Page 72 - ITU Kaleidoscope 2016

• If this policy is to be proposed by the regulation au-
0
thority, it has to be considered in a competition market r · g [b] − t = 0 (10b)
structure. A reduced termination fee will be granted to | {z }
h
CPs and more content financed by themselves will be
available to end users. Following the implicit function theorem where :
In conclusion, the expansion of this policy provides bene- db ∂h db 1
∂t
= − =⇒ = (11a)
fits in terms of participation of indirect financing of univer- dt ∂h dt r · g [b]
00
∂b
sal service. Indeed, CPs are not involved in the universal
service programs with a corresponding participation being The exact value of b in equation (11a) is b [t], according to equation
taxes, funds or compensations. (10b), b depends on t at the equilibrium. However we note it only b
to simplify concepts, in a strict sens the exact value is defined as:
Defining a limited Internet service as a policy to increase In-
ternet penetration, the benefits merit less concern about the
db 1 0
competitive effects, specially in regions where a large income = 00 = b [t] (11b)
dt r · g [b [t]]
difference between their population is present.
From equation (11b) we can get:
Appendix 2 0 000
d b b [t] · g [b [t]]
= − 2 (12)
00
Proof of Proposition 1: optimal traffic data volume for CP, on dt 2 r · g [b [t]]
page 3
Replacing (11a) in equation (12):
We consider the following payoff from content provider:
1 000 000
2
d b r·g 00 [b] · g [b] g [b] 00
= − = − = b [t] (13)
arg max v cp [b] = r · g [b] − b · t dt 2 r · g [b] 2 r · g [b] 3
00
00
2
b
s.t. b ≥ 0
Proof of Theorem 1: optimal termination fee (t) monopolistic ISP,
where b is the optimization variable, v cp is the utility function for on page 3
content provider, in order to maximize v cp [b], we define a Lga-
We now optimize the ISP program under the assumption of a con-
grange’s function on Kuhn-Tucker conditions:
cave function:
L = r · g [b] − b · t − λ(−b)
π ISP = t · b [t] + (p z − c z ) α (14)
The first order condition is defined by:
Under universal service condition p z is defined as the net cost to
∂L 0 provide a limited bandwidth Internet service over the network. p z =
= r · g [b] − t + λ = 0 (7) c z. Replacing in (14), we get:
∂b
complementary slackness Kuhn-Tucker conditions for a point to be
π ISP = t · b [t]
a maximum are:
∂π ISP 0
= b [t] + t · b [t] (15)
λ(−b) = 0 (8) ∂t
λ ≥ 0 (9) We obtain t from equation (15):
∗
Solutions of (7) for λ are given by b [t]
∗
t = −
0
b [t]
0
λ = t − r · g [b] (10a)
Replacing (11a) in (15) we obtain:
t
0
00
∗
g [b] = t = −b · r · g [b] (16)
r
00
t > 0 because g [b] concave g [b] < 0.
Proof of Lemma 2: optimal traffic data volume for CP, on page 3
In the same way, the second derivative of π isp is simplified by (11b)
0
If t − r · g [b] > 0 =⇒ λ > 0. the condition −b = 0 is strictly and (13) .
necessary to obtain λ > 0, according equation (8). In other words,
the constraint is binding. 2 0 000
0 d π isp 1 − t g [b]
In contrast, if t − r · g [b] ≤ 0 =⇒ λ = 0. According to equation = − 3 t
00
00
2
dt 2 r · g [b] r · g [b]
(10a) where λ = 0, and replacing λ in equation (7), we get:
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