Competitive Equilibrium
Equilibrium and
and Regulatory
Regulatory
Competitive
Bias in
in Converging
Converging Technologies
Technologies
Bias
VíctorPavón
PavónVillamayor
Villamayor
Víctor
DepartmentofofEconomics
Economics
Department
OxfordUniversity
University
Oxford
“CompetitionininNetworking”
Networking”Conference
Conference
“Competition
LondonBusiness
BusinessSchool
School
London
13-14May
May2004
2004
13-14
Converging Technologies:
Technologies:
Converging
“Setofoftechnological
technologicalplatforms
platformsthat,
that,although
althoughtechnically
technically
“Set
differentiated,tend
tendtotosupply
supplysimilar
similartypes
typesofofservices”
services”
differentiated,
Convergenceisisaaconsequence
consequenceofoftwo
twotrends……
trends……
Convergence
‰ Network
Network Convergence:
Convergence:
‰
“…increasingability
abilityofofnetworks
networkstotocarry
carryan
anincreasing
increasing
“…increasing
numberofofservices”
services”
number
‰ Interface
Interface Convergence:
Convergence:
‰
“…increasingability
abilityofofterminal
terminaldevices
devicestotobe
bean
anefficient
efficient
“…increasing
mediumfor
foraccessing
accessingaanew
newplethora
plethoraofofservices”
services”
medium
convergenceaadriver
driverofofregulatory
regulatoryharmonization
harmonizationbetween
between
IsIsconvergence
industries?….
industries?….
US Broadband
Broadband Market
Market
US
‰ Incumbent
Incumbent Phone
Phone Companies:
Companies:
‰
¾Broadband
Broadbandretail
retailofferings
offeringssubject
subjecttotoprice
priceregulation
regulationby
by
¾
eitherstates
statesor
orthe
theFCC
FCC
either
¾Network
Networkfacilities
facilitiesmust
mustbe
beavailable
availabletotocompetitors
competitors
¾
(by1996
1996TA)
TA)
(by
contrast…..
InIncontrast…..
US Broadband
Broadband Market
Market
US
‰ Cable
Cable TV
TV Companies:
Companies:
‰
¾They
Theyare
arenot
notregulated
regulatedwith
withrespect
respecttotobroadband
broadband
¾
connections
connections
¾The
Theissue
issuehere
hereare
are“Open
“OpenAccess”
Access”requirements
requirements
¾
So,asymmetric
asymmetricregulation
regulationisisstill
stillan
anopen
openissue……
issue……
So,
Research Agenda:
Agenda:
Research
Convergence
Convergence
Competition
Competition
Regulatory Asymmetry
Asymmetry
Regulatory
Welfare
Welfare
Westart
startdiscussing
discussingthe
thefirst
firstissue……
issue……
We
Framework of
of Analysis:
Analysis:
Framework
ASSUMPTIONS:
ASSUMPTIONS:
Twoplatforms
platforms(A
(A&&B)
B)offering
offeringbundles
bundlesofofservices
services
Two
Thereisisaacontinuous
continuousset
setofofservices:
services:xx∈∈[0,1]
[0,1]
There
Bundlescontain
containservices
serviceswith
withdifferent
differentfunctionality
functionality
Bundles
Functionalityofofservice
servicexxisislower
lowerthe
thehigher
higherthe
the
Functionality
distancebetween
betweenservice
servicexxand
andthe
theprovider’s
provider’slocation.
location.
distance
¾ Platforms
Platformsare
areassociated
associatedtotoscopes,
scopes,ss∈∈(0,1]:
(0,1]:
¾
setofofservices
servicessupplied
suppliedw/
w/++functionality
functionality
set
¾
¾
¾
¾
¾
¾
¾
¾
Technologies:
Technologies:
Consumers:
Consumers:
Monopolistic Equilibrium:
Equilibrium: No
No Convergence
Convergence
Monopolistic
Monopolistic Equilibrium:
Equilibrium: No
No Convergence
Convergence
Monopolistic
Utilityofofaaconsumer
consumerlocated
locatedatatyyconsuming
consumingservices
servicesfrom
from
Utility
platformA:
A:
platform
y+r / 2
U ya =
∫

y
λa ( x, s )dx = r 1 − 
 s
y −r / 2
¾IfIfp=U(y*)
p=U(y*)⇒
⇒all
allconsumers
consumerstotothe
theleft
leftofofy*
y*will
willdemand
demand
¾
servicesfrom
fromplatform
platformAA(Mantena
(Mantena&&Sundararajan,
Sundararajan,2003)
2003)
services
¾Then
Thenp=U(y*)
p=U(y*)represents
representsan
aninverse
inversedemand
demandfunction
function
¾
Monopolistic Equilibrium:
Equilibrium: No
No Convergence
Convergence
Monopolistic
Platform A optimises:

q + r / 2
max Π A = nq a  λa ( x, s )dx − c a 


qa

 q − r / 2
∫
which gives:
q a* =
s (r − c a )
2r
 r + ca 
p a* = 

 2 
Competitive Equilibrium:
Equilibrium: Convergence
Convergence
Competitive
Competitive Equilibrium:
Equilibrium: Convergence
Convergence
Competitive
Utility needs to be re-defined as follows:
pa = U ya − U yb + p B
Observe that, under competition, platform A expects:
p Be ∈ [c B ,U B ( y )] ⇒ p Be = θ aU B ( y )
where: θ a ∈ 

,1
U B ( y ) 
cB
Competitive Equilibrium:
Equilibrium: Convergence
Convergence
Competitive
Competitive Equilibrium:
Equilibrium: Convergence
Convergence
Competitive
Platform A optimises:
 y+r / 2

 y+r / 2




c
(
)
max
Π A = nq a  λa ( x, s, z )dx −  λb ( x, s, z )dx  1 − θ a − ca 
qac


 y −r / 2

y
−
r
/
2




∫
∫
which gives:
s(rδ a − c a (1 − s ))
q =
2r (1 − z )(1 − θ a s )
c
a
where: δ a
= 1 − θ a s − z (1 − θ a )
 rδ a + c a (1 − s ) 

p = 
2(1 − s ) 

c
a
Competitive Equilibrium:
Equilibrium: Convergence
Convergence
Competitive
SolvingOut
Outfor
forLinear
LinearExpectations
Expectations
Solving
Observe that:
z = 0 ⇒θ =1
z =1⇒θ = 0
Thus, θ must be a decreasing function of z:
θ i ( z) = 1 − z
∀i = a, b
Competitive Equilibrium:
Equilibrium: Convergence
Convergence
Competitive
SolvingOut
Outfor
forLinear
LinearExpectations
Expectations
Solving
(
)
s(1 − s ) δˆa − ca
q =
2r (1 − z )(1 − (1 − z )s )
c
a
where: δˆa
z 

p ac = r (1 − z )1 +
 + ca 2
 1− s 
z 

= r (1 − z )1 +

 1− s 
Competitive Equilibrium:
Equilibrium: Convergence
Convergence
Competitive
∂q ac
r (1 − z )(1 − s )  1

> 0 ⇔ σ0 =
>
− 2s  = σ 1
∂z
ca
1− z

Competitive Equilibrium:
Equilibrium: Convergence
Convergence
Competitive
∂p ac 1  r (s − 2 z ) 
s
= 
0
z
<
⇔
>
∂z
2  1 − s 
2
Asymmetric Regulation
Regulation && Convergence
Convergence
Asymmetric
INDUSTRY A
q
Regulator optimises:
max Wa =
q
∫
( pa (t ) − ca )dt
0
Proposition1.1.The
Theregulator’s
regulator’soptimisation
optimisationproblem
problemhas
hasfirstfirstProposition
andsecond-best
second-bestoptimums
optimumscharacterized,
characterized,respectively,
respectively,by:
by:
and
s (r − c a )
f
qa =
p af = c a
r (1 − z )
s
r
q =
−
1− z 2
s
a
r 2 (1 − z )
p =
2s
s
a
Asymmetric Regulation
Regulation && Convergence
Convergence
Asymmetric
INDUSTRY B
Platform B optimises:
y+r / 2
 y+r / 2



ˆ
max Π B = nqb  λb ( x, s, z )dx − λa ( x, s, z )dx + p a − cb 
qb
 y −r / 2

y −r / 2


∫
p̂a
∫
: price chosen by the regulator in industry A.
Asymmetric
AsymmetricRegulation
Regulation&&&Convergence
Convergence
Asymmetric
Regulation
Convergence
INDUSTRY B
Optimal Service:
(
1 − s )[r (1 − z ) + s ( pˆ a − cb ))]
qb =
2r (1 − z )
Suppose: ca = cb . If a first-best prevails in industry A:
q
f
b
(
1 − s)
=
2
r (1 − z )
p = cb +
2s
f
b
But, if a second-best prevails in industry A:
2


(1 − z ) − 2scb
r
1
s
−



qbs = 
1
+
 
2r (1 − z )
 2   



r (1 − z )(2 + r ) 
1
pbs =  cb +

2
2s

Asymmetric
AsymmetricRegulation
Regulation&&&Convergence
Convergence
Asymmetric
Regulation
Convergence
Welfare
WelfareAnalysis
Analysis
Welfare
Analysis
By construction:
Waf > Was
Proposition 2.2. When
When aa first-best
first-best isis implemented,
implemented, the
the effect
effect ofof
Proposition
convergence on
on welfare
welfare across
across industries
industries isis asymmetrical:
asymmetrical:
convergence
welfare isis strictly
strictly increasing
increasing inin industry
industry AA but
but strictly
strictly
welfare
decreasingininindustry
industryB:
B:
decreasing
2
∂W af
2 sr (r − c )
>0
=
2
∂z
[2r (1 − z )]
Wb f
∂Wb f
3r (1 − z )(1 − s )
<0
=
⇒
8s
∂z
Final Remarks
Remarks
Final
Harmonisationofofregulatory
regulatoryframeworks
frameworks
Harmonisation
Convergenceofofregulatory
regulatoryinstitutions
institutions
Convergence