of cloud computing services is studied. Through discussions on three pricing methods, charging a lump-sum fee, charging a per-transaction fee and two-part tariff, the pricing of cloud computing services in a competitive situation is optimized. And it draws the main factors affecting pricing, and explores the most appropriate pricing model. Finally, it provides a unique analysis perspective on the market pricing and the competitive equilibrium of cloud computing industry.
The rest of this paper is organized as follows. Section 2 describes two-sided markets attributes for cloud computing services. Section 3 discusses the best price in competition respectively from a lump-sum fee, a per-transaction fee and a two-part tariff. Section 4 compares the three pricing mode to get a suitable pricing method and analyzes the main factors that impact the pricing. Section 5 concludes the study by summarizing key finding and giving suggestions for further research.
2. Two-sided markets for cloud services
According to the NDC report [4], the industrial chain of cloud computing mainly has ten components: hardware suppliers, cloud platform developers, system integrators, cloud application
developers, cloud resources providers, cloud services providers, cloud application service providers, network operators, terminal vendors and end-users. It is showed in Figure 1.
Figure 1. The structure of cloud computing industrial chain
In addition, the industrial chain can be divided into three categories: developers, users and carriers.
Developers including hardware suppliers, cloud platform developers, system integrators, and cloud applications developers, are mainly responsible for providing resources and research and development on cloud platform. Users, which include enterprise users, individual users and government users, are those purchasing products and services through cloud platform. Carriers that are composed of cloud resources providers, cloud services providers, and cloud application service providers, operate cloud platform to provide hardware, platform maintenance, customer service and other service. It can be seen that cloud platform which is operated by carriers is in the middle position of the industrial chain. So there are some characteristics of cloud platform.
2.1. Typical two-sided markets
In the academic circles, the definition of two-sided markets is proposed by Rochest and Tirole (2005) has been widely accepted. They gave a specific definition from the view of platform pricing structure, and they pointed out that the market for interactions between buyers and sellers is two-side if the volume V of transactions realized on the platform varies with p or p while the aggregate price level p = p+ p is kept constant (p and p are the platform charging per-interaction charges to the buyer and seller sides). In other words, the volume of transactions between the buyer and seller sides depends on the price structure, rather than the fees charged by the platform [5].
Typical two-sided markets involve buyers, sellers and the third-party platform. The transactions between buyers and sellers are conducted on the platform. While cloud computing services are provided by carriers, which offer an open service mode to users and developers, and contribute to the formation of exchanges. The market of cloud computing services is a typical form of two-sided markets. Products or services are provided based on cloud platform. In addition, on cloud platform the products or services are sold by using certain pricing strategies, for example charges for users and developers, and trades are secured between users and developers. Then, in the market of cloud computing services, users and developers as two-sides on cloud platform, carry on the principle of
mutual needs, i.e., developers need as many users as possible to use their products, meanwhile users need to have the products they need and more developers to choose. Therefore, for the market of cloud computing services, the more developers it can have, the more users it can get, and vice versa.
2.2. Network effects
Network effect is the basis for the existence of a two-sided market. It can be divided into two kinds:
cross-side network effect and same-side network effect [5, 6]. By cross-side network effect, we mean that if the number of buyers on one side of platform increases, sellers on the other side of platform may have more possibility to find suitable buyers and to close the deal.
When the scale of the participants on one side is affected by the quantity of participants in the same group, it has become common to discuss same-side network effect. This network effect can also be further divided into two parts, positive and negative. Negative same-side network effect often is related with sellers in a two-sided market, because larger number of sellers always results in the more intensive competition for buyers among sellers.
Cloud platform as a typical two-sided market also has the significant network effects, and the phenomenon of these network effects are as follows.
· Cross-side network effects between users and developers: the more developers access a cloud platform, the more users are attracted to use the cloud platform, and as a result there will be more developers willing to carry out transactions on the cloud platform.
· Positive same-side network effect among users: as the number of users accessing a cloud platform increases, the visibility of the cloud platform increases, and more users are attracted.
· Negative same-side network effect of developers: the more developers access the cloud platform, the tenser of the competition there exists.
In this paper, in order to be simple, we assume that each user or each developer chooses to join a single cloud platform, which is called single-homing. And we only consider the cross-side network effects between users and developers, and the positive same-side network effect among users.
3. The models
This model uses a Hotelling specification [7, 8] and involves competing platforms.
The market structure is depicted in Figure 2.
Cloud platform A Cloud platform B
y 1-y
x 1-x
Users
Developers
Figure 2. Market structure 3.1. Basic assumptions
1. Carriers, as well as users and developers accessing to cloud computing services platform are rational.
2. Suppose there exist two cloud platforms in the market, denoted by cloud platform A and B, and cloud platform A is located at 0 and cloud platform B is located at 1.
3. The market is fully covered users and developers, who either join in cloud platform A or cloud
platform B.
4. Users and developers with mass 1 each, are both uniformly distributed on the linear city of unitary length.
In the next part, the models are presented.
3.2. Charging a lump-sum fee
A lump-sum fee is the one-time expanse that users or developers need to pay before they access a cloud platform, and later do not need to pay any other fees. It is similar to subscription pricing model that users or developers sign contracts with carriers to use services of cloud platform at a fixed price within a certain period of time [3]. However, the price obtained in this paper is based on the changes of the market supply-demand, not simply decided by carriers.
Suppose pand p are lump-sum fees that cloud platform i charges a user and a developer, respectively. The user and the developer obtain the respective utilities {u, u} if they join cloud platform i (i=A, B).
The user and the developer locate at x, y in the unit interval in order to join cloud platform A. If cloud platform A attracts n users and ndevelopers, the utilities on this cloud platform are
u= v+ αn+ γn− p− tx, (1) and
u= v+ βn− p− ky, (2)
where t , k > 0 are the transportation costs that the user and the developer incur per unit distance traveled. And these parameters describe the sensitivity degree of users and developers to the differentiation of the two cloud platforms in the market. The parameter α > 0 measures the cross-side network effect that a user gets from each developer on the same cloud platform and the parameter β > 0 measures the cross-side network effect that a developer enjoys from interacting with each user on the same cloud platform. The parameter γ > 0 measures the same-side network effect that a user obtains from the users in the same cloud platform. The parameter v> 0 is the intrinsic utility from the service that a user or a developer benefits.
The utilities for a user and a developer that join cloud platform B are given by
u= v+ αn+ γn− p− t(1 − x), (3) and
u= v+ βn− p− k(1 − y), (4) Before turning to the equilibrium analysis, the following assumptions are made.
Assumption 1[7] The cross-side network effect parameters {α, β} are relatively small compared to the transportation cost parameters {t, k}.
Assumption 2 The parameters, k, t, γ, α and β satisfy the following inequality
4k(t − γ) > (α + β). (5)
According to the Hotelling specification, i.e., u= u and u= u, the number of users and developers who join cloud platform A are given by
⎩
⎨
⎧n=1
2+α(n− n) + γ(n− n) − (p− p) 2t
n=1
2+β(n− n) − (p− p) 2k
. (6)
Using the fact that n+n= 1, n+n= 1, the market shares are
⎩⎪
⎨
⎪⎧ n=1
2+k(p− p) + α(p− p) 2[αβ − k(t − γ)]
n=1
2+β(p− p) + (t − γ)(p− p) 2[αβ − k(t − γ)]
. (7)
And the profit of cloud platform i is
π= (p − f)n + (p − f)n. (8) where f measures the cost for serving a user and f measures the cost for serving a developer.
Here we consider the case of a symmetric equilibrium, i.e., p= p and p= p.
Then due to Assumption 1 and Assumption 2, expression (8) is concave in these prices. So Putting (7) and (8) together, differentiating the new expression with respect to the prices and setting the resulting first-order conditions to 0, we obtain equilibrium prices.
Proposition 1 With the condition of charging a lump-sum fee, the equilibrium prices charged by cloud platform i are
p = (t − γ) + f− β, (9)
and
p = k + f− α. (10)
Equilibrium prices lead to the number of users and suppliers:
n= n=1
2 , n= n=1
2. (11)
The profit for cloud platform i amounts to
π=t + k − γ − α − β
2 . (12)
3.3. Charging a per-transaction fee
Users or developers pay in the function of the quantity they trade with the other side. It is called charging a per-transaction fee, which is similar to pay per use mechanism. In this pricing mode, users or developers need to pay in service unit [3].
In this section we discuss the case that cloud platforms charge transactions fee to the users and the developers, given Assumption 1 and Assumption 2 still hold.
Suppose that cloud platform i charges θ per transaction for each user, and θ per transaction for each developer.
And μ represents the expected number of transactions completed by each user or each developer. It as a exogenous variable, is constant in the derivation process of mode. λ is the probability that users or suppliers complete transactions (0 ≤ λ ≤ 1) [9]. In the actual market, the case of λ = 1or λ = 0 is rare.
So the utilities for a user and a developer enjoys from joining cloud platform A and B are given by u= v+ αn+ γn− θμ − tx, u= v+ αn+ γn− θμ − t(1 − x), (13) and
u= v+ βn− θμ − ky, u= v+ βn− θμ − k(1 − y). (14) Similarly, the number of users and developers in cloud platform A are
⎩⎪
⎨
⎪⎧ n=1
2+μk(θ− θ) + μα(θ− θ) 2[αβ − k(t − γ)]
n=1
2+μβ(θ− θ) + μ(t − γ)(θ− θ) 2[αβ − k(t − γ)]
. (15)
The profit function of cloud platform i is
π= (θ − c)μ(λn) + (θ − c)μ(λn). (16) where cmeasures the cost for serving a user in per trading, and c measures the cost for serving a developer.
By maximizing the profit functions above, we achieve the following result.
Proposition 2 With the condition of charging a per-transaction fee, the equilibrium prices charged by cloud platform i are
θ = c+(t − γ − β)
μ . (17)
and
θ = c+(k − α)
μ . (18)
So the profit of platform i is
π=λ(t + k − γ − α − β)
2 . (19)
3.4. Two-part tariff
A two-part tariff is a pricing scheme in which the price is composed of two parts, a lump-sum fee and a per-transaction fee. When a user or a developer joins a cloud platform for the first time, he needs to pay a registration fee to the carrier. Then he is charged a transaction fee for each trading.
Similar to the previous variable assumptions, cloud platform i offers the lump-sum price pairs (p, p ) and the per-transaction price pairs θ, θ.
Here the utilities of a user is given by
u= v+ αn+ γn− p− θμ − tx. (20) and
u= v+ αn+ γn− p− θμ − t(1 − x). (21) So the number of users who join cloud platform A given by the Hotelling specification is
n=1
2+k(p− p) + α(p− p) + kμθ− θ + αμθ− θ
2[αβ − k(t − γ)] . (22)
The number of developers is given in a similar way:
n=1
2+β(p− p) + (t − γ)(p− p) + βμθ− θ
+ (t − γ)μθ
− θ
2[αβ − k(t − γ)] . (23)
Due to the two-part tariff mechanism, the profit of cloud platform i is made up of two parts:
π= [(p − f)n+ (p − f)n] + θ − cμλn + θ − cμλn. (24) In the same manner, the best prices are presented.
With the condition of two-part tariff, the equilibrium prices charged by cloud platform i are p = (t − γ) + f− β − θ − cμλ, (25) and
p = k + f− α − θ − cμλ. (26) Finally, we can get the profit of cloud platform i:
π=t + k − γ − α − β
2 . (27)
4. Discussion
In this section we compare the cases analyzed so far.
First of all, we conclude the equilibrium prices charged by cloud platforms and the profits for cloud platforms in the tree charging methods. It is showed in Table 1.
Table 1. Pricing formulae and profits of three charging methods
Charging methods Pricing formulae Profit
A lump-sum fee p = (t − γ) + f− β, p = k + f− α t + k − γ − α − β 2 A per-transaction fee θ = c+(t − γ − β)
μ , θ = c+(k − α) μ
λ(t + k − γ − α − β) 2
Two-part tariff p = (t − γ) + f− β − θ − cμλ, p = k + f− α − θ − cμλ
t + k − γ − α − β 2
From Table 1, we note that
> 0,
> 0,
> 0and
> 0 in all the cases. It implies that the prices charged by cloud platforms to users or developers are affected by the transportation costs. That is to say, the prices are related with the differentiation of the two cloud platforms. And the discussion is summarized in the next proposition.
Proposition 3 In a competition market, when each user or each developer chooses to join a single cloud platform, the prices they pay to cloud platform rise proportionately to the sale of the differentiation between cloud platforms.
Then, we consider the influence brought by the cross-side network effects between users and developers on the prices.
It is obvious that
α < 0,
β < 0,θ
α < 0 and θ
β < 0. It indicates that the increasing of the cross-side network effects leads to the reducing of the prices. And it is because these network effects are transformed into price by cloud platforms to balance the need of users and developers.
Meanwhile, we have
γ < 0 and θ
γ < 0. When the same-side network effect among users is increasing, the users' prices are decreasing. This is because with the increasing of the number of users, the cost that cloud platforms allocate to each user declines, thus the prices for users are reduced.
We summarize the above discussions by the following proposition.
Proposition 4 In a competition market, when each user or each developer chooses to join a single cloud platform, the prices that users and developers pay for are inversely proportional to cross-side the network effects between them; and the users’ prices are also in inverse proportion to the same-side network effect among users.
Similar to the analyses above, we have π
> 0,π
> 0 ,π
γ < 0,π
α < 0 and π
β < 0 in all the cases. It turns out that the profit for each cloud platform is directly proportional to the transportation costs, and is inversely proportional to the cross-side network effects and the same-side network effect among users. So Proposition 5 is presented as follow.
Proposition 5 In a competition market, when each user or each developer chooses to join a single cloud platform, the marketing differentiation strategy of cloud platforms and the scale effect of users, could improve the profit of cloud platforms; the dependence between users and developers could lead to the decline of the profit.
Ultimately, we compare the prices and the profits in the three charging methods.
Owing to 0 ≤ λ ≤ 1, the profit by charging a lump-sum fee is smaller than the one by charging a per-registration fee as well as the one by two-part tariff unless λ= 1. However, that all the tradings are successful is a rare occurrence. Then, under the same profitable condition, the prices by charging a lump-sum fee are lower than the ones by two-part tariff. Now from the perspective of users and developers, they are more willing to join the cloud platform, which offers a cheaper registration fee, and to make the next payment depending on their actual needs. So they tend to accept the mode of two-part tariff.
Proposition 6 In a competition market, taking into account the ideas of the users and the developers, two-part tariff for a cloud platform is the optimal pricing strategy.
From Proposition 6 we can note that charging a per-transaction fee, namely pay per use mechanism, is not the best pricing, which could not bring the most profit for a cloud platform. While in the real market, Amazon, Google and other cloud computing services carriers have mostly chosen pay per use mechanism, which does not maximize their profits. Therefore, a more reasonable pricing strategy is an inevitable choice.[10]
5. Conclusion and future directions
This paper analyzes the pricing strategy of cloud computing service by using the theory of two-sided markets. By discussing the pricing models from three charging mode, charging a lump-sum fee, charging a per-transaction fee and two-part tariff, and comparing the prices and the profits of the three cases, the following conclusions were obtain:
· The prices for users or developers and the profits of cloud platforms are both directly proportional to the marketing differentiation strategy of cloud platforms and are inversely proportional to the dependence between users and developers and the scale effect of users.
· In the case of all users and developers are single-homing, cloud platforms should adopt the way of two-part tariff.
· The pricing mechanism being used by Amazon, Google, Microsoft, and other foreign cloud computing service carriers are not the best one.
The discussions in this paper are all based on the assumption of the single-homing of users and developers. In fact, both of them can also be multi-homing or partial multi-homing in the market. And
this paper does not cover the discussion of differentiated services on cloud platforms. These issues will be analyzed in further papers.
6. Acknowledgement
This work is supported by National Key Technology Research and Development Program of the Ministry of Science and Technology of China under Grant No. 2012BAH19F00 and by Doctoral Thesis Foundation of Donghua University under Grant No. 12D10818.
7. References
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