Under ex ante access regulation entrants often claim that access fees are excessive. I show that this is only the case if further entry is admitted. If the entrant is protected from further entry it would agree with the incumbent upon a strictly positive access fee which may exceed the efficient level. Ex post regulation facilitates this type of collusion and should be abandoned. --entry deterrence,access regulation,network infrastructure,vertical differentiation

Beschorner, Patrick Frank Ernst

English

Research Papers in Economics

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Beschorner, Patrick Frank Ernst
Working Paper
Ex Post Regulation Facilitates Collusion
ZEW Discussion Papers, No. 08-099
Provided in cooperation with:
Zentrum für Europäische Wirtschaftsforschung (ZEW)
Suggested citation: Beschorner, Patrick Frank Ernst (2008) : Ex Post Regulation Facilitates
Collusion, ZEW Discussion Papers, No. 08-099, http://hdl.handle.net/10419/27581Dis  cus  si  on  Paper  No.  08-099
Ex Post Regulation Facilitates Collusion
Patrick BeschornerDis  cus  si  on  Paper  No.  08-099
Ex Post Regulation Facilitates Collusion
Patrick Beschorner
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ftp://ftp.zew.de/pub/zew-docs/dp/dp08099.pdfNon-technical Summary
Deregulation and privatization of public utilities in grid-based industries
raises the question on how to provide an ecient access to the network in-
frastructure to entering service providers. Often the incumbent rm which
controls the grid is also active on the service market which requires access
to the network and where it is competing with entering rms. Balancing
the eciency of service provision and the incentive to invest in the network
infrastructure suers a lack of information and creates a range of discretion
to the regulator. Typically, the regulator has to mediate the conict between
the incumbent, which demands a high access fee, and the service entering
providers, which complain about excessive access fees.
The present analysis indicates for markets in which quality competition
is essential that a vertically integrated incumbent benets from a high access
fee. Both the revenue from the access fees and preventing tough price com-
petition are benecial eects to the incumbent. Entrants will recognize that
the access fee is above marginal cost and this gives rise to complaints and
requests for reviews of the access rate by the regulatory body.
However, if there is a single entrant which is protected from further entry
the two active rms may agree upon an access fee that is higher than the
marginal cost, which would be the ecient level. The reason is that the
higher access fee serves as a commitment device to not engage in tough
price competition. Therefore, the incumbent is also willing to raise its price,
which results in higher revenue. In this situation a regulator does not face
conicting arguments by the incumbent and the entrant and, under ex post
regulation, may not be alerted to review the level of the access fee.Zusammenfassung
Die Deregulierung und Privatisierung  oentlicher Versorgungsunternehmen
wirft in netzgebundenen Industrien die Frage auf, wie der eziente Zugang
zum Netzwerk durch Wettbewerber auf dem Dienstleistungsmarkt gew ahrleis-
tet werden kann. Oft wird das Netzwerk von einem Unternehmen kontrolliert,
das zugleich Dienste unter Nutzung des Netzes erbringt und auf diesem Markt
mit neuen Unternehmen in Konkurrenz steht. Der ezienten Bereitstellung
der Dienstleistungen durch eine niedrige Zugangsgeb uhr steht entgegen, dass
der Netzwerkbetreiber ein Anreiz haben muss, das Netzwerk zu unterhalten
und auszubauen. Typischerweise, muss der Regulierer in dem Konikt zwis-
chen dem Netzbetreiber, der einen hohen Zugangspreis bevorzugt, und den
Diensteerbringern, die  uberzogene Zugangspreise monieren, vermitteln.
Diese Untersuchung zeigt f ur einen Markt, in dem Qualit atswettbewerb
vorherrscht, dass der Netzwerkbetreiber, der auch auf dem Servicemarkt t atig
ist, einen Anreiz hat, eine inezient hohe Zugangsgeb uhr zu verlangen. Er
protiert dann sowohl vom dem Erl os aus der Zugangsgeb uhr, als auch von
dem anbeschw achten Wettbewerb auf dem Servicemarkt. Die neuen Un-
ternehmen stellen fest, dass die Zugangsgeb uhr  uber den Grenzkosten liegt
und verlangen eine  Uberpr ufung dieser Geb uhr durch die Regulierungsbe-
h orde.
Wenn hingegen das eintretende Unternehmen keinen weiteren Marktzutritt
zu bef urchten hat, vereinbaren die beiden aktiven Unternehmen eine Zutritts-
geb uhr, die  uber dem ezienten Ma liegt, das den Grenzkosten entsprechen
w urde. Der Grund liegt darin, dass eine hohe Zugangsgeb uhr den Preiswett-
bewerb durch das eintretende Unternehmen unterbindet. In der Folge kann
das etablierte Unternehmen seinen Preis erh ohen und einen h oheren Erl os
erzielen. In einer solchen Situation erhebt das neue Unternehmen nicht den
Vorwurf einer exzessiven Zugangsgeb uhr. Unter einer ex post Regulierung,
bei der der Regulierer erst einschreitet, wenn die Unternehmen keine Eini-
gung erzielen, kann eine inezient hohe Zugangsgeb uhr unbemerkt bleiben.Ex Post Regulation Facilitates Collusion
Patrick F.E. Beschorner
December 4, 2008
Abstract
Under ex ante access regulation entrants often claim that access
fees are excessive. I show that this is only the case if further entry
is admitted. If the entrant is protected from further entry it would
agree with the incumbent upon a strictly positive access fee which
may exceed the ecient level. Ex post regulation facilitates this type
of collusion and should be abandoned.
Keywords: entry deterrence, access regulation, network infrastructure, verti-
cal dierentiation
JEL: K21, K23, L42, L51
ZEW Centre for European Economic Research, Mannheim, P.O.Box 10 34 43,
68034 Mannheim, Germany, tel. +49-(0)621-1235-175, fax. +49-(0)621-1235-170,
beschorner@zew.de. I would like to thank Jeanine Mikl os-Thal for her helpful sugges-
tions and comments. This paper was written while I was a visiting researcher at U.C.
Berkeley. I thank the Department of Economics and Prof. Bronwyn Hall for their hospi-
tality. Financial Support from the Deutsche Forschungsgemeinschaft through SFB/TR15
and from RNIC Research Network on Innovation and Competition Policy is gratefully
acknowledged.2
1 Introduction
Following the liberalization of formerly publicly provided utilities, e.g. tele-
communications and electricity, often access regulation has been set up where
competing service providers rely on access to the infrastructure which is an
essential facility and which constitutes a natural monopoly (Hellwig (2008)).
Under ex ante regulation a regulation authority imposes an access fee for
service providers who are connecting to the incumbent's network. Ex post
regulation relegates this process to after the incumbent and the entrant(s)
have or have not come to an agreement. The regulator has to balance the
benecial eect of downstream competition on the service market against
the network provider's incentive to maintain and enhance the network in-
frastructure. It is beyond the scope of this article that to some extent access
regulation is a negotiation process involving the incumbent network provider,
entering rms, and the regulation authority such that is adopts traits of col-
lusion and price control (Rey (2003)).
The model relies on previous research by Gabszewicz and Thisse (1979)
and Gabszewicz (1980) on consumer choice under vertical dierentiation
products, Shaked and Sutton (SS) (1982, 1983) providing the foundation
of a natural oligopoly in markets with vertically dierentiated products, se-
quential entry (Hung and Schmitt (HS) (1988), and quality dependent costs
(Lutz (1997)).
I go beyond this literature in analyzing the potential for collusion under
ex ante and ex post access regulation with (limited) entry in a market with
vertical product dierentiation. Section 2 presents a simple model of vertical
dierentiation, which is analyzed in section 3. Section 4 provides a discussion
of the results: Ex post regulation creates an incentive to collude with respect
to the access fee, free entry prevents incentive for such collusion, and access
should be facilitated.
2 Model
Consumers, which have unit mass, dier by their uniformly distributed in-
come m on the interval [a;b]. Their utility is dened by U(m;t) = m  t
where t 2 [t;t] is the quality of the product of which they purchase exactly3
one unit or none at price p.1 The price of the reservation quality is zero.
y1 = (p1t1   p2t2)=(t1   t2) denes the consumer who is indierent between
quality and price (t1;p1) and (t2;p2) where t1 and t2 are the qualities of the
two products. For the analysis I assume t1 > t2 and I will show later that
rm 2 prevents the entrant's oering superior quality. Consumers y > y1
prefer 1 over 2. Similarly, y2 = p2t2=(t2   t) is indierent between (t;0) and
(t1;p1). Further, assume a < y2 < y1 < b. An entering rm bears sunk cost
f > 0 and a per unit access fee c payable to the incumbent. The rms' prots
are given by
1 = p1(b   y1) + (y1   a)c
2 = (p2   c)(y1   a)   f:
The sequence of the game is as follows: The incumbent decides upon c before
entry occurs. We will see that at most one rm enters the market in the case
where further entry would be admissible. Then, the incumbent sets his qual-
ity before the entrant and nally both rms compete in prices simultaneously.
We solve for the subgame perfect equilibrium.
The equilibrium prices after the rms have set t1 and t2 in the previous
stage are
p1 = A

1  
t2
t1

+
2t1 + t2
3t1
c (1)
p2 = B

t1
t2
  1

+
t1 + 2t2
3t2
c (2)
where
A =
2b   a   c
3
; B =
b   2a + c
3
and the payos resulting from the price stage are
1 = A
2

1  
t2
t1

+ c(b   a) (3)
2 = B
2

t1
t2
  1

  f: (4)
1This utility function has the property that consumers dier in their valuation for
quality according to their wealth or in come. It has been employed in all six papers listed
as previous research.4
3 Analysis
Relying on the result by SS that at most two rms can be protably active
under vertical dierentiation I show that the incumbent has an incentive to
raise the access fee and the entry cost. Further, a higher entry cost results in
a higher degree of product dierentiation, thus approaching the same degree
of product dierentiation as under free entry, but with higher prices. I start
with the analysis of free entry, which is analogous to HS before considering
protected entry.
3.1 Free Entry
Lemma 1 of HS states that for 2a < b < 4a there are at most two rms having
positive market share and covering the entire market with goods of distinct
qualities. To ensure that it is active on the market the entrant chooses its
quality
t2 = t1 
B2
B2 + f
(5)
such that 2(t1;t2) = 0 in order to prevent further entry. If it earned strictly
positive prot, a third party could oer (t2   ";p2) and drive it out of the
market.
The incumbent prevents leapfrogging by the entrant, i.e. the latter does
not oer higher quality than the incumbent. By choosing t1 > 0 the en-
trant cannot earn positive prot even when oering the highest quality. The
condition
A
2 

1  
t1
t

  f < 0
transforms into
t1 >

1  
f
A2

 t  
0:
Observing (5), the entrant sets t2. It covers its xed cost f as long as
t1 >

f
B2   1

 t  
00:5
If 00 > 0 there is no leapfrogging and the entrant earns negative prot.
Otherwise, entry is accommodated according to Lemma 2 in HS.
Now, I analyze the incumbent's incentive to set c. The proportionality
of t2 and t1 implies that (3) is not aected by the choice of c when c = 0,
such that the incumbent is indierent between all t1 2 [max(0;00);t], which
follows from Proposition 1 of HS. Inserting (5) into (3) yields
1 =
A2f
B2 + f
+ c(b   a) =
(2b   a   c)2f
b   2a + c)2 + 9f
+ c(b   a):
Proposition 1 The incumbent's prot is increasing in the access fee c and
the entry cost f.
Proof. @1=@c > 0 and @1=@f > 0 are shown in the appendix. 
Remark 1 The access fee increases the entrant's price. This relaxes price
competition, thus allowing for both prices to rise (See (1), (2)).
Remark 2 The access fee drives t2 towards t1, but this eect is mitigated
by:
Remark 3 An increase in f forces t2 to stronger dierentiate from t1 (See
(5)).
3.2 Protected Entrant
The rms maximally dierentiate, t1 = t and t2 = t in order to relax com-
petition. This follows immediately from rm 1 and 2 maximizing prots (3)
and (4) with respect to t1 and t2, respectively. This result is in line with
SS and HS. This eect is mitigated as quality dependent costs reduce the
incentive to oer the maximum quality (Lutz (1997)).
Lemma 1 The incumbent benets from a high access fee.
Proof. Inserting t1 = t and t2 = t into (3) results in 1 = A2  d + c(b   a)
where d = (t   t)=t.
@1
@c
=
5b   7a + 2c
9
+
4b   2a   2c
9

t
t
> 0: (6)
6
Lemma 2 The entrant benets from a high access fee.
Proof. @2=@c > 0 follows immediately from inserting d into (4). 
Remark 1 The entrant's price is rising in c. This is technically limited by
the assumption y2 < y1 < b. For c = 2b a the incumbent has no sales,
but has revenue purely from access fees c(b   a).
Remark 2 The eect of the access fee on the incumbent's price is ambigu-
ous, because a rise in p2 relaxes price competition while a rise in p1
lowers overall demand.
Remark 3 The positive access fee serves as a commitment for the entrant
not to lower its price.
Proposition 2 Both rms will agree upon a strictly positive access fee.
Proof. This follows immediately from the two Lemmata. 
4 Policy Implications
The model advocates ex ante access regulation because ex post regulation
creates incentives for excessive access fees. An entrant tends to mandate a
review of an allegedly excessive access fee if it faces potential competition.
Otherwise, if further entry is inhibited, it is willing to agree upon a strictly
positive access fee and any such fee necessarily exceeds the marginal cost
which is normalized to zero in this model. Consequently, ex post regulation
is ineective for inhibiting this form of collusion. Thus, ex post regulation
may delay the regulator's setting an ecient access fee when quality is the
prevalent dimension of competition. This eect is amplied because balanc-
ing the eciency of the service provision and the incentive to invest in the
network infrastructure opens a range of discretion to the regulator.
Moreover, the regulator has to enforce free access by entrants to and
compatibility with the network. The xed entry costs are due to technical
issues on interconnection and compatibility, which are to some extent subject
to the incumbent's discretion. They constitute a sunk investment and provide7
to the incumbent a subtle instrument to aict service competition. Thus,
the incumbent may hinder compatibility in order to prevent entry through
narrowing the parameter ranges where he accommodates entry.8
References
Hung, N.M., Nicolas Schmitt (1988), Quality Competition and Threat of
Entry in Duopoly, in: Economics Letters 27, 287-292.
Gabszewicz, Jean Jaskold (1980), Entry (and exit) in a dierentiated indus-
try, Journal of Economic Theory 22, 327-338.
Gabszewicz, Jean Jaskold and Jacques-Fran cois Thisse (1979), Price compe-
tition and income disparities, Journal of Economic Theory 20, 340-359.
Hellwig, Martin (2003), Competition Policy and Sector-Specic Regulation
for Network Industries, Preprints of the Max Planck Institute for Re-
search on Collective Goods No.209.
Lutz, Stefan (1997), Vertical Product Dierentiation and Entry Deterrence,
in: Journal of Economics 65(1), 79-102.
Shaked, Avner and John Sutton (1982), Relaxing Price Competition Through
Product Dierentiation, in: Review of Economic Studies 49, 3-13.
Shaked, Avner and John Sutton (1983), Natural Oligopolies, in: Economet-
rica 51, 5, 1469-1483.
Rey, Patrick (2003), Towards a Theory of Competition Policy, in: Advances
in M. Dewatripont, L. P. Hansen and S. J. Turnovsky (eds.), Economics
and Econometrics: Theory and Applications - Eight World Congress,
Series Econometric Society Monographs, Vol.II, No.36, Cambridge Uni-
versity Press, 82-132.9
Appendix
Proof of Proposition 1
@1
@c
=
 2f(2b   a   c)[(b   2a + c)(3b   3a) + 9f]
[(b   2a + c)2 + 9f]2
Inserting the smallest admissible value for b = 2a yields
 2f(3a   c)[3ca + 9f]
[(b   2a + c)2 + 9f]2 + a
and a=3 > 0 for c = 0.
@1
@f
=
(2b   a   b)2(b   2a + c)2
[(b   2a + c)2 + 9f]2 > 0:


Ex Post Regulation Facilitates Collusion

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