Allocating and funding universal service obligations in a competitive market

International Journal of Industrial Organization1 (2002) 1247–1276

www.elsevier.com/ locate/econbase

Allocating and funding universal service obligations in acompetitive market

a , b c*´Philippe Chone , Laurent Flochel , Anne PerrotaINSEE and CREST-LEI, Division Redistribution et Politiques Sociales, Timbre G211, 15Bd

Gabriel Peri, 92245 Malakoff Cedex, FrancebGATE, UMR 5824 CNRS — University Lumiere Lyon 2, Lyon, France

cCREST-LEI and EUREQua—University of Paris I, Paris, France

Received 24 March 2000; received in revised form 14 March 2001; accepted 19 April 2001

Abstract

We examine, in a network market open to competition, various mechanisms for allocatingand funding universal service obligations among agents (rival firms and consumers). Theobligations we consider are geographic ubiquity and nondiscrimination. We analyze, fromboth the efficiency and equity point of views, the respective advantages of a ‘restricted-entry’ system (where the entrant is not allowed to serve high cost consumers) and a‘pay-or-play’ system. We show that pay-or-play regulation always dominates restricted-entry regulation under ubiquity constraint alone. This result no longer holds when theregulator imposes also the nondiscrimination constraint. 2002 Elsevier Science B.V. All rights reserved.

JEL classification: H23; H25; L43; L51; L52

Keywords: ; Universal service obligations; Cross-subsidies; Redistribution; Regulation

1. Introduction

The transition towards a more competitive regime on the markets of publicutilities raises a number of new questions. In network utilities like telecommunica-

*Corresponding author. Tel.:133-1-4117-5993; fax:133-4-1176-045.É-mail address: [email protected] (P. Chone).

0167-7187/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved.PI I : S0167-7187( 01 )00077-7

´1248 P. Chone et al. / Int. J. Ind. Organ. 20 (2002) 1247–1276

tions, electricity and gas, the regulator often values an ‘equal access’ of all1consumers to the service at an ‘affordable tariff’ . Whereas networks were

previously operated by monopolies who were in charge of these universal serviceobligations (USOs), and used cross-subsidies between ‘profitable’ and ‘unprofit-able’ users, the arrival of new entrants on markets that are now open tocompetition induces cream skimming on profitable segments of the market andmakes former monopolies unable to finance these obligations through cross-

2subsidies . Moreover, competition leads to outcomes that are not necessarilydesirable from the regulator’s point of view. Without regulatory constraints, someusers would then be excluded from the market, and users with differentconsumption or cost characteristics would face different tariffs. If the regulatorvalues equality with respect to tariffs and/or access of all users to the market, hemust then impose ‘universal service obligations’ (USOs).

In this paper, we focus on the geographical component of universal service3obligations . This component can be divided into two obligations: ubiquity and

nondiscrimination. The ‘ubiquity constraint’ states that all consumers should beconnected to a network, whatever their location. The ‘nondiscrimination’ con-straint states that the same tariff should be proposed to all those consumers,whatever their location or their connection cost. These constraints may be imposed

4together or independently . Those constraints are particularly relevant in de-veloped countries for promoting access of a large number of consumers to new

´technologies, like the Internet (see Cremer, 2000). In developing countries (see forinstance Laffont and N’Gbo, 2000), and particularly in case of privatization, thoseconstraints are crucial to ensure a large development of networks.

Most of the recent literature giving normative foundations to the existence ofUSOs investigates this question in a monopoly context (Riordan, 2001; Laffontand N’Gbo, 2000; Laffont and Tirole, 2000). Few papers focus on USOs undercompetition (see, however, Gasmi et al., 2000; Anton et al., 1999; Barros et al.,2000). In this paper, we do not try to give economic foundations for the existenceof USOs. We consider these constraints as given and examine the costs associatedwith different regulatory choices in a competitive framework. Of course, acomplete view of that question should rely on an analysis of both the cost side andthe social benefits.

Universal service obligations in a competitive market raise two series ofquestions. First, which USOs should be imposed upon whom (the allocation

1See Federal Communications Commission, 1996.2For a complete theory of competition in the sectors of public utilities, see Armstrong et al. (1994).3A social component is sometimes also imposed. This obligation imposes low tariffs for targeted

consumers (see Gasmi et al., 2000).4For instance in France, the provision of gas is not submitted to the ubiquity constraint: Gaz De

France may choose not to serve a given area. But when it serves it, it is subjected to anondiscrimination constraint, that is, it must offer the same tariff (or the same menu) to any consumerof the areas that are served.

´P. Chone et al. / Int. J. Ind. Organ. 20 (2002) 1247–1276 1249

problem) and second, who should pay for USOs (the funding problem). Thecombination of various solutions to the first and to the second question definedifferent regulatory mechanisms that have different implications in terms of globaland/or partial surplus. Compared to unconstrained competition between networkproviders, universal service obligations induce distortions on the competitive entryprocess and on the equilibrium market structure. These distortions generate bothsocial benefits and social costs. The question of how to share these costs andbenefits becomes one of the main questions for regulators and has received variousanswers in different countries.

The main tasks for regulators consist in determining optimal rules for allocatingand funding USOs. The question of the funding of USOs is twofold. First, onemay choose to restrict attention to ‘self funded systems’, that is, to mechanismswhere the losses are funded through cross subsidies or through taxes levied onconsumers or firms involved in the market. Taxes may themselves be assessedthrough different channels: unitary taxes may be levied on consumers or on firms;or lump sum taxes may be levied on profits. The other possibility is to finance thetransfers through taxes levied on taxpayers, that is, on agents that may be externalto the market. Second, whatever the type of transfer is chosen (i.e. taxes on theconsumption of the good or lump sum transfers levied on taxpayers), the regulatorcan determine the level of compensation offered to the firm in charge of USOsaccording to various principles that will be analyzed further.

The allocation problem refers to the question of which operator will be assignedUSOs. In most countries, after opening up to competition, only the incumbent isassigned USOs. In some cases, productive efficiency would require that com-

5petitors incur some of USOs. For instance, USOs can be auctioned (see Milgrom,1996).

The goal of this paper is twofold: positive and normative. First, we characterizethe welfare losses of different systems that are at work in practice on the fundingand on the allocating sides. We concentrate mainly on two regulatory rules:‘restricted-entry regulation’ adopted for instance in the telecommunications sector

6in many European countries, and the ‘pay-or-play’ system (PoP) . In the‘restricted-entry’, the incumbent must serve nonprofitable users at the same tariffas profitable consumers, whereas under ‘pay-or-play’ regulation, the entrant mayalso serve the market. In the last case, the allocation of USOs between operators isendogenous. We compare those two regulatory rules from global and partialsurplus points of view. Second, the normative aspect of the last section of thepaper is an attempt to give a broader analysis of the costs and benefits associatedwith various theoretical approaches of these problems.

5For instance, USOs are auctioned for the postal service in Germany or for telecommunications inthe US (and more recently in Germany and Austria).

6Pay-or-play regulation is applied in Australia and has been discussed in the UK for thetelecommunication sector.


We examine various procedures of tax determination. Among others, we analyzethe case of a competitively neutral tax: if possible, the incumbent should obtain thesame level of profit as under a competitive regime. This view is meant to represent

7that developed in the US in the Telecommunication Act of 1996 . However, itdiffers greatly from a determination of taxes through a first best principle, and thusinduces social losses. An important remark is thus that the ‘cost of universalservice’ is conditional to the way it is funded. As pointed out by Panzar (2000),‘‘ any USO costing exercise must begin with a careful specification of anunsubsidized market scenario that would prevail in the absence of USO’’. Manyproposed measures of USO costs (in particular the accounting approach of ‘‘net

8avoidable costs’’ ) ignore this basic requirement. In this paper, we define preciselythe benchmark situation, where no USO is imposed, and then we carefully list andevaluate the economic distortions due to the presence of the tax. In our framework,the market structure as well as the cost of USOs are endogenous to the regulationrule and the tax determination procedure: although the maximal number of firms isfixed in our model, the identities of the firms that serve each segment of themarket, as well as the number of active firms at equilibrium, are endogenous.

We build a model where two operators compete for a market for a networkgood. Consumers are heterogeneous with respect to their connection costs. Theregulator imposes different combinations of USOs, and the system is self-fundedthrough taxes levied on consumers. The incumbent firm is the carrier of last resort.We then compare the ‘restricted-entry’ and ‘pay-or-play’ system. We examine theequilibria of the corresponding games, and compare them in terms of socialwelfare and in terms of transfers between agents.

Section 2 presents the model. Section 3 presents the equilibrium regimes anddiscusses allocating and funding systems. Section 4 examines restricted-entryregulation firstly when only the ubiquity constraint is imposed and further whenthe nondiscrimination is added. In Section 5, we examine pay or play regulation inthe same framework and compare both regimes. In the last section, we sum up themain results of the paper and discuss the case of second-price auctions on themarket for non profitable users.

2. Model and notation

2.1. The framework

Consider the following situation. Two firms,I andE, compete for the market fora network good. This network possesses the feature of a public utility, that is, thepublic authority may pursue social objectives such as ‘equal access’ of all

7See Pub. L. No. 104-104, 110 Stat. 56 (1996) (1996 Act), 47 U.S.C. 254(b).8See for instance WIK (1997).


consumers to the service provided by the network. Typically, this situation reflectsliberalization of a network market, such as electricity, gas, telecommunications orairlines, where an incumbent firm (I) faces a entrant (E).

There are two types of consumers: a proportiona of low connection cost (m)] ]] ]and a proportiona of high connection cost (m). For instancem is a measure of the

] ]cost of connection in high density areas (urban areas), whereasm corresponds tolow density areas (rural areas).

9A consumer who buysq units of the good and who is charged a tariffT(q)receives a net surplus equal to:u 5w(q)2T(q), where w(q) is increasing andconcave. Here, the only element of heterogeneity concerns the connection costs.The demand addressed to firmK by a consumer facing the tariffT(q) is given byw9(q)5T 9(q). One should note that the demand of a particular consumer isindependent of its connection cost.

Firms are endowed with the following technologies. FirmK 5 I, E incurs a cost¯C (q, m), when providingq units to consumerm 5m, m. We assume thatK ]

¯C (q,m),C (q, m ) (1)K K]

¯for all q and for both firmsK 5 I, E. If the consumersm andm are respectively]urban and rural users, this assumption expresses the fact that connecting rural users

to the network is more costly for both firms than connecting urban users, whatever10their consumption level . A typical example of cost function satisfying (1) is

¯C (q, m)5 c q 1F (m), with F (m),F (m ), wherec is the marginal cost ofK K K K K K]firm K (associated with the provision of a marginal unit of traffic) andF (m) is theK

cost of connecting consumerm to the infrastructure. The fixed cost captures thenetwork characteristic of the sector. Since we want to exhibit general properties,we do not work with a specific functional form of the cost function in the sequel.

The profit per consumer of firmK is thenp (q, m)5 T (q, m)2C (q, m).K K K

Remark 1. It is equivalent to work with tariff variablesT(m, q) or with variablesuandq, whereu denotes the utility level delivered to a consumer. We deal hereafter

]with (u, q). We denote byu (respectivelyu ) the utility delivered by firmK toK K] ]consumers of typem (respectivelym).]

Remark 2. The surplus derived from the relationship between a consumer of typem and firm K is S (m, q)5w(q)2T (q, m)1p (m, q)5w(q)2C (q, m).K K K K

9Under the assumption of homogeneous preferences, a two-part tariff allows achieving the sameallocation as more general nonlinear tariffs. In a more general model, consumers could be heteroge-neous in their tastes for the good.

10In order to focus on questions related to universal service obligations, we do not consider anyproblem of interconnection between networks, which amounts to assuming that the interconnectioncharge between networks is zero. For more details on the interconnection problems, see Armstrong etal. (1996).


FBThe first best quantity is defined byq 5argmax S (m, q). The first bestK q>0 KFB FB FBsurplus isS (m)5w(q )2C (q , m) if q . 0. This valueS (m) is the valueK K K K

to be shared between the firm and the consumer, the share of the consumer being]¯u . For simplicity, we writeS 5 S (m) and S 5 S (m).K K K K K] ] 11We shall maintain the following assumption throughout . First, high cost

consumers are not profitable and would not be served by any firm withoutuniversal service obligations, that is

¯ ¯max(S , S ), 0,min(S , S ). (2)I E I E] ]

Second, the market is viable under both the incumbent’s and the entrant’smonopoly:

] ]¯ ¯aS 1aS .0 andaS 1aS . 0. (3)I I E E]] ]]

In this model, there is no further benefit of connecting high cost consumers. Wecould add such benefits and make them endogenous by introducing networkexternalities, that would depend on the specific context: communication exter-nalities in a telephone network, regional effects in the transportation sector,diffusion of knowledge in the case of Internet. Introducing such effect would,however, make the model less general and much more difficult to handle.Therefore we decide to treat the social valuation of the USOs as exogenous andrestrict attention to the most efficient way to make the USO constraints effective.

2.2. Benchmark: duopoly without USOs

As a benchmark, we study the case where no firm has to comply with any USOconstraint, that is, each firmK can offer a perfectly discriminatory tariff to anyconsumer. Because of our assumption (2), firms then compete on userm only. The

]profit of firm E is given by:

a(S (q)2u ) if u .uE E E I] ] ] ] ]p (u , q )5HE E E] 0 if u ,u .E I] ]FBThe profit of firm I has a symmetric expression. It is clear that we haveq 5 qK K

when the consumer is served by firmK. Therefore in what follows, we will call‘strategies’ the choices of the variableu by firm K 5 I, E.K]

Each firm reacts to the strategy of its rival by choosing the share of the surplusit delivers to the consumer. We can then compute the best reply function of firmEin response to the strategyu of firm I.I]

Facingu , firm E can deliveru 1´ if p 5a(S 2u 2´) remains positive, thatI I E E I] ] ] ] ]

11Except in Section A.6, where we relax this assumption in order to study the impact of imposingonly a nondiscrimination constraint.


is, as long asu ,S . If u .S , firm E has no incentive to be active. Thus the bestI E I E] ] ] ]reply function ofE to u is given by:I]

u if u ,SI I E] ] ]u (u )5HE I] ] any value in [0,u [ if u .S .I I E] ] ]

In what follows, we will use as a benchmark the sequential game in which firmIis the leader. This representation of the competition process suits better to the casewhere a (dominant) incumbent faces a new entrant. Finally, as we will see in thenext section, the allocation of universal service obligations gives the incumbent afirst mover advantage.

The sequential game (where firmI acts as a leader) may lead to a continuum ofsubgame perfect equilibria (SPE). When 0,S ,S , any valueu [ [0, S ] leads toI E I E] ] ]the same profit for firmI, namelyp 50 sinceE serves the consumer.I

Lemma 1. The subgame perfect equilibria of the game where firm I acts as aleader are defined as follows:

– if 0,S ,S , there is a unique SPE: firm I serves the consumer m, deliversE I] ] FB ]him u 5S and q 5 q , and makes profit p 5a(S 2S );I E I I I I E] ] ] ] ]]– if 0,S ,S , there is a continuum of SPE, parameterized by u [ [0, S ]:I E E E] ] ] ]Firm E serves the consumer m, who obtains any value u [ [0, S ]. Firm E getsE E]]p 5a(S 2u ) and firm I stays out of the market.E E E] ] ]

2.3. Taxes and distortions

In what follows, we will often consider the case where firmE pays a taxt oneach unit sold to consumerm. We now state a few useful results concerning the

]surplus of the relationship between firmE and the consumerm, in presence of the]unit tax t. In the sequel, the presence of a tilde indicates the dependence of the

variable on the tax ratet.Let T(q) be the tariff posted by the firm andq be the quantity of good purchased

by a consumerm. The profit per customer of firmE is]

p 5 T(q)2C (q,m)2 tq,E E ]

˜wheret is the tax rate. We denote byS the surplus from the relationship betweenE

E andm]

˜ ˜S (t, q)5p 1w(q)2 T(q)5w(q)2C (q,m)2 tq.E E E ]

˜Let S (t) be the maximum value overq > 0 of the surplus:E

S (t)5max hw(q)2C (q,m)2 tqj.E q>0 E ]


˜Let q be the value ofq for which the maximum is attained. The following lemmaE

is proved in Appendix A (Section A.1).

Lemma 2. The following properties are true:

˜1. The total surplus function S is convex with respect to t;E˜ ˜ ˜2. The functions S and S 1 tq are nonincreasing with respect to t;E E E

e e3. There exists a tax level t such that for t > t , firm E can extract no surpluse˜from consumers m : S (t )5 0.E]

˜ ˜The sumS (t)1 tq (t) represents the total amount that can be extracted from theE E˜relation betweenE and the consumerm, that is S (t), on the one hand, and theE]ãmount of tax collected,tq , on the other hand. The higher the tax, the lower thisE

total amount. This partial effect should lead the regulator to choose not too hightaxes.

Lemma 2 shows that the entrant is active on the market only when the tax leveleis not too high (t , t ). Very high tax levels prevent firmE from competing with

firm I.

2.4. Definitions of and interactions between USOs

The Universal Service Obligations consist of two different constraints imposedby the regulator on the incumbentI:

– Ubiquity constraint (thereafter, the subscript U will identify the variablesunder this constraint): each consumer should have access to the good, that is, eachconsumer must face a tariff such that he obtains a nonnegative utility level (thewhole market is ‘covered’);

– Nondiscrimination constraint (ND): if the incumbent chooses to serve bothtypes of consumers, it must offer the same tariff to both. The incumbent mayprefer to serve only one type;

– Ubiquity and nondiscrimination constraints (UND): the incumbent must offerall consumers the same tariff and this tariff must be such that all consumers have anonnegative utility level.

Recall that we model competition between firmsI andE as a sequential game,where firm I is the leader: whatever the regulation framework, firmI first

¯announces a pair (u , u ). USOs may thus be represented by constraints on theI I]incumbent’s strategy space:

¯USO5U: u >0, u > 0I I]¯ ¯USO5ND if u >0, u > 0 thenu 5 uI I I I] ]

¯USO5UND u 5 u > 0.I I]


Note, however, that these restrictions onI’s strategies imply (at equilibrium)restrictions onE’s strategies as well. Suppose for example that under USO5UND,

¯firm E serves all the consumers. Then, clearly the consumersm and m get the]¯same utility level at equilibrium (u 5 u ).E E]

Imposing ND alone may lead to some paradoxical effects. It may happen thatwith no constraint, the incumbent would have served both types of consumers, yet

]under the ND constraint, it stops serving typem consumers. Therefore, a constraintU may be required together with ND in order to make ND effective (see SectionA.6 for more details). In this paper, we focus on constraints U and UND.

3. Possible choices of the regulation pattern

The purpose of this paper is to examine the consequences for consumers’surplus, profits, and global surplus of different combinations of allocation andfunding of USOs (U or UND). In this section, we clarify some preliminaryquestions relative to the main possible choices relative to the funding system onthe one hand and to the allocation system on the other hand.

Recall that the timing of the model is the following: first the regulatorannounces its regulatory choices; each possibility induces a particular gamebetween operators. Then firms compete and finally, if necessary, transfers aremade. We call thereafter ‘regime’ the situation that prevails at the equilibrium ofthe complete game.

3.1. The various regimes and welfares

As we will see further, the regulatory rules may lead at equilibrium to oneamong the following possible situations.

– Firm I serves both types of consumers and cross-subsidizes between them.We call this regime ‘I cross subsidizes’ (ICS). No transfer is either raised orreceived.

– Firm E serves both types of consumers and cross-subsidizes between them.We call this regime ‘E cross subsidizes’ (ECS). No transfer is either raised orreceived.

– Firm I serves the high cost consumers,E serves the low cost consumers andpays a unit tax. We call this situation the ‘taxation regime’ (TR).

– Firm I serves the high cost consumers,E (or I) serves the low costconsumers and firmI receives a lump sum transfer levied on taxpayers. The costof transfer of public funds isl. We call this regime the ‘lump sum transfer regime’(LSR).

– High cost consumers are excluded from consumption of the good, low cost


consumers being served by either of the two firms. We call this regime ‘exclusionregime’ (ER).

Global welfares associated with these regimes are respectively:

]]W 5aS 1aS in the ICS regimeII I I] ]]W 5aS 1aS in the ECS regimeEE E E]]]˜ ˜ ˜W 5a(S 1 tq )1aS in the taxation regimeEI E E I] ] ]]W 5aS 1aS in the taxation regime witht 50EI E I]

T TW 5W 2lT orW 5W 2lT in the lumpsum transfer regimeII II EI EI

W 5aS in the exclusion regime (firm K servesm)K0 K] ]

]In the benchmark case analyzed above, and under our assumptionS , 0 (K 5 I,K

E), welfare isW or W according to which firm serves the market for low costsI0 E0

consumers. Note also that the following remark results readily from Lemma 2.

˜Remark 3. Welfare in the taxation regimeW is nonincreasing with respect to theEI

tax level t.

USO˜Let W be the global welfare value at the competitive equilibrium,W (t) theUSOglobal welfare value at equilibrium with USO and tax andW (T ) the global

welfare value at equilibrium with USO and transfer. The differencesDW(t)5USO USOW (t)2W andDW(T )5W (T )2W measure respectively the cost of univer-

sal service obligations when the deficit is funded through taxes and through lumpsum transfers. The variations of the global welfare can also be decomposed intoindividual contributions that allow evaluation of the redistributive consequences ofa given regulatory pattern. Of course, imposing USO also generates welfarebenefits, the representation of which deserves further analysis. For instance, onecould take into account the social value of connecting any user, and introduce asocial valuation of the reduction of the gap between high cost and low costconsumers. However, this lies beyond the scope of our paper, which rather focuseson the costs induced by each regulatory rule.

Two kinds of efficiency losses may result from the introduction of USOs: first,according to the regulatory rule at work, a type of consumer may be served by afirm which is not the most efficient to serve these consumers. Second, funding thelosses incurred by the firm in charge of high cost consumers may generatedistortions. This leads us to define as benchmarks two different concepts ofproductive efficiency. We say that we have

– strong productive efficiency, when the highest welfare level amongW ,W ,II EE

andW is achieved;EI


– weak productive efficiency, when the highest welfare level amongW ,W ,II EEãnd W is achieved.EI

We now turn more in detail to some possible regulatory patterns.

3.2. Allocation rules: ‘ restricted-entry’ regulation versus ‘ pay or play’regulation

Under ‘restricted-entry’ regulation, firmE is not allowed to serve high cost]consumersm. Under USO5U or UND, these consumers are served by the

incumbent. Two regimes may occur under a self-funded system: ICS and TR.]Under ‘pay-or-play regulation’ firmE is allowed to serve consumerm. WhenE

]chooses to servem, it does not pay or receive any tax. Therefore, firms’ payoffs12are not symmetric . Under pay-or-play regulation, the identity of the firm that

]servesm is endogenously determined. Three regimes may occur under a self-funded system: ICS,TR and ECS. Under restricted-entry regulation, firmE9sstrategy reduces to the choice ofu . Under pay-or-play regulation, firmE may inE]] ]addition choose to servem consumers and thus also chooseu . In the last sectionE

of the paper, we discuss other allocation rules, such as auctions, which are moresuited to asymmetric information contexts.

3.3. Internal versus external funding of USOs

From a normative perspective, a first issue is whether the funding of USOsshould be obtained from an external source (taxpayers), or should rely only ontransfers internal to the market (cross subsidies or transfers between consumersand/or firms). Our model does not allow for a general comparison between thetwo systems, since it lacks any representation of the taxpayers’ side. However, inthe context of our model, it is easy in some cases to compare welfare properties ofinternally vs. externally funded systems.

Suppose for example that USO5U and the funding is made through lump sumtaxes levied on taxpayers. We sum up all the distortions in the cost of transfer ofpublic fundsl. Assume also that restricted-entry regulation prevails. Then theincumbent’s profit is:

¯¯ ¯a(S 2S )1aS 1 T if I servesm andmI E I] ] ] ]p 5I H ¯¯ ¯aS 1T if E servesm andI servesm.I ]

Note thatp can also be written:p 5max(W 2aS 1T, W 2aS 1 T ). ThusI I II E EI E]] ]]the incumbent chooses to serve both consumers whenW .W and to serve onlyII EI

12By contrast, auction mechanisms generally lead to symmetric payoffs (see for instance Anton etal., 1999).


high-cost consumers in the other case. It follows that welfare is at equilibriumW5max(W , W ). When ubiquity is funded through a unit tax, we shall see thatII EI

˜welfare isW5max(W , W ).II EI

It is thus straightforward that if max(W , W )5W , then a lump sum transferII EI II

system is always dominated by an internal system, since we have obviouslyW >W 2lT.II II

If max(W , W )5W , the result is less clear cut. The lump sum transfer systemII EI EI

leads to a welfare level equal toW 2lT, whereas the internal funding one leadsEI˜to max(W , W ). The lump sum transfer system thus implies strong productiveII EI

efficiency, but also entails a deadweight losslT due to the tax. On the others dhand, the internal funding system only involves weak productive efficiency. Themost efficient system thus depends on the values ofT and t. The followingproposition sums up the results.

Proposition 1. When USO5U, under restricted-entry regulation, internal fundingis more efficient than lump sum transfers when:

(i) W .W , orII EI˜(ii) W ,W and max(W , W ).W 2lT.II EI II EI EI

Each system also has different redistributive properties. In the above example,under the lump sum transfer system, low cost consumers obtainu 5S ; thus highI] ]cost consumers are funded by transfers imposed on taxpayers. In the internal

˜ ˜funding system, we haveu [ 0, S or u 5S 2 tq , according to the regime. Inf gE I E] ] ]any case, we haveu ,S , which shows that high cost consumers are funded byI] ]taxes paid by low cost consumers. The choice of a particular funding system isthus not neutral with respect to redistribution. Moreover, internal systems give tothe regulator, through the choice of the tax level, a tool for redistributive

13purposes .In most parts of the paper, we focus on self-funded systems and leave aside

systems that involve external funding.

3.4. The choice of the tax level

Another question is that of the principles that should guide the choice of aparticular tax or lump sum transfer level. This choice depends on the objectivespursued by the regulator. We focus here on three particular approaches: the firstbest, the second best (or budget balance) and competitive neutrality.

13On the political side, the need for reducing or at least stabilizing the tax level, may be a factor infavor of an internal funding system.


The first best tax is the tax level that maximizes social welfare under a selffinanced system.

The second best (or budget balanced) tax is defined by the maximization ofwelfare under the constraint that the amount of tax collected compensates for the

USO˜losses incurred by the incumbent, that is,p 5 0 under the (internal) taxIUSOsystems,T 5 2p under a lump sum tax systemI

The competitively neutral tax compensates firmI up to the profit level it wouldUSOreach under the benchmark case. This defines the tax ratet as the level

USO˜determined by the equalityp 5p under the tax funded system, and definesI IUSOthe lump sum tax asT 5p 2p .I I

The idea of competitive neutrality is that the funding and the presence of USOsare designed not to affect the profit of firmI with respect to the unconstrainedsituation (benchmark).

Budget balance and competitive neutrality may coincide or not, according towhat happens in the benchmark case.

4. Restricted-entry regulation: firm I serves high cost consumers

Recall that under restricted-entry rule, USOs are imposed on the incumbent(firm I) and that the entrant (firmE) cannot choose to serve the consumersconcerned by the USO instead of paying the tax. We consider successively thecases where USO is restricted to U only, and defined by UND. We first derive theequilibria of the game, identify thereafter the possible inefficiencies generated bythe situation and finally proceed with the welfare and redistribution analysis.

4.1. Equilibria of the competition process under USOs

The constraints U and UND that the regulator can impose on firmI havedifferent consequences on the equilibrium configurations and on their welfareimplications. We examine successively these various constraints. Recall that we

¯ ¯restrict ourselves to the case whereS , 0 andS , 0.I E

4.1.1. Equilibria under ubiquity constraint aloneAs explained in the introduction, the market (for a given tax levelt) is modeled

as a sequential game, where the incumbent acts as a leader: firmI announces two¯ ¯valuesu andu such that:u > 0 andu >0 (ubiquity constraint). Since firmE isI I I I] ]

¯ ¯not allowed to serve consumerm, we clearly have:u 50. Firm E’s profit functionI

is

0 in the ICS regimep 5HE ã(S 2u ) in the taxation regime.E I] ]


˜Firm E chooses to servem if and only if u , S . Therefore the announcement ofI E]] ˜u determines the regime that will prevail:u , S leads to the taxation regime,I I E] ]˜u . S leads to the ICS regime. FirmI’s profit function is then given byI E]

˜¯¯a(S 2u )1aS if u . S ICS regimeI I I I E] ] ] ]p 5HI ˜¯˜ ¯atq 1aS if u , S taxation regimeE I I E] ]

Then the strategy of the incumbent reduces to the choice of the regime: in the˜taxation regime, firmI’s profit does not depend on 0<u , S (which leads to aI E]

multiplicity of equilibria); in the ICS regime, firmI’s optimal announcement is of˜courseu 5 S . Then firmI has to compare the corresponding values of its profit.I E]

We have:

˜ ¯ ¯˜ ˜¯ ¯p 5maxa(S 2 S )1aS , atq 1aS .s dI I E I E I] ] ]

In the sequel, we will express the profits of firmI in the different regimes in termsõf the corresponding welfares. We can rewritep asI

˜ ˜ ˜p 5maxW 2aS , W 2aS .s dI II E EI E] ]

˜Up to a constant (aS ), the profits ofI in the regimes ICS and TR coincide withE] ˜the corresponding welfaresW andW . We introduce the following convention toII EI˜express the fact that firmI’s compares the quantitiesW and W when choosingII EI

the regime:

˜ ˜P 5max(W , W ).I II EI

˜The notationP denotes the profit ofI (in presence of the taxt) in the regimes ICSI

and TR up to a constant. This leads to the following proposition.

Proposition 2. ((Restricted-entry regulation, USO5U)) For any tax level, thesubgame perfect equilibria lead to the regime associated to the highest welfare

˜value: firm I chooses the taxation regime when W .W and it chooses toEI II˜cross-subsidize when W .W .II EI

It is interesting to note that since the regulator can transfer its objective to theincumbent, restricted-entry regulation avoids incentive problems that could appeardue to informational asymmetries between parties: even if the regulator observesneither the costs of the firms nor consumers’ characteristics, delegation of theubiquity constraint to the incumbent solves the adverse selection problems

14associated with unobservability of the firms’ and the consumers’ characteristics .˜ ˜By Lemma 2, the functionW decreases witht. Then ifW 5W (0),W , weEI EI EI II

14However, second-price auctions would also solve such informational problems.


˜have: W (t),W for all t > 0 and the ICS regime occurs for all tax levels. IfEI IIUW >W , there exists a tax levelt such thatEI II

UW (t )5W .EI II

U UThe taxation regime occurs fort <t and the ICS regime fort .t . It is quiteintuitive that when the tax rate is high, the entrant prefers to stay out of the market.

˜ Ã given tax level generates a given level of the sumS 1 tq , which measures theE E

‘efficiency’ of the relationship betweenE and them consumer, conditional ont.]Recall that this quantity is a decreasing function oft.

The following result gives consumer’ surpluses in the different regimes.

Corollary 1. ((SPE in the restricted-entry game, USO5U)) In both regimes, the¯ ¯consumer m gets u 50. The utility of consumer m depends on the regime:

]

˜u 5 S in the ICS regimeI E]u 5H] ˜u [ [0, S ] in the taxation regime.E E]

The cross-subsidy regime corresponds to a situation whereI is relatively moreefficient on the market for low cost consumers thanE when the latter faces the tax.In this case,I announces for both types of consumers values thatE cannot match

˜ ˜because the tax is too high (and thus the quantityS 1 tq is too small). Therefore,E E

I serves both types of consumers and cross-subsidizes between them (that is,Ifinances the deficit created by the constraintU on high cost consumers by atransfer levied on low cost consumers).

In contrast, in the taxation regime, the sum of the surplus generated by therelationship betweenE andm and the amount of taxes collected is sufficiently high

]to allow both firms to be active, each of them serving a different segment of the15market. In this regime, there are multiple equilibria which can only be selected

by an additional criterion: a criterion of dominance for firms would implyu 5 0,]

whereas if there would exist a second entrant, competition form consumers would]˜lead tou 5 S . An important consequence of this result is the following.E]

Recall that under ubiquity, a criterion of strong efficiency would consist in thecomparison ofW andW . By Proposition 2, we know that firmI comparesWII EI II

˜ ãnd W . Since W ,W , it follows that the ICS regime is ‘too often’ im-EI EI EI

plemented with regard to ‘strong’ productive efficiency.However, a reasonable criterion of productive efficiency should take into

account the fact that ubiquity is funded through taxes. If we define productive˜efficiency as the comparison betweenW and W , we see that the delegation ofII EI

15If we had used a simultaneous game instead of a sequential game, the equilibrium would havebeen unique. Note, however, that a Nash equilibrium may fail to exist when the regulator also imposesthe nondiscrimination constraint.


the regulator’s objective function to firmI allows choosing the socially preferredregime.

In addition, a tax rate equal to 0 allows to achieve strong productive efficiency.A zero tax, however, may fail to fulfill any of the tax constraints (budget balanceof the incumbent or competitive neutrality).

4.1.2. Equilibria of the restricted-entry game with nondiscrimination constraintThe regulator imposes that each consumer receives the same nonnegative

surplus. This constraint is implemented by restricting the space of strategies of the¯incumbent (u 5 u >0). The proof of the following proposition can be found inI I]

Appendix A (Section A.2).

Proposition 3. ((Restricted-entry regulation, USO5UND)) Firm I’s profit isgiven, up to a constant, by

˜ ˜ ˜¯P ;max(W 2aS , W ).I II E EI

In contrast with the case USO5U (see Proposition 2), the incumbent’s profitdoes not coincide with the welfares in the regimes ICS and TR. Under UND, thechoice of the incumbent differs from that of the regulator ( for any given tax levelt).

UND˜ ˜¯By Lemma 2, the functionW 1aS is decreasing int. Let t be the taxEI E

value for which

UND UND]˜ ˜W (t )5W 2aS (t ).EI II E

UND UIt is worth noting thatt >t . We have the following

Corollary 2. ((SPE in the restricted-entry game, USO5UND)) The ICS regimeoccurs if and only if

UND˜ ˜¯W <W 2aS or, equivalently t >t .EI II E

The taxation regime can occur only if S .aS . In that case, it appears whenE I] ]]UND0< t ,t . Consumers’ surplus depends on the regime:

] ˜– Cross-subsidy regime (ICS): u 5u 5 u 5 S ;I I I E]]– Taxation regime (TR): u 5u 5 0.]

Recall that we have identified a first distortion due to the tax: under USO5U,˜ ˜firm I comparesW andW , instead ofW andW . The tax distortionW 2WII EI II EI EI EI

implies that the ICS regime is implemented too often.Proposition 3 brings out an additional distortion under USO5UND, coming

] ]˜from the fact that under UND firmI has to leaveaS to them consumers. TheE


˜¯distortionaS has the opposite impact: compared to productive efficiency, firmIE

chooses to remain in the taxation regime for a set of parameters that is too large,UND Uinstead of choosing the ICS regime (t >t ). The ND constraint softens

competition: Since the incumbent has to deliver the same utility to both16consumers, it is less aggressive on the low-cost consumers’ market . By contrast,

the taxation regime allows the incumbent to leave a zero utility to high costconsumers.

The distortion due to ND appears particularly clearly in the following case.]Suppose that firmI is more efficient on both markets of consumersm and m

] ] ](0,S ,S and S ,S , 0, so thatW .W ). When ubiquity (U ) alone is atE I E I II EI] ] ]work, firm I servesm andm (cross-subsidy regime). Under UND, however, firmE]servesm if and only if the condition

]

˜ ˜¯W ,W ,W 1aSEI II EI E

˜¯is satisfied. This condition expresses the fact that the ND distortion (aS )E˜dominates the tax distortion (W 2W ). In that case, firmE is active on theEI EI

market whereasI is more efficient.We now can analyze the welfare and redistributive implications of imposing

USOs depending on whether their funding is realized through cross-subsidies ortaxation.

4.2. Welfare and redistribution analysis

Consider first the case where U is imposed alone. The following proposition,which follows directly from Proposition 2, states the implications of U in terms ofwelfare.

Lemma 3. ((Restricted-entry regulation, USO5U, welfare analysis)) Welfareunder restricted-entry regulation and with the ubiquity constraint is given by

U ˜W (t)5max(W (t), W ).re EI II

UThe function W is nonincreasing and continuous with respect to the tax level t.re

More precisely, it is strictly decreasing in the taxation regime and then constantin the cross-subsidy regime.

Consider now the case where both constraints are imposed together (UND). Wehave the following lemma.

Lemma 4. ((Restricted-entry regulation, USO5UND, welfare analysis))Welfare under restricted-entry regulation with USOs U and ND is given by

16This result is also present in Anton et al. (1999).


˜ ˜ ˜¯W if W >W 2aSEI EI II EUNDW (t)5Hre ˜ ˜¯W if W <W 2aS .II EI II E

UNDThe function W is nonincreasing with respect to t and discontinuous atreUNDt 5t .

A consequence of this proposition is that the tax level which maximizes welfare(that is, the first best tax), in the case where the taxation regime exists, i.e. when

FBW .W , is t 50. In the cross-subsidy regime, welfare is constant with respectEI IIFBto the tax rate. However, for this levelt of the tax rate, firmI incurs a deficit.

BBTherefore it is interesting to examine what happens for the tax levelt thatBB˜guarantees the budget balance of firmI: p (t )5 0. This is done in the followingI

proposition.

] ]Proposition 4. Assume S , 0,S ,0 and S ,S or W ,W . The incumbent’sE I I E II EI] ]profit in the benchmark case is p 50. Then, whatever USOs are at work:I

– Competitive neutrality and budget balance are equivalent.– The taxation regime exists for small values of t and the first best tax is

]FB ]˜t 5 0. This first best tax implies a deficit for the incumbent: p (0)5aS , 0.I I

– There exists at least a competitively neutral tax.

The last point of Proposition 4 follows from the continuity of the profit function]e ]˜ ˜ ˜p with respect tot. Sincep (0),0 andp (t )5aS 1aS . 0 (by assumptionI I I I I]]

˜(2)), there exists at least a solution to the equationp (t)50.I

] ]Remark 4. Suppose nowS .S (and still S , 0, S , 0).I E E I] ]

– The profit of firmI in the benchmark case is:p 5a(S 2S ).0. Therefore,I I E] ] ]competitive neutrality implies budget balance for the firmI.

– If USO5U, the cross-subsidy regime prevails for allt. The welfare does notdepend on the tax level.

UND– If USO5UND, the taxation regime occurs whent ,t if S .aS .E I] ]]]]– In both cases, ifaS 1aS > 0, then there exists a competitively neutral tax.E I]]

At this stage, we can discuss the social costs of USOs.] ]

Assume for instance thatS ,S (and still S , S ,0). Then, in the benchmarkE I I E] ]case, firmI serves the low cost consumers and high cost consumers are not served;welfare is thenW . If UND is imposed, then welfare is given by Lemma 4. In theI0

taxation regime (see point 3 of the above remark), the social cost of the UNDconstraint can be written as:

UND ˜ ˜¯ ˜¯DW 5W 2W 5aS 1a(S 1 tq 2S )1a(S 2S ).EI I0 I E E E E I] ] ] ] ]


¯¯The term aS represents the cost associated with the connection of theseI

consumers. The third term represents the loss inallocative efficiency (distortion ofthe surplus due to the taxation). The last term represents theproductive inef-ficiency, due to the fact that the most efficient firm for serving these consumers,that is, firm I is replaced by firmE (less efficient).

The choice of a tax level has also important consequences in terms ofredistribution. We now compare the benefits obtained by the various classes ofconsumers across the various possible regimes.

Suppose first that UND is at work. If the tax ratet leads to the regime whereI¯cross-subsidizes, then both types of consumers obtain a positive surplusu 5 u 5I I]

S . 0, which depends ont. As Gasmi et al. (2000) point out, cross-subsidizationE

corresponds to implicit taxation and has important redistributive effects.¯In the taxation regime, all consumers haveu 5 u 50. Therefore, the choiceE I]

between cross-subsidies or taxation regime raises an equity issue, that has to besolved by political choices and not throughex-ante criteria such as competitiveneutrality.

Suppose now USO5U. In the taxation regime, the sharing of the surplusbetweenm consumers andE cannot be determined. However, consumers have

]˜ ˜u 5 S in the cross-subsidy regime andu < S in the taxation regime. High costI E E E] ]¯consumers are indifferent, as whatever the regime, they haveu 5 0. The ubiquityI

constraint generates no redistributive effect between consumers. However, bothconsumers are better off in the ICS regime.

5. Pay-or-play: the entrant may serve high cost consumers

In this section, we investigate the alternative allocation rule where the entrantmay choose to serve the nonprofitable users instead of paying the tax. As in theprevious section we consider separately the effects of U and of UND.

5.1. The ubiquity constraint under pay-or-play rule

We first compute the equilibria of pay-or-play game and then examine itswelfare properties.

5.1.1. Equilibria of the competition processThe first important result shows that the profit of firmI coincides again with that

of the regulator and that the social objective can thus be decentralized. Butcompared to restricted-entry regulation, pay-or-play regulation allows achievinganother regime where firmE serves all consumers (the ECS regime) and financesits deficit on high cost consumers through cross-subsidies. Lett be the tax valuepop

for which


]]ã S 2 S 1aS 5 0s dE E E] ]

˜that is,aS 5W . If t is lower than this threshold, thenE has no incentive toE EE]serve the nonprofitable users whereas if it is higher,E can profitably serve bothclasses by cross-subsidization.

The proposition and the corollary below are proved in Appendix A (SectionA.3).

Proposition 5. ((Pay-or-play regulation, USO5U)) Under pay-or-play regula-tion, when only the ubiquity constraint is at work, the ECS regime may appearonly for t .t . The incumbent’s profit is given (up to a constant) bypop

˜max(W , W ) if t <tII EI popP 5I H ˜max(W , W ,W ) if t .t .II EI EE pop

Therefore the profit is identical, up to a constant, to welfare in the correspondingregime.

As in restricted-entry regulation, the choice of the regime by firmI is thus thatof the regulator (for a given tax level) who can thereby decentralize the socialoptimum.

However, pay-or-play regulation now introduces, for some tax rate values, thepossibility that firmE serves both classes of consumers, a situation which was notachievable under restricted-entry regulation. The following lemma now gives theequilibria of the game.

Corollary 3. ((Pay-or-Play, USO5U, Perfect equilibria)) At equilibrium ofpay-or-play regulation with ubiquity constraint, two cases may appear, accordingto the tax value.

(i) When t <t , the situation is identical to restricted-entry regulation. Thepop

regime ICS and TR may occur. Welfare is given by

U U ˜W 5W 5max(W , W ).pop re EI II

The equilibria are the same as in the restricted-entry game:

]˜ ˜– if W ,W : I cross-subsidizes (ICS), u 5 S , u 50EI II I E I] ]˜ ˜– if W .W : taxation regime (TR), u [ [0, S ], u 5 0.EI II E E I]

(ii) When t .t , three regimes (ICS, TR, ECS) may occur. Then welfare ispop

given by

U ˜W 5max(W , W , W ).pop EI II EE


The equilibria are given by

U ]– if W 5W , I cross-subsidizes (ICS) and (u , u )[D .pop II I I II]U ]˜– if W 5W , the taxation regime occurs (TR), and (u , u )[D .pop EI I I EI]U ]– if W 5W , E cross-subsidizes (ECS) and (u , u )[D wherepop EE I I EE]

]] ]] ] ]]˜D 5 (u , u ) /au <a(S 2 S )1aS and au 1au <Wh jEE I I I E E E I I EE] ] ] ]]] ]]˜D 5 (u , u ) /u > S and au 1au 5Wh jII I I I E I I EE] ] ]]

]] ]] ]˜ ˜D 5 (u , u ) /au 5a(S 2 S )1aS and u < S .h jEI I I I E E E I E] ] ] ]

Pay-or-play regulation has a number of welfare implications that are nowexamined more in detail.

5.1.2. Welfare consequences of the ubiquity constraint: a comparison betweenrestricted-entry and pay-or-play regulations

The virtue of pay-or-play regulation, compared to restricted-entry regulation, isthat it allows assigning the market for high cost consumers to firmE in situationswhere it is more efficient. It follows that pay-or-play regulation offers anadditional possibility for the allocation of users compared to the restricted-entryone. It thus enhances productive efficiency. Moreover, it is easy to check thefollowing points:

]– In the taxation regime, high cost consumers obtainu 5 0 in restricted-entry]] ] ]˜regulation, andu 51/a a(S 2 S )1aS . 0 in pay-or-play regulation. Thereforef gE E E] ]

the high cost consumers prefer pay-or-play regulation.]¯– In the regime whereI cross-subsidizes, consumersm have u 5 0 in

] ˜restricted-entry regulation and a valueu [ 0,W 2aS in pay-or-play regulation;f gEE E]˜consumersm haveu 5 S under restricted-entry regulation, whereas they obtain aE]]˜value u [ S , W in pay or play regulation. Thus both classes of consumersf gE EE]benefit from pay-or-play regulation instead of restricted-entry.

– In the regime whereE cross-subsidizes, there is a multiplicity of equilibriathat share the surplus between consumers and firmE differently.

An important consequence of the first remark is that pay-or-play regulationinvolves redistribution between consumers, despite the fact that the ND constraintis not imposed (this redistribution does not appear in restricted-entry regulation,under USO5U). These remarks lead to the following proposition.

Proposition 6. ((USO5U, Welfare and utility comparison)) When the ubiquityconstraint alone is at work, welfare and consumer’ surplus are both at leasthigher under pay-or-play regulation than under restricted-entry regulation.


We have seen that the welfare configuration depends on the comparison betweenthree terms:W , W , W . More precisely, at equilibrium, welfare exhibits theII EI EE

following properties.

– If W is the highest, then welfare is flat (constant with respect tot), theII

equilibrium configuration is that whereI cross-subsidizes. Whatever the value oft,the profit of firm I is p 5W 2W . 0. Every t is then a first best tax.I II EE

– If W is the highest, then the first best is achieved for allt .t . For suchEE pop

values oft, we havep 50, and these tax rates verify the budget constraint and areI

competitively neutral.– If W is the highest, the first best is achieved fort 5 0 and for that value, theEI ] BB]˜profit of firm I is p 0 5aS , 0. The balanced-budget taxt is thus a seconds dI I

best. Budget balance and competitive neutrality coincide, but this (common) taxlevel may lead to any of the possible regimes.

5.2. Ubiquity and nondiscrimination under pay-or-play regulation

We now examine the case where the incumbent is tied down by a nondiscrimi-¯nation constraint. FirmE is allowed to serve the high cost consumersm. Since we

¯ ¯assumeS , 0, it is clear that firmE never serves consumerm only. Consider theE

case (ECS) where firmE serve both types of consumers. Recall thatI must¯announceu 5 u > 0 because of the ubiquity and nondiscrimination constraints. ItI I]

follows that, in the case (ECS)

¯u 5 u > 0.E E]

In other words, firmE also has to fulfill both constraints (in case it servesm and]

m ). Therefore, in that case, there is no reason forE to pay a tax when it servesboth markets and cross-subsidizes (ECS regime).

Recall that we have definedt bypop

˜¯¯aS 1aS 5aS .E E E]] ]

¯We introduce another thresholdt, defined by

˜¯¯aS 1aS 5 S .E E E]]

˜ ¯SinceS is decreasing with respect tot, we have:t < t. As usual, the regimes atE pop

equilibrium follow immediately from the profit function of firmI. The propositionbelow (proved in Appendix A, Section A.4) gives the incumbent’s profit in thedifferent regimes.

Proposition 7. ((USO5UND, Pay-or-play regulation, SPE)) Under pay-or-playregulation and USO5UND, the profit function of firm I is given (up to aconstant) by


˜ ˜¯max(W 2aS , W ) if t <tII E EI pop

˜ ˜ ˜¯P 5 ¯ ¯max(W 2 [S 2 (aS 1aS )], W , W ) if t < t <tI II E E E EI EE pop]]5¯max(W , W ) if t < t.II EE

Three configurations may prevail at equilibrium, according to the tax rate:

– when the tax rate is very low, it is never profitable for firmE to serve bothmarkets. Therefore, two regimes may appear, ICS or TR, according to the taxvalue;

– for intermediate tax rate values, lettingE cross-subsidize may appear atequilibrium, depending on the efficiency of both firms;

– when the tax rate is very high, the total amount generated by the taxationregime is so low that this regime disappears, and the equilibrium is either ICS orECS, according to the respective efficiency of both firms.

Note that with regard to ‘strong’ productive efficiency, the first two configura-tions involve a distortion, due to the nondiscrimination constraint. However, thisdistortion is different in the two cases. More precisely, the distortion induced by

˜¯the nondiscrimination constraint isaS for t <t (as under restricted-entryE pop˜ ¯¯ ¯ ¯regulation),S 2 (aS 1aS ) for t < t <t and 0 for t >t. It is easy to checkE E E pop]]

that the distortion is continuous and decreasing with respect to the tax rate.In the following proposition (see Section A.5 for the proof), we compare

welfares under restricted-entry and PoP regulation (for USO5UND).

Proposition 8. ((USO5UND, Welfare comparison)) If t <t , welfare is thepop

same in PoP regulation as in restricted-entry regulation. If t .t , this is nopop

longer the case. Welfare under PoP regulation may be strictly lower than under]]

restricted-entry regulation.

(i) Suppose first

˜ ˜¯¯ ¯t < t <t or, equivalently, aS <aS 1aS < Spop E E E E] ]]˜ ¯¯ (4)W ,W ,W 1 [S 2 (aS 1aS )]EE II EE E E E]]5 ˜ ˜¯W 1aS ,W .EI E II

Then under restricted-entry regulation, the ICS regime prevails and welfare is W ,II

while PoP regulation leads to the ECS regime, where welfare is W ,W .EE II

(ii) Suppose now

˜ ¯¯ ¯t .t or, equivalently, S <aS 1aSE E E]]HW .max(W , W ).EI EE II


Then under restricted-entry regulation, the taxation regime prevails and welfare isW , while the PoP regime leads to the regimes ECS or ICS, and thus to a lowerEI

welfare.

Unlike what happens when the ubiquity constraint alone is at work (seeProposition 6), welfare in Pay-or-play regulation may be strictly lower than in

]]restricted-entry regulation. The loss of welfare when it appears may come from the

˜ ¯¯distortion S 2 (aS 1aS ) due to the ND constraint (case (i) above) or to theE E E]]disappearance of the taxation regime in PoP regulation for high tax level values(case (ii) above).

According to Proposition 7,ex-ante criteria (competitive neutrality, . . . ) mayrule out some socially optimal regimes. The regulator should take this into accountwhen determining the tax level and choosing the regulation rules.

6. Conclusion

In this paper, we assume that two universal service obligations are imposed by aregulator: geographical ubiquity and non discrimination. We focus on internallyfunded systems: USOs are funded through cross-subsidization or a unitary tax. Wecompare two allocation mechanisms: the restricted-entry case (RE) (only theincumbent can serve high cost consumers) and pay-or-play regulation (PoP),where the incumbent can choose to serve high cost consumers and not to pay thetax.

The main conclusions of the model are the following:

1. Under USO5U, we have weak productive efficiency at equilibrium. Thisdoes not occur under USO5UND, because of an additional distortion implied bythe ND constraint;

2. Under USO5U, welfare is always larger at equilibrium under PoP regulationthan under restricted entry regulation. This is false under USO5UND. Inparticular, PoP regulation may induce the entrant to be ‘too’ active on the market(with respect to productive efficiency);

3. Under USO5U, consumers prefer PoP regulation than RE. In particular,high cost consumers may obtain a positive surplus under PoP in all regimes(taxation and cross-subsidization), while their utility is always zero under RE;

4. Under USO5U and for a given tax level or lump sum transfers, the regulatorcan decentralize the maximization of welfare to the incumbent. This does notoccur under USO5UND.

Once the tax level is chosen, the regulator does not need to know the costparameters of the firms or the consumers’ characteristics if only the ubiquityconstraint is imposed. It is clear, however, that the regulator needs this information


to determine the optimal tax level or lump sum transfer (whatever the criterion ofoptimality: second best or competitive neutrality). In an asymmetric informationcontext between the regulator and operators, auctions can be a useful tool toreduce informational rents (see for example Anton et al., 1999).

Auctions, however, are not always compatible with self-funding and generallyimply the use of public funds for transfers. This may be a drawback when the costof such transfers is high (see Laffont and Tirole, 2000). When the competitivepressure is too strong, it may happen that auctions cannot be funded through lumpsum transfers between firms. Internal taxes can be a useful tool in such a case todiminish competitive pressure.

Moreover, externally funded auctions completely disconnect the differentsegments of market (profitable and nonprofitable consumers) and do not allowtransfers from one market to another. A systematic comparison between auctionmechanisms and self-funded systems (e.g. unitary taxes) is left for further research.

Acknowledgements

We are grateful to Farid Gasmi, Jean-Jacques Laffont, Helmut Cremer,Tommaso Valletti and Bernard Sinclair Desgagne for helpful comments, as well asseminar participants at MIT, Toulouse, Lyon, Stockholm, Evry, Paris, ITSconference in Turin, Econometric Society World Congress in Seattle and EEAConference in Bolzano. We also thank S. Martin and an anonymous referee forcomments that improved a first version of this paper. Financial support from the

´ Ćommissariat General du Plan (Paris) is gratefully acknowledged. All remainingerrors are ours.

Appendix A

A.1. Proof of Lemma 2

˜The function S is a maximum of affine functions, therefore it is a convexE

function. By the envelop theorem,we have

˜dS (t)E ˜]]5 2 q .Edt

˜The functionq is therefore decreasing and we haveE

˜dqd E˜ ˜] ]S 1 tq 5 t < 0.f gE Edt dt


¯ 9To see the last point, taket 5w9(0)2 c , where c .C (q, m) for all q (theE E E ]9marginal costC (q, m) is assumed to be bounded). Then the functionE ]¯w(q)2C (q,m)2 tqE ]

˜ ¯is decreasing forq > 0. Therefore, it attains its maximum atq 5 0 andS (t )5 2Ee e˜ ˜C (0, m)< 0. The continuity ofS gives the existence oft such that:S (t )5 0.E E E

A.2. Proof of Proposition 3 and Lemma 2

We consider restricted-entry regulation, with USO5UND. Recall that the¯incumbent announces one valueu > 0. Since firmE is not allowed to servem, itsI

profit function is

0 ICS regimep 5HE S 2u taxation regime.E I]

˜Firm E chooses to servem if and only if u , S . Therefore the announcement ofI E]] ˜u determines the regime that will prevail:u , S leads to the taxation regime,I I E] ]˜u . S leads to the ICS regime. FirmI’s profit function is then given byI E]

˜¯¯aS 1aS 2 u if u . S ICS regimeI I I I E]] ]p 5HI ˜¯˜ ¯atq 1a(S 2 u ) if u , S taxation regimeE I I I E] ]

Then the choice of the incumbent reduces to the choice of the regime: in thetaxation regime, firmI’s profit is maximum foru 50 (unique equilibrium); in theI

˜ICS regime, firmI’s optimal announcement is of courseu 5 S . Then firm I hasI E]to compare the corresponding values of its profit. We have:

˜¯ ¯˜ ˜¯ ¯p 5maxaS 1aS 2 S , atq 1aS .s dI I I E E I]] ]

˜The profitp can be written asI

˜ ˜ ˜ ˜˜ ¯p 5maxW 2aS 2aS , W 2aS ,s dI II E E EI E] ]

which gives Proposition 3 and Lemma 2.

A.3. Proof of Proposition 5 and Lemma 3

We consider PoP regulation, with USO5U. Recall that the incumbent an-¯nounces two valuesu > 0 andu >0. The profit of firmE is given byI I]

0 ICS regimeã(S 2u ) taxation regimep 5 E IE ] ]5 ¯¯ ¯a(S 2u )1a(S 2 u ) ECS regime.E I E I] ] ]


Firm E prefers ECS to TR if and only if

˜¯¯ ¯ ¯au <aS 1aS 2aS .I E E E]] ]

The preceding inequality is possible only if

˜ ¯¯aS <aS 1aSE E E] ]]

or, equivalently,t >t . Therefore, ift ,t , the ECS regime cannot occur andpop pop

PoP regulation leads to the same equilibria as restricted-entry regulation.¯For t >t , the three regimes may appear, according to the valueu , u :pop I I]

˜¯¯ ¯ ¯au 1au >aS 1aS andu > S ⇒ ICSI I E E E]] ]] ]˜ ˜¯¯ ¯ ¯au >aS 1aS 2aS andu < S ⇒ TRI E E E I E]] ] ]˜¯ ¯¯ ¯ ¯ ¯ ¯ ¯au <aS 1aS 2aS andau 1au <aS 1aS ⇒ ECS.I E E E I I E E]] ] ]] ]]

The profit function of the incumbent is

¯¯ ¯a(S 2u )1a(S 2 u ) ICS regimeI I I I] ] ]¯p 5 ˜ ¯ ¯atq 1a(S 2 u ) taxation regimeI E I I]5

0 ECS regime.

¯In the ICS regime, it is optimal for the incumbent to announceu , u such thatI I]¯¯ ¯ ¯au 1au 5aS 1aS . In the taxation regime, it is optimal forI to announceuI I E E I]] ] ]] ˜¯¯ ¯ ¯such thatau 5aS 1aS 2aS . In the ECS regime, all the possible values of (u ,I E E E I]] ] ]˜u ) lead to the same profit, namelyp 5 0. Finally firm I’s profit isI I

˜¯ ¯ ¯ ¯˜ ˜¯ ¯ ¯ ¯p 5maxaS 1aS 2aS 2aS , atq 1aS 2 [aS 1aS 2aS ],0 ,s dI I I E E E I E E E]] ]] ] ]] ]

which can be written as

˜p 5maxW 2W ,W 2W , W 2W .s dI II EE EI EE EE EE

A.4. Proof of Proposition 7

We consider PoP regulation with USO5UND. Recall that the incumbentannounces one valueu . The other firm’s profit isI

0 ICS regimeã(S 2 u ) taxation regimep 5 E IE ]5 ¯¯aS 1aS 2 u ECS regime.E E I]]

Firm E prefers ECS to TR if and only if

˜¯¯ ¯au <aS 1aS 2aS ,I E E E]] ]

which is possible only if


˜ ¯¯aS <aS 1aSE E E] ]]

or, equivalently,t >t . Therefore, ift ,t , the ECS regime cannot occur andpop pop

PoP regulation leads to the same equilibria as restricted-entry regulation.¯For t < t <t, we have:pop

˜¯¯ ¯0< u < [aS 1aS 2aS ] /a ⇒ ECSI E E E]] ]˜ ˜¯¯ ¯(aS 1aS 2aS ) /a < u < S ⇒ TRE E E I E]] ]

S < u ⇒ ICSE I

The profit function of the incumbent is

¯¯aS 1aS 2 u ICS regimeI I I]]¯p 5 ˜ ¯atq 1a(S 2 u ) taxation regimeI E I I]5

0 ECS regime.

˜¯¯ ¯The optimal announcement leading to TR is of courseu 5 [aS 1aS 2aS ] /aI E E E]] ]ãnd the optimal announcement leading to ICS isu 5 S . This gives the profitsI E

˜ ˜¯ ¯˜ ˜¯ ¯ ¯p 5maxaS 1aS 2 S , atq 1aS 2 (aS 1aS 2aS ), 0 ,s dI I I E E I E E E]] ] ] ]] ]

which can be written

˜ ˜¯˜ ¯p 5maxW 2 [S 2aS 2aS ] 2W , W 2W , W 2W .s dI II E E E EE EI EE EE EE]]

¯For t < t, we have:

¯¯0< u <aS 1aS ⇒ ECSI E E]]¯¯aS 1aS < u ⇒ ICS.E E I]]

¯¯The optimal announcement in ICS is of courseaS 1aS , which gives the profitE E]]

¯ ¯˜ ¯ ¯p 5maxaS 1aS 2aS 2aS , 0 ,s dI I I E E]] ]]

which can be written

p 5maxW 2W , W 2W .s dI II EE EE EE

A.5. Proof of Proposition 8

¯ ¯(i) We first show that for each (S , S ) there exists (S , S ) such that theE E E I] ]conditions (4) are satisfied. The third inequality of (4) is obtained by takingSI]¯large enough. Now we can chooseS to ensure the second condition of (4).I

˜ ˜¯SinceW ,W 2aS , restricted-entry regulation leads to ICS regime. By usingEI II E

assumptions (4), we obtain

˜ ˜ ˜¯¯ ¯W .W 2 [S 2 (aS 1aS )] .W 2aS .W .EE II E E E II E EI]]


It follows that PoP regulation leads to ECS regime (see Proposition 7).(ii) The proof is straightforward.

A.6. Imposing ND alone under restricted-entry regulation

¯ ¯In this section, we assume:S , 0, S . The incumbent can profitably serve theE I

high cost consumers. We assume that the regulator imposes only the nondiscrimi-¯nation constraint and that firmE cannot servem (restricted-entry regulation). Firm

¯E cannot be constrained by ND, since it never serves consumerm. Firm I iscompensated for the constraint ND by a taxt.

Lemma 5. ((Perfect Equilibria in the restricted-entry game, USO5ND)) Wemake the following assumptions

¯ ¯S , 0, SE I

¯¯aS .aS 1aSI I E] ]˜S , S .I E

Then there exists a unique subgame perfect equilibrium in which firm I serves only˜ ¯m (giving them u 5 S ), m consumers being then excluded from the market.I E]]

Although I would serve both types of consumers in the benchmark case,imposing ND alone has the counterveiling effect of excluding high costsconsumers from the market: FirmI prefers to disconnect (or not to connect) theseconsumers rather than incurring losses due to cross-subsidization between bothclasses of consumers. This should lead the regulator to impose both constraintssimultaneously.

Proof of Lemma 5. The possible regimes are ICS, TR and the exclusion regime,¯wherem is served byI and m is not served. FirmE’s profit function is

]

ã(S 2u) taxation regimeE] ]p 5 0 ICS regimeE 5

0 exclusion regime (firm I),

It follows that the profit ofI is

¯ ˜¯ ¯a(S 2 u )1atq taxation regimeI I E]¯ ¯˜ ¯p 5 aS 1aS 2u ICS regimeI I I] ]5

a(S 2u) exclusion regime (firm I),I] ] ]

The optimal announcement in the taxation regime and in the exclusion regime is of˜courseS . Therefore firmI maximizesE


˜ ˜¯ ¯ ¯˜ ˜¯ ¯p 5max[aS 1atq , aS 1aS 2 S , a(S 2 S )].I I E I I E I E] ] ] ]˜The assumptions of the lemma ensure that the maximum isa(S 2 S ) (exclusionI E] ]

regime).

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Allocating and funding universal service obligations in a competitive market