International Journal of Scientific & Engineering Research, Volume 5, Issue 5, May-2014 1339
ISSN 2229-5518
Evaluation of Different Tariff Rate offered by Mobile Telephone Operators Using Personal Social Network Model
S. M. Yahea Mahbub1, Md. Rashedul Islam2, Sheikh Rashel Al Ahmed3
Pabna University of Science and Technology1, 2, 3
Abstract— Different tariff offer of the mobile telecommunication operator Grameenphone (Telenor Group) is evaluated using personal social network model. It is found that the offer of price is valid and provides some consumer surplus also. An optimum point of call rate is found beyond which consumer surplus becomes negative. So this personal social tie network model can be used for evaluation as well as for optimization of any tariff offer.
Index Terms— Social tie, Tariff plans, Pricing policy, Consumer Surplus, Telecommunication Market, Utility, Network Externality.
—————————— ——————————
etwork externality or Network effect is a very important parameter in telecommunications market. When con- suming a network good, consumers’ value is not only from quality and quantity of certain products, but also
from the size of the network of the product, which means the number of users in the network increase, the value of the net- work to other users also changes [1]. In case of telecommuni- cations market the subscriber will use the telecommunication service to communication with each other and consumers will value more of a certain network if more number of people in that telecommunications network.
The cheaper the tariff rate or the price of the service, the more communication will be created and the more value of consumer will be produced. The closer the relation between the communicator, the more demand for the telecommunica- tion service will generate. Therefore, the lower tariff rate or the price of the service between the communicator with close tie or relationship will produce large consumer value and sur- plus.
If we shift our focus from consumption of network to con- sumption of individual communication through the network, the personal social network’s impact on consumer’s value and demand becomes very important [1]. For example, a mobile phone subscriber evaluates his certain call with someone else on the basis of the relationship with this personal he talks with through mobile network. This user’s utility would be high if talking with closed friends or family members, while his utili- ty would be minimized when he receives a call from a sales agent who has weak tie with him. Thus we can say that the marginal utility obtained by this subscriber from strong tie communication is bigger than marginal utility from weak tie communication. Therefore the subscriber’s demand for the communication with someone with strong tie with this sub- scriber is higher than the demand for communication with weak-tie person.
Let us consider a telecommunications market that consists of N subscribers who demand for the communication service. The value of the communications between a pair of subscriber depends on the strength of their social tie.
We represent strength of tie between two subscribers with a one-dimensional index variable, denoted by t. Consistent with literature on social network analysis, we assume three levels of tie strength: strong ties (denoted by t = s), weak ties (t=w), and absence of tie (t=0). [2] [3] [4]
A subscriber will obtain positive utility from the communi- cation with another subscriber if and only if these two sub- scribers have either a strong (t=s) or weak (t=w) tie. Commu- nication between a pair of subscriber with no social tie (t=0) will produce zero utility or negative utility. Let us define these subscribers with whom a subscriber has either a strong or a weak tie as the consumer’s personal communication network,
where 𝑡 ∈ {𝑠, 𝑤}.
The telecommunications service providers follow discrimi- natory pricing scheme by offering different price plan for dif-
ferent social tie network. Let us define a price plan (𝑝𝑠 , 𝑝𝑤 ), where 𝑝𝑠 for the communications between subscribers with strong ties and 𝑝𝑤 for the communications between subscrib-
ers with weak tie. Amount of service consumption can be
measured either in minutes or seconds.
But the numbers of strong tie within the consumer’s per-
sonal communication network is limited by the telecommuni-
cations service providers’. The numbers of strong tie within
the consumer’s personal communication network, which we
call the numbers of Friends and Family (FnF) member, vary
with different telecommunications service providers’. The var-
iable fees of the price plan generally depend on strength of
ties. We call the difference between two variable fees tie
strength-based discount. This discount, in another word, is the
consumer surplus.
A consumer’s utility from communications with another person depends on strength of their tie. For a pair of subscribers with a tie
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International Journal of Scientific & Engineering Research, Volume 5, Issue 5, May-2014 1340
ISSN 2229-5518
1 𝑠 − 𝑝 )2 (7)
strength t, we let 𝑢𝑡 (𝑞) denotes each subscriber’s utility from their
communications of amount 𝑞 and propose a quadratic utility func-
𝑣𝑠 (𝑝𝑠 ) =
2𝛼𝑠 (𝛼1 𝑠
tion as follows:
𝑢𝑡 (𝑞𝑡 ) = 𝛼𝑡 𝑞 −
1 𝑡
𝛼𝑡 𝑞 2
𝑡
, where 𝛼𝑡 > 0, 𝛼𝑡 > 0 and 𝑡 ∈ {𝑠, 𝑤}
1 2
Let us consider two tariff packages of the mobile telephone op-
erator “Grameenphone”:
Smile
[5] (1)
The values of the social tie strength coefficients 𝛼𝑡 and 𝛼𝑡 de-
1 2
pend on the strength of social tie (t). The concave utility function in
equation (1) implies a decreasing marginal utility when amount of
communication increases. As people tend to transmit more im-
portant information at the beginning of their conversations, such
utility function fit well in the telecommunications market analysis.
We also assume the absence of income effect because consumers’
Baadhon
Now in “Smile” package:
Normal Grameenphone to Grameenphone tariff rate is = 1.50
taka/min
FnF (3 FnF) tariff rate, 𝑝𝑠 = 0.49 taka/min [6]
So for strong tie network consumer get a surplus, 𝑣𝑠 (𝑝𝑠 )= (1.50-
0.49) =1.01 taka/min
Thus for “Smile” package equation (7) becomes:
communication expense typically accounts for a small proportion
1.01 = 1
(𝛼 𝑠 − 0.49)2
of their budget.
Now to find out the optimal amount of communication of a
subscriber with another subscriber we need to solve the consumer
utility maximization problem with respect to 𝑞.
𝑞𝑡 (𝑝𝑡 ) = arg max{𝑢𝑡 (𝑞𝑡 ) − 𝑝𝑡 𝑞𝑡 } (2)
Here 𝑢𝑡 (𝑞𝑡 ) is consumer utility function and 𝑡 ∈ {𝑠, 𝑤}.
When the optimal quantity of communication is positive, we
could get an optimal quantity of communication through solving
first-order condition of equation (2) i.e.:
𝑑 {𝑢 (𝑞 ) − 𝑝 𝑞 } = 0 (3)
2𝛼2
≫ 2.02𝛼 𝑠 = 𝛼 𝑠 2 − 0.98𝛼 𝑠 + 0.2401 (8)
2 1 1
Now in “Baadhon” package:
If a subscriber migrate his package from “Smile” to “Baadhon”
then he have to talk to his strong tie network at a flat rate of 0.79
taka/min, as “Baadhon” package has no different price plan for
FnF. But the subscriber can still enjoy talking to his strong tie net-
work at a lower rate than Smile which creates a surplus.
Tariff rate, 𝑝𝑠 = 0.79 taka/min [7]
So consumer surplus, 𝑣𝑠 (𝑝𝑠 ) = (1.50-0.79) = 0.71 taka/min
𝑑𝑞
𝑡 𝑡
𝑡 𝑡
Thus for “Baadhon” package equation (7) becomes:
Putting utility function from equation (1) into equation (3) and
0.71 = 1
𝑠 (𝛼1 − 0.79)
solving the equation (3) we get as follows:
2𝛼2
𝑠
𝑠 2 𝑠
𝑡 𝑡
≫ 1.42𝛼2 = 𝛼1
− 1.58𝛼1 + 0.6241 (9)
𝑝𝑡 = 𝛼1 − 𝛼2 𝑞𝑡 (4)
Equation (4) indicates that, for two subscribers that have a tie of
𝑡
Now solving equation (8) and (9) we get:
𝑠 2 − 1.8𝛼 𝑠 + 0.91974 = 0 (10)
strength of t, the marginal value of their communications is 𝛼1 for
𝑡
0.6𝛼1 1
the first unit of consumption and then decreases by 𝛼2 for each
additional unit of consumption.
Equation (4) is called the “Inverse Demand Function”. We know
Using standard solution system of a quadratic equation we get
from equation (10):
𝜶𝒔 = 𝟐. 𝟑𝟑𝟑𝟑𝟐 𝒐𝒐 𝟎. 𝟑𝟔𝟑𝟔𝟑
quantity demanded (Q) is a function of price (P). The inverse de- mand function treats price as a function of quantity demanded, i.e.
𝑃 = 𝑓−1 (𝑄). It is also called the “Price Function”.
Now putting the values of 𝛼 𝑠 in equation (8) we get:
𝜶𝒔 = 𝟔. 𝟕𝟎𝟑𝟕𝟑 𝒐𝒐 𝟎. 𝟎𝟔𝟑𝟔𝟑
So have two sets of solutions:
𝑠 𝑠
Rearranging equation (4) we get the optimal demand:
Solution Set 1: (𝛼1 , 𝛼2 ) = (2.34682, 1.70676)
𝑡 𝑠 𝑠
𝑞𝑡 =
𝛼1 −𝑝𝑡
𝑡
2
Solution Set 2: (𝛼1 , 𝛼2 ) = (0.65318, 0.01318)
Let 𝑣𝑡 (𝑝𝑡 ) denotes the consumer surplus of a subscriber from the consumption of the communications service of amount 𝑞𝑡 . Substituting 𝑞𝑡 from equation (5) into the utility function (equa-
tion 1) we obtain the equation for the consumer surplus:
In this following section will use the solution sets, obtained in the previous section, into equation (7) to generate some graphs
1 𝑡 2
𝑣𝑡 (𝑝𝑡 ) =
2𝛼𝑡 (𝛼1 − 𝑝𝑡 )
(6)
(plot of tariff rate vs. consumer surplus) using MATLAB. We will
observe the variation of consumer surplus in accordance with the
tariff rate.
Using Solution Set 1 equation (7) becomes:
In this following section we have evaluated the social tie
𝑣 (𝑝 ) = 1 (2.34682 − 𝑝 )2
3.41352
(11)
𝑡 𝑡
strength coefficients 𝛼1 and 𝛼2 under some certain conditions using
Using Solution Set 2 equation (5.7) becomes:
equation (6). We have chosen the most popular mobile telephone
operator in Bangladesh “Grameenphone” for our research work
𝑣𝑠 (𝑝𝑠 ) =
1
0.02636
(0.65318 − 𝑝𝑠 )2 (12)
and taken their tariff packages as reference price plan. For simplici- ty we have only taken the tariff rates-
at “peak” hour
between the same telecom operator
between strong tie network (i.e. within FnF member) and
without VAT and call establishment or connection charg-
es
Considering only strong tie network i.e. in our real case scenario
only within FnF members, equation (6) becomes:
Now we will use equation (11) and (12) to generate our desired
plot.
Using Solution Set 1 the plot is like bellow:
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International Journal of Scientific & Engineering Research, Volume 5, Issue 5, May-2014 1341
ISSN 2229-5518
Fig 1: Variation of consumer surplus with tariff rate
(for Solution Set 1)
Using Solution Set 2 the plot is like bellow:
Fig 2: Variation of consumer surplus with tariff rate
(for Solution Set 2)
When the tariff rate is zero then the maximum consumer sur- plus that a subscriber can gain should be equal to the highest of- fered tariff rate. From figure 1 we see that at zero tariff rate the con- sumer surplus is approximately equal to 1.5 Tk/min which is the highest offered tariff rate of the two price plans we considered. At tariff rate 2.37 Tk/min the consumer surplus is zero. This is the optimum tariff rate that this mobile telephone operator can charge for these two tariff plans. Beyond the optimum tariff rate the con- sumer surplus is actually negative, though it appears to be positive. To explain the situation better that any price more than the amount that makes the consumer surplus zero will make consumer surplus negative. That means the tariff rate will become beyond consum- er’s expectation.
The company offers a tariff rate of 1.5 Tk/min and subscribers get some amount of consumer surplus. The company does it delib- erately to increase the amount of communication by the subscribers that eventually increase the revenue of the company. The company always offers a tariff rate lower than the hardest rate (rate with zero consumer surplus). This operator can charge tariff rate up to 2.37
Tk/min. But how much lower rate it will offer depends on the de- tailed financial analysis of the operator, which includes operator’s investment return rate, profit target and market competitiveness etc.
Figure 2 exhibits unrealistic nature. Here at zero tariff rate the consumer surplus is 16 Tk/min, which is not possible because con-
sumer surplus cannot be more than offered price. Thus solution pair 2 is not acceptable.
But both the figures 1 and 2 shows that the subscribers of the mobile telephone operator enjoy an increasing consumer surplus as the call rate decreases. This result fits very much from both the point of views of standard economics and our general perception. Thus the price plan is justified from the point of view of our per- sonal social network model.
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[3] Wasserman, Stanley and Katherine Faust. (1994). Social Net- work Analysis: Methods and Applications, Cambridge Uni- versity Press
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[5] R. M. Shi, "Social Network-Based Discriminatory Pricing Strat- egy,”.http://www.researchgate.net/profile/Mengze_Shi/pu blication/5152935_Social_Network- Based_Discriminatory_Pricing_Strategy/file/50463529e2f7a7d
3ae.pdf.2003
[6] Grameenphone. [Online].http://www.grameenphone.com/
products-and-services/packages/smile.2011
[7] Grameenphone. [Online]. http://www.grameenphone.com/
products-and-services/packages/baadhon.
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