Vertical separation, Investment incentives and Collusion in network industries Rafika KHABBOUCHI*
*
Laboratoire d’Analyse en Sciences Economiques de Richter LASER , Université de Monttpellier1
[email protected],
[email protected]
ABSTRACT This paper analyses the investment incentives
The most of studies ask whether there exists
in a vertical separation structure with symmetric costs
an optimal access pricing rule that both preserves
and its impact on firms'behaviors on the downstream
socially optimal investment and competition's level.
market which are competing under Bertrand duopoly
Gans(2001) show that regulation could be effective in
and are differenciated horizontally à la Hotteling. We
promoting downstream competition but it will be less
find that when firm less value the investment made
incentives to invest in essential facilities. In the same
upstream, it will be more encouraged to deviate from
way, Gautier and Mitra (2005) consider a vertically
the collusive agreement. It is also shown that firms will
integrated firm owning an essential facilities and
have more incentives to collude when the difference
competing with a potential entrant in the downstream
between their ability to use infrastructure investment
market: it is showing that even if the regulation
will increase too.
mechanism objectives are to ensure financing of the
Keywords: Networks industries, investment,
essential
facilities
and
encouraging
competition,
inefficient entry occurs and captures the trade off
collusion,
between market efficiency and infrastructure financing.
1.
INTRODUCTION One of the main concern of the regulation is
how to enhance competition and investment incentives. It is commonly suggested, because of the higher costs, that it is socially optimal to have a natural monopoly in charge of infrastructure and provding access to firms competing on the retails market.
So, we could ask
about vertical separation or integration structure depending on the essential facilities provider will operate both in the upstream and the downstream market. In the case of studying investment incentives and regulating firms' behaviors, it is commonly dealed with the vertical integration stucture. The most important concern that was studied until now was
Valetti and Cambini (2003) propose a model built on the framework of ALRT(1998)1 considering the case where operators have to invest in their own network facilities with vertical differenciation. They study the impact of access charges on the investment incentives in networks showing that higher access charges induce firms to less invest and the same quality's impact generates tacit collusion. Kotakorpi (2006) whose study is close to ours with some specifications and with more focus on the impact of the investment decision made upstream on firms' behaviors in the retail market. Where in this paper we consider a vertical separation structure, Kotakorpi proposes a model with vertically integrated
granted to the impact of regulator's decisions on access to essential facilities on firms' behaviors.
1
1
Amstrong, Laffont, Rey and Tirole.
monopolist network provider who faces rival operators in the retail market. He also examines the networks operator's incentives for infrastructure investment finding that access price regulation reduces investment incentives and underinvestment may have negative effects on the viability of competition. Foros (2004) studies also the regulation of access and the investment incentives in vertical integration structure. He proposes
It could be asked whether the investment will be more beneficial to this or that firm depending on their ability to use new technology involved by infrastructure’investment. In Valletti&Cambini (2005), the quality level representing the operator’s investment affects both quantities and utilities. In our paper, the parameter k represents the level of investment and has an effect on consumers’utilities. The facility based firm incurs quadratic investment costs
1 2
μk 2
where
μ f0
. We
a model where retailers differ in their ability to offer a
assume that customers have unit demand: so the one who subscribes to a firm i pays pi for single unit of
value added service showing that competition in the
services. The utility from bying a unit of service is growing with the firm’s ability to use new technology:
downstream market will depend on whether it will be
U i = u + σ i k − pi − txi
access regulation or not and vertically integrated firm will use overinvestment for forecolsure. As shown, it is more common to consider vertical integration structure to deal with investment incentives and firms' behaviors. This paper propose to deal with a vertical separation market structure where the access to essentials facilities will be provided by a monopoly
As in Valletti&Cambini (2005) and LRT2 (1998), the parameter u represents a fixed surplus component from subscribing, supposed to be large enough as all customers prefer to be always connected and the market will be always covered. As networks are horizontally differentiated à la Hotteling so a customer will incur the cost t as not being subscribing to a one not replying to his own preferences. with t > 0 A customer buys from the network i if and only if:
operating on the upstream market and that decide to
Ui > U j
invest : the idea is to examine the impact of investment decision made upstream on firms'behaviors competing downstream
under
Bertrand
duopoly
in
the
donwnstream market depending on firms'collusion incentives.
In our game, there will be three stages. We calculate the network’s profits corresponding to the strategies applied in the downstream market: deviation, collusion or competition respectively that we note as:
πD, πC
and π . We than calculate the collusion threshold δ i that we define as follow:
δi = 2.
THE MODEL
We propose to study a model that is built on the framework of Foros (2004), Valletti&Cambini (2005) and Kotakorpi (2006). We consider an horizontal differentiated networks where an investment stage is prior to the competition one. However, we focus on the case of vertical separation where the essential facilities will be provided by an independant firm operating in the upstream market. As in Foros (2004), we assume that consumers are heterogenous in their basic willigness to pay for service. As networks use the same essential facilities and will benefit from infrastructure’s investment , so we will present this specification through the parameter
σ i ∈ ] 0,1[ . We
2
π iD − π iC π iD − π iCC
The idea is to compare the firm’s collusion threshold in a vertical separated market structure in order to find which one will have more incentives to collude in respect to investment made upstream. We model the case where the essential facility will be provided by an independant firm operating in the upstream market to the networks competing on prices ( à la Bertrand) in the downstream one. We consider that both firms have the ability to use the new technology involved by the investment made upstream as σ 1 > σ 2 . The game consists of three stages: 1. First, the independant firm operating in the upstream market chooses to invest in infrastructure and sets the level k .
consider, unlike in Kotakorpi (2006),
that in the case of vertical separation, the firm 1 will be also favored as σ 1 > σ 2 .
CC
2
Laffont, Rey and Tirole.
2. Second, the access price a will be fixed. 3. Third and finally, networks compete on prices in the downstream market. The idea is to see if networks will have an incentive to collude or not depending on the provided investment and access level, repsectively represented by k and a . We will consider that networks will be symetrics in cost as they only have to pay the access provided upstream by an independant firm. Both networks operate independently of the upstream market, they are differentiated horizontally à la Hotteling. So let the firm located at the origin indexed by 1 and that located at the end by 2 . The profit function is writen as follows:
Maxπ i = ( pi − a ) qi 1
We ∂p2CC ∂σ 1
< 0,
note
∂p1CC ∂σ 2
∂p1CC ∂σ1
that
∂p1CC ∂σ 2
> 0,
< 0 and
> 0.
When networks have the same ability to use the infrastructure’s invesment level càd σ 1 = σ 2, they will charge the same price p = a + t which is equal to the marginal cost and which obviously depends on the access. Replacing (2) and (3) in (1) , we obtain the equilibruim profits : CC
π 1CC
(1)
( 3t + (σ =
1
−σ2 ) k )
( 3t − (σ =
2
π 2CC
18t
1
−σ2 ) k )
18t
(4)
Hence, a customer who chooses to subscribe to the firm 1 and respectively 2 will have an utility function equal to :
σ1 = σ 2 ,
When
firms will always make
positive profits that only depend on t : π
U1 = u + σ 1k − p1 − tx
CC
= 2t > 0 .
2. Collusion: We know that as networks are horizontally differentiated and competing on prices in the retail market so they may collude. In this case, they will conduct as a monopoly. The collusion price for each network will be equal to that maximizing the monopoly profit:
and
U 2 = u + σ 2 k − p2 − (1 − x)t
We are going now to illustrate the different strategies that firms may adopt in the downstream market. We start by calculating the equilibruim prices ans quantites. Than, we will draw the corresponding equilibruim profits.
p 1C =
4u − 2t +
(3 σ
1
+ σ
2
)k
4
(5 ) p
1. Competition
C 2
=
4 u − 2 t + (σ 4
1
+ 3σ
2
)k
Each network tends to maximize its profit such that:
π i = ( pi − a ) qi
The difference between equilibruim prices, in this case, depends on both σ 1and σ 2 .
the equilibruim quantities are equal to:
We note that when networks share the same ability σ 1 = σ 2 = σ , prices will be equals and will
q1CC =
3t + (σ 1 − σ 2 ) k 6t
q2CC =
3t − (σ 1 − σ 2 ) k also depend on the investment level k such that 2 C 2u −t + 2σ k 6t :p = . 2 (2)
Where the collusion quantities for each firm will be equal to:
It is clear that firms are active if and only if 0 < 3t < Δσ k as σ 1 > σ 2 . the equilibruim prices are such that :
p1CC = a + t +
(σ 1 − σ 2 ) k 3
p2CC = a + t −
q1C =
(σ 1 − σ 2 ) k 3 3
(3)
The collusion profits :
π1C = (7)
3
2t + (σ 1 − σ 2 ) k C 2t − (σ 1 − σ 2 ) k q2 = (6) 4t 4t
( 2t + (σ
1
− σ 2 ) k ) ( 4u − 4a − 2t + ( 3σ 1 + σ 2 ) k ) 16t
2
π 2C =
( 2t − (σ
1
− σ 2 ) k ) ( 4u − 4a − 2t + (σ 1 + 3σ 2 ) k ) 16t
σ1 = σ 2 = σ
When
, they will share the
market and make the same profit:
π = C
( 2 u − 2 a − t + 2σ k ) 4
When
.
the equilibruim prices will be equal to:
4 u + 4 a + 2 t + (5 σ 8
2
− 5σ
2
(8 ) 4 u + 4 a + 2 t − (σ 8
1
the deviated quantities for each network are such that:
4u − 4a + 2t + ( 5σ1 −σ2 ) k 16t 4u − 4a + 2t −(σ1 −5σ2 ) k q2D = 9 16t
q1D =
(9)
σ i , i = 1, 2 .
After calculating the equilibruim quantities and replacing the corresponding prices into the profit function, we find :
π
( 4u − 4a + 2t + ( 5σ =
π 2D =
−σ2 ) k )
2
− 5σ 2 ) k )
2
1
128t
1
2 u − 2 a + t + 2σ k ) 32 t
10
In order to insure the existence of duopoly model, the following restrictions on parameters should be satisfied :
2
.
δi > δ ∗
δ1 =
9( 4u−4a−6t +(σ1 +3σ2 ) k)
4u − 4a + (σ 1 + 5σ 2 ) k 4u − 4a + ( 3σ 1 + σ 2 ) k 0
with respect to (11) and u > a
σ1 > σ 2
and in
respect to their corresponding collusion threshold, firm (10) 1 will have more incentives to collude than the firm 2 since that δ1 < δ 2 : Thus, the critical threshold under Bertrand dupoly is equal: δ∗ =
9( 4u − 4a − 6t + ( 3σ 1 + σ 2 ) k )
2
(12a − 12u − 30t + 11σ 1k − 23σ 2 k )(12a − 12u + 18t − 5σ 1k − 7σ 2 k )
with respect to (11) and u > a (11)
4
>0
(12)
As we have considered below
128t
( 4u − 4a + 2t − (σ
2 u + 2 a + t + 2 kσ 4
As we have previously indicated, the essential facility will be provided by an independant firm on the upstream market to the operators k )operating competing on prices ( à la Bertrand) in the downstream one. The idea is to compare both firm’s incentives to collude depending on the their ability to use the upstream provided investment. )k Both networks independently operate from the upstream market, they are horizontally diffirentiated à la Hotteling: the network located at the origin (8) is represented by the index 1 and that located at the end by 2 . The correspending discount factor for both firms, in the case of vertical separation structure, will be equal to:
The deviated price depends on the the access price a , the investment level k and the parameter σ i .It is clear that for each firm, prices are increasing in
D 1
=
lower than the market structure is effective:
− σ
1
πD = (
D
We are going to study the impact of investment decision on the incentives to collude between both networks operating in the downstream market. We calculate the collusion threshold: its value will be even
Maxπ i = ( pi ( p cj ) − a ) qi ⎛⎜⎝ pi , p cj ⎞⎟⎠
their own ability
networks will share the
making so the same profits:
When networks deviate from the collusif agreement, they consider as given the price charged by their rival (fixed at the collusif level), so a network i maximizes its profit such that:
p 2D =
σ1 = σ 2 ,
market and charge the same price p
3. Deviation:
p 1D =
It is shwon that the main difference between networks still remain on their ability to use new technology. We find that the equilibruim profits depend both on the investment level k , the access charge a and the degree of product substitutability t .
As shown below, we can note that collusion incentives raise with the investment level k . In the context of market structure vertically separated and when σ 1 > σ 2 , the sustainability of collusion increases with the investment evel k . It is quite obvious that the networks incentives to collude increases with investment as it allows them to improve the quality of their services So, when firm i decides to collude when
δ i > δ ∗ . Otherwise,it prefers to deviate. As well as , δ1 = δ 2 if and only if σ 2 = σ 1 , both firms have the same collusion’s incentives as they are symmetrics and share the market:
δσ∗ =σ = (( 2u − 2 a +5t + 2σ k )) .
Proposition 2. : In the case of vertical separation with symmetrics cost, the critical discount factor δ increases with Δσ so firms will be more incentives to collude when the difference between their ability to use infrastructure investment will increase too. ∗
It is shown that incentives to collude will increase when the difference between ability of using investment made upstream is large enough. This could be explained by the fact that when one firm benefit more than the other from the investment, the first makes more profits than the second which decide to deviate in order to get more benefits.
2 u − 2 a − 3t + 2σ k
2
1
Proposition 1: In the case of vertical separation with symmetrics cost, the firm that less value the investment made upstream σ 1 > σ 2 , will have more incentives to agrement. δ1 < δ 2
Otherwise, when
deviate
from
σ 2 = σ 1 , they
the
collusive
will have the same
incentives. We obviously conclude that the firm’s ability of using upstream invesment have an impact on their incentives to collude as profits will be different. With vertically separated market structure, symmetric costs and the same ability of using the infrastructure investment or the new technology σ 1 = σ 2 , collusion will be sustainable since firms are sufficiently differenciated. Whereas, when firms differently value the investment made upstream σ 1 > σ 2 , the one which less use will have more incentive to deviate from the collusive agrement δ 2 > δ1 . This could be explained by the fact that for the firm 2, profits are decreasing when
Δσ = (σ 1 − σ 2 ) increases. σ Its Its profits will be lower than those of its rival. Thus, it prefers to deviate in order to increase its benefits. We can ask the question: how large or small difference in σ ( Δσ ) may induce firms to collude? We derive now the critical discount factor δ with respect to Δσ : ⎡ ⎤ ∂δ ∗ 8 ⎣⎢3u (σ 1 − σ 2 ) − 3a (σ 1 − σ 2 ) + 2t (σ 1 + σ 2 ) + 2tσ 2 ⎦⎥ ∗
∂k
=
3
( 2u − 2a + 5t )
2
∂δ ∗ 32 tσ = > 0 when σ 1 = σ 2 3 ( 2u − 2a + 5t ) 2 ∂k ∂δ ∗2 8 3u − 3a + 2t = > 0 as u > a ∂k ∂σ 1 3 ( 2u − 2a + 5t ) 4 and ∂δ ∗2 8 −3u + 3a + 4t = > 0 if and only if 3a + 4t > 3u ∂k ∂σ 2 3 ( 2u − 2a + 5t ) 4
3-CONCLUSION Through this paper, we try to examine the firms' behaviors in vertical separation market structure with symmetric costs and which are only differentied through their ability to use the investment made upstream by an independant firm. The idea is to study the impact of the investment decision on the firms' behaviors competing in the donwnstream market. We find that the firm less valuing the investment made upstream will have more incentive to deviate from the collusive agreement. It is also shown that more firms are differentied in their ability to use infrastructure invesment, more firms will have incentives to deviate from the collusive agreement. We conclude that even if market structure are vertically seprated and so there will be less abuse by the vertically integrated firm, there still be anticompetitive behaviors. Hence, regulators have to ensure optimal infrastructure share between firms in order to avoide > 0 collusive behaviors..
with respect to u > a REFERENCES
5
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