Cross Subsidies inPublic Services:

Some Issues

Paulina Beato

Inter-American Development Bank

Washington, D. C.

Sustainable Development DepartmentTechnical Papers Series

Cataloging-in-Publication provided byInter-American Development BankFelipe Herrera Library

Beato, Paulina. Cross subsidies in public services : some issues / Paulina Beato.. p. cm. (Sustainable Development Dept. Technical papers series ; IFM-122) Includes bibliographical references.

1. Human services--Finance. 2. Subsidies--Costs. I. Inter-American DevelopmentBank. Sustainable Development Dept. Infrastructure and Financial Markets Divi-sion. II. Title. III. Series.

361.25 B42--dc21

Paulina Beato is Principal Economist in the Infrastructure and FinancialMarkets Division, Sustainable Development Department. The author isgrateful to Antonio Vives and William Savedoff for comments to a previousversion of this paper.

The opinions expressed in this paper are the responsibility of the author anddo not necessarily reflect the official position of the Inter-American Devel-opment Bank.

January 2000

This publication (Reference No. IFM-122) can be obtained from:

IFM PublicationsInfrastructure and Financial Markets DivisionMail Stop W-0508Inter-American Development Bank1300 New York Avenue, N.W.Washington, D.C. 20577

E-mail: sds/ifm@iadb.orgFax: 202-623-2157Web Site: http:www.iadb.org/sds/ifm

Foreword

The past decade has seen the reform of industries that historically operated under heavy governmentcontrol, giving rise to a new model of infrastructure provision. Three features characterize this newmodel. First, ownership, management and financing of infrastructure assets are increasingly in the handsof private sector firms. Second, the public sector exercises a regulatory function that complements thefunctioning of the market. Third, consumer prices cover total costs and return on investment compen-sates capital.

Multilateral lending institutions have issued recommendations for providing infrastructure services thattake this new model into account. One of the topics covered in these recommendations is pricing policy.Pricing recommendations advocate that prices should be set to cover the total cost of the service andcross-subsidy schemes avoided. Although straightforward, the application of these recommendations toreal world infrastructure services may be complex because uniform pricing may not be fully compatiblewith total cost coverage and welfare goals when technologies have increasing returns that may result inprice discrimination and cross subsides.

This paper explores the economic literature for rules on applying these principles to concrete worldinfrastructure services. It constitutes an important tool for the staff of multilateral institutions as well asfor national policymakers and other interested parties in ensuring that private participation in infrastruc-ture improve access and service options for the poor.

Pietro MasciChiefInfrastructure and Financial Markets Division

CONTENTS

Introduction1

1. Cross Subsidies and Consumer Separation: An Example3

2. Price Schemes with Cross Subsidies5

3. Cross Subsidies and Market Efficiency7

4. Prices Should Cover Marginal Costs10

5. Can Cross Subsidies Destroy Markets?13

6. Regulatory Approaches15

7. Conclusions17

Annex18

References21

1

INTRODUCTION

During the past decade, many industries that histori-cally operated under heavy governmental controlhave undergone a substantial reform process. A newmodel of infrastructure provision has emerged andextended worldwide. Three features characterize thenew model. First, the property, financing and man-agement of infrastructure assets rests, at least tosome extent, on private sector firms. Second, thepublic sector has a regulatory role that should notsubstitute for the market but complement it. Third,consumer prices should cover total costs. Multilat-eral institutions have prepared recommendations forproviding infrastructure services through the newmodels which deal with several topics, ranging fromthe selection of the private sector firm to the organi-zation of the regulatory institutions, from pricingpolicy to entry and exit control and from financingpolicies to the role of markets.

Pricing policy recommendations are based on twoprinciples. One is that prices should cover the totalcost of the service. The other is that cross subsidyschemes1 should be avoided. Although both princi-ples may appear simple, their application to realworld infrastructure services may be complex. Thereason is that among the several notions of freecross subsidy prices only one is fully compatiblewith both covering total cost and welfare

1 There are several definitions of cross subsidyschemes, in the economic literature, which are dis-cussed in section 2 of this paper. For the purpose ofthis introduction, a price scheme has cross subsidies ifprices for some consumers are below average costs andprices for other consumers are above average costs.

goals when technologies have increasing returns.2

This paper explores the economic literature for ruleson applying these principles to real world infra-structure services. The discussion is based on apartial equilibrium approach that uses market sur-plus as a proxy for social welfare and efficiency.3

Although equity issues are important and are relatedto cross subsidy pricing, they are not addressed inthis paper because these two issues require differentanalytical frameworks. For efficiency issues marketsurplus is enough, while for equity issues socialwelfare functions and income distribution goals areneeded. Therefore, a partial equilibrium analysis isappropriate for the former and a general equilibriumframework is best suited for the latter.

This article reaches three main conclusions. First, ifa uniform price schedule is established and pricesdiverge from marginal cost, then social welfare canbe increased by establishing appropriate price dis-crimination schemes that have cross subsidies. Thisdoes not mean that all schemes with cross subsidiesincrease welfare, but some do. For instance, crosssubsidy schemes where prices are lower than mar-ginal cost are not appropriate from the welfarestandpoint, whereas cross subsidy schemes withprices below average cost may be welfare optimal.Second, from a voluntary

2Although increasing returns are not always equivalentto decreasing average cost functions, for simplicity thispaper considers both terms equivalent. The paper as-sumes that the conditions for such equivalence holds.See Panzar, 1989.

3The terms Asocial welfare@ and @efficiency@ are used assynonyms.

2

sustainability4 standpoint, some cross subsidyschemes are not suitable, whereas others are appro-priate. Third, sometimes, optimal and voluntarysustainable price schedules are not compatible. Inthese cases, a trade-off between optimality andsustainability is often necessary. The regulator=schoice should be based on a comparison betweenefficiency losses and the cost of maintaining a priceschedule that drives some consumers away from theregulated firm or forces the exclusion of other con-sumers.

Section 1 provides an example that sets forth themain issues discussed in the paper. Section 2

4A precise definition of voluntary sustainability is givenin section 4. The idea is that a public service is volun-tarily sustainable when consumers are not willing tochange to a different supplier. That is, all consumergroups are better off if the regulated firm continuesproviding the service.

reviews several definitions of cross subsidy priceschedules. Section 3 discusses the conditions underwhich price schemes with cross subsidies increaseefficiency. Section 4 defines conditions for efficientprice allocations. Section 5 explores the notion ofvoluntary sustainability. Section 6 discusses the casewhere a price schedule that is both optimal andsustainable does not exist. General conclusions arefurther elucidated in section 7. An annex to thepaper provides an example of a case where optimalprices are not sustainable.

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1.CROSS SUBSIDIES AND CONSUMER SEPARATION:

AN EXAMPLE

To illustrate the issues discussed in this paper,assume that a profit-regulated firm provides waterto two neighborhoods, a and b. Water supply re-quires two types of investments. The first type ofinvestment, distribution pipelines, is specific foreach neighborhood. Investments of the second type,storage tanks and pumps, can be used by bothneighborhoods. The regulated firm=s total costs arethe capital cost of investments and the cost of elec-tricity for pumping water from the river to neigh-borhoods. The regulator sets the same price for bothneighborhoods, which equals total average cost.5

The manager of the regulated firm notices that thecompany may increase its profit by providing waterto a new neighborhood, c, at a lower price than thatcharged neighborhoods a and b. The manager setsprices in neighborhood c so that revenues areslightly above that neighborhood´s costs, as well as,the pipeline distribution cost and the electricity cost.Nevertheless, he does not charge for the cost of thestorage tank and pumps. After starting the newpolicy, the firm profits and total consumption in-crease.

The regulator imposes a penalty on the managerbecause by setting lower prices in the new neighbor-

5The average cost for the case of a multiproduct firmmay be ambiguous due to the assignment of the com-mon cost among products. For this example, the regu-lator defines the average cost of servicing water as fol-lows: pump cost plus storage tank cost plus distributioncost to neighborhoods a and b plus electricity cost for neighborhoods a and b, divided by the amount of serv-ice water in both neighborhoods.

hood, he is in noncompliance with existing regula-tions. The manager claims that the new price policyincreases social welfare, arguing that if consumerspay voluntarily, then consumer welfare should belarger than consumer payments. He also says that ifrevenues from new consumers are larger than incre-mental cost, the welfare gains are larger than theincrease in social costs, that is, a net increase ofsocial welfare occurs.

In spite of the manager=s claims, the regulator forcesthe manager to distribute the cost of the tank andpumps uniformly among the three neighborhoods.The new price policy means an insignificant reduc-tion in the prices paid by the consumers in neigh-borhoods a and b, and a large increase in the pricespaid in neighborhood c. The results of this regula-tory policy are a dramatic fall in consumption inneighborhood c, while consumption in neighbor-hoods a and b remains at approximately the previ-ous levels.

The manager=s arguments did not convince theregulator, but real life facts make him reconsider themanager=s proposal. Thus, the regulator contracts aconsultant to evaluate the manager=s price policy.The consultant agrees that the manager=s proposalincreases social welfare, and points out that furtherincreases of welfare can be brought to the commu-nity if a full price discrimination scheme is setacross the three neighborhoods. He recommendsincreasing prices in neighborhood a, decreasingthem in neighborhood b, and maintaining the man-ager´s price proposal in neighborhood c. He sup-ports his recommendations with the following ar-gument: Prices should be increased in neighborhooda because the area only has tourist hotels and the

4

volume of water consumed by tourists is not sensi-tive to price increases6 Thus, prices can be increasedin neighborhood a to include the entire cost of thestorage tank and pumps in addition to distributioncosts, without resulting in a decline in water con-sumption. Prices can then be brought down inneighborhood b where consumers are sensitive toprices and the regulated firm would not incur anylosses. The increase in consumption in neighbor-hood b is higher than the decrease in the neighbor-hood a and total consumption and social welfareincrease.

6 The consultant is not able to estimate demand func-tions for each neighborhood due to a lack of pricevariations changes during the last period. However, theconsultant calculates the demand of neighborhood abased on the demand for tourists. By doing so, the con-sultant does not mention in the analysis that the hotelscan use well water as a source of supply.

The regulator carries out the consultant=s recom-mendations. During the first months, the newmeasures are very popular. After six months, how-ever, company revenues drop due to a decrease inconsumption in neighborhood a, despite the fact thatthe number of tourists has increased sharply. Furtherinvestigations point to the fact that each hotel has itsown well water system. Tourists may have low priceelasticity but hotels do not. The results are highersocial costs for the communities and large losses forthe regulated firm. The regulator tries to forbid theuse of well water, but is unsuccessful.

5

2.PRICE SCHEMES WITH CROSS SUBSIDIES

Are the proposals made by the regulator, the man-ager and the consultant free of cross subsidies? Theanswer depends on how a price scheme that is freeof cross subsidies is defined. The notion of crosssubsidies has been developed for dealing with therelation between service payments from a group ofconsumers and the costs associated with providinga service or related services to them. However,several definitions have been used for price schemesfree of cross subsidies. The following definitions areused in this article.

DEFINITION 1:MARGINAL COST CRITERION

Under this criterion, a price scheme is said to havecross subsidies, if some consumer prices are lowerthan the marginal cost. Otherwise, if all consumerprices are equal or above marginal costs, then theprice scheme is subsidy free. Notice that accordingto this criterion, a price scheme in which all con-sumer prices just equal marginal cost is cross sub-sidy free. However, such a scheme may not raiseenough revenues to cover the total cost of the serv-ice. In the previous example, the proposals made bythe regulator, the manager and the consultant arefree of cross subsidies according to this criterionbecause the prices proposed by each cover neigh-borhood electricity costs in all three neighborhoods.

DEFINITION 2:AVERAGE COST CRITERION

Under this criterion, a price scheme is said to havecross subsidies if some consumer prices are belowaverage costs and others are above. This criterion

may be difficult to apply to multiproduct firmsbecause their average cost schedules may not bewell defined. In particular, when some costs areshared among different products, the average costschedule cannot be precisely defined. For example,the regulated firm in the previous example may beconsidered a multiproduct firm if providing water toneighborhoods a and b is viewed as two differentproducts. Therefore, an average cost schedule foreach neighborhood cannot be precisely defined dueto the different ways of distributing common costs.Nevertheless, for purposes of illustrating the aver-age cost criterion, the average cost is defined as thesum of all costs (pumps, storage, distribution andelectricity) in both neighborhoods divided by theamount of delivered water to both neighborhoods.That is, water provision is considered a uniqueproduct regardless of where it is delivered. Accord-ing to this definition of average cost, the manager=sproposal has cross subsidies since the price forneighborhood c is below average cost while pricesin neighborhoods a and b are above average costs.

DEFINITION 3:INCREMENTAL COST CRITERION

Under this criterion, a price scheme is said to havecross subsidies if revenues from a consumer or agroup of consumers are less than the incrementalcost of providing services to that consumer or groupof consumers. In the example, the incremental costfor neighborhood c is the cost of electricity forpumping (marginal cost) plus the cost of pipelinesin neighborhood c. The incremental costs for theother neighborhoods are similarly defined. There-fore, according to the incremental cost cri-

6

terion, the manager´s price schedule is subsidy freesince all neighborhood revenues cover variable anddistribution costs for each neigborhood.

DEFINITION 4:STAND-ALONE CRITERION

Under this criterion, a price scheme is said to havesubsidies if the revenues from a consumer or groupof consumers are larger than the cost of providingservice alone to this consumer or group of consum-ers. In the example, the price scheme proposed bythe consultant is not subsidy free because revenuesfrom neighborhood a are higher than the cost of producing the service for this neighborhood usingwells.

This leads to the following observations: First,definitions 1 and 2 compare prices with the actualcosts of providing services, whereas definitions 3and 4 compare prices to the costs of other alterna-tives for providing the service. This means that, forassessing price schedules according to criteria 1 and2, only the knowledge of the regulated firm costschedule service is required, while for assessingprice schedules according to 3 and 4, criteria infor-mation about other technologies is needed. Sec-ond, it is necessary to examine all groups of con-sumers in order to establish that a price scheme issubsidy free under definitions 3 and 4. In otherwords, it is not enough to test some individuals orsome groups. Thus, definition 3 requires that all consumers and consumer groups

Quantity

C*

C’

X Xm

Marginal Cost

Costs

Average Cost

Figure 1

7

pay the incremental costs that correspond with theactual technology used by the regulated firm and anyother available technologies. Definition 4 requiresthat all consumers and all consumer groups preferthe service of the regulated firm to all other alter-natives. Third, with increasing returns, a pricescheme that is free of cross subsidies according tothe average cost criterion will be also

subsidy free according to the marginal cost criterionsince marginal costs will be below average costs when average costs are decreasing. Increasingreturn technologies have decreasing average costs(see figure 1). Fourth, if the profit of the firm iszero, then a price scheme is subsidy free accordingto definition 3 if, and only if, the price scheme issubsidy free according to definition 4.7

7 For a proof, see Breutigam, 1989.

8

3.CROSS SUBSIDIES AND MARKET EFFICIENCY

In the previous example, the proposal of the man-ager of the regulated company is supported by well-known theoretical results which state that any uni-form price schedule different from marginal cost canbe welfare dominated by a nonuniform price sched-ule if consumers have different price elasticities.These findings are relevant for setting discrimina-tory prices in infrastructure services because mar-ginal cost pricing does not cover total cost in thepresence of increasing returns, a common feature ofinfrastructure. Therefore, if revenues from infra-structure services cover total costs, then prices mustdiverge from marginal cost. In other words, from awelfare standpoint, price discrimination schedulesmay be better than a uniform price when the uniformprices do not equal marginal cost and price elastici-ties differ among consumers.

However, price discrimination may or may notimply cross subsidies. If regulators set prices so that they just cover costs without yielding extraordi-nary profits, then any price discrimination schemehas implicit cross subsidies according to the averagecost criterion. The reason is that consumers who payhigher prices are paying more than average costs,while consumers who pay lower prices are payingless than average costs. In these cases, the alloca-tions resulting from pricing with cross subsidiesaccording to the average cost criterion may domi-nate, from an efficiency standpoint, allocationsresulting from uniform prices. It may occur that aprice scheme that increases welfare with respect touniform prices has cross subsidies according to theaverage cost criterion and does not have them ac-cording to the stand-alone or the incremental crite-rion. However, it may also be the case that a pricescheme appropriate for

welfare purposes has cross subsidies according tothe average cost, the stand alone, and incrementalcost definitions. Nevertheless, as discussed in thenext section, prices must be free of cross subsidyaccording to the marginal cost criterion for welfaregoals.

Although a formal proof of the above is not in-tended, the following arguments may be useful inunderstanding them. Notice that if the price is above marginal cost and if consumers have differentprice elasticities then welfare may be increased byreducing prices to consumers with a high priceelasticity of demand and increasing prices to con-sumers with a low price elasticity of demand. Thisis so because the increase in consumption and con-sumer surplus of the former group would compen-sate for the decrease in consumption and consumersurplus of the latter group.

In figure 2, m is the marginal cost schedule of pro-viding an infrastructure service. Each neighborhooddemand function is represented by Da and Db re-spectively. The price elasticity of demand for neigh-borhood b is larger than the price elasticity of de-mand for neighborhood a. Prices are equal in bothneighborhoods and they are higher than marginalcosts in order to cover fixed costs. The gray arearepresents revenues over variable costs that can beused to cover fixed costs. The black area representsthe welfare loss with respect to the maximum wel-fare that could be achieved (the maximum welfare isattained when prices equal marginal costs). Thewelfare loss is larger in neighborhood b than inneighborhood a. The reason is that given the differ-ence in the price elasticity of demand between thetwo neighborhoods, consumption in neighborhood

9

b diminishes less than in neighborhood a as pricesincrease from marginal cost to P*a.

Figure 3 shows what happens when a discriminatoryprice schedule is established. In neighborhood a,prices are now higher than in figure 2 (i.e., P**a ishigher than P*a), while in neighborhood b, pricesare lower (i.e., P**b is lower than P*b). The new

prices are above marginal costs. The differencebetween revenues and variable cost is larger (thegray area) in figure 3 than in figure 2. Welfarelosses with respect to maximum welfare are smallerin figure 3 than in figure 2 (i.e., black area). Theprice scheme in figure 3 with price discrimination isbetter from a welfare point of view than the pricescheme in figure 2.

10

Pa

Da

m

Pb

m

Db

Y*a

P*aP*b

Neighborhood a Neighborhood b Y*b

Figure 2

11

4.PRICES SHOULD COVER MARGINAL COSTS

The previous sections have shown that price dis-crimination and cross subsidies, in the increasingreturns and a no-losses restriction, may increasesocial welfare. Yet, they are far from showing thatall discriminatory schemes are appropriate forimproving welfare. This section discusses threeimportant considerations in analyzing the welfareimplication of schemes with price discriminationand cross subsidies.

First, cross subsidy schemes with prices lower thanmarginal costs are not appropriate from the effi-ciency standpoint. The reason is simple, if the pricepaid by a consumer is lower than marginal costs, thesocial cost of this consumer service is larger than thebenefit to the consumer, as measured by the price. Ifthere are no externalities,8 welfare is increased byjust reducing production in the amount correspond-ing to the underpriced consumer. Therefore, a firstrule is that consumer prices should be greater thanmarginal cost. This rule sets a lower bound for priceschedules.

Figures 4 and 5 illustrate this rule. Comparison ofboth figures shows that welfare increases just byincreasing prices in neighborhood b and keepingprices level in neighborhood a. The price increasesbring down consumption and losses, while im-

8 If there are externalities, subsidy schemes may need tobe implemented to increase consumption. Direct subsi-dies, as in Chile, are preferred from an efficiency pointof view. Nevertheless, the administrative cost of directsubsidies is usually large.

proving welfare. That is, the black areas are smallerin figure 4 than in figure 5. (As in figures 2 and 3,black areas are a measure of welfare loss with re-spect to maximum welfare.)

Second, schemes with cross subsidies and pricediscrimination increase welfare only if they increasethe level of consumption, since price discriminationand cross subsidies causes marginal rates of substi-tution to be different among consumers. Therefore,for a given amount of consumption, they are sociallyinferior to uniform prices. However, if a cross sub-sidy scheme is successful in increasing the con-sumption level, the welfare improvement fromgreater consumption may be larger than the welfareloss from the difference in marginal rates of substi-tution. It should be clear that if some prices arebelow marginal costs, then welfare may increasewhen these prices increase up to marginal costs

Third, under increasing returns and the restriction ofno losses in the regulated firm, a necessary conditionfor welfare maximization is that the deviation ofprices from marginal cost in each market should beinversely related to the price elasticity of demand in each market.9 Prices should be higher in markets with lower price

9A formal proof of this can be found in Boiteux, 1971.If nonlinear prices are allowed, then price discrimina-tion is not a necessary condition for maximizing wel-fare (Willig, 1978).

12

P**a

mP**e

m

y**ey**a

Neighborhood b Neighborhood a

Figure 5

13

lower price elasticity than in markets with higherprice elasticity. This result shows that if welfaremaximization is the goal, then price discriminationis appropriate. It also means that prices for someconsumers will be higher than average costs and forothers they will be lower. In other words, there arecross subsidies among consumers, which redistrib-utes income away from low-elasticity groups towardconsumers in the high-elasticity groups.10 Thus, ifconsumers do have different elasticities, optimalprices are not subsidy free according to the averagecost criterion. This result does not say whetheroptimal prices hold for the stand-alone and theincremental cost criteria for price schemes

10 Optimal prices would improve income distribution iflow elasticity groups are the wealthier consumers. Thisis an empirical matter, nevertheless it seems plausiblethat wealthier consumers could have a lower priceelasticity.

to be subsidy free (for a discussion of this issue, seesection 5).

Although, the third point relies on increasing returntechnologies and the no losses restriction for theregulated firm, it is, nevertheless, relevant as a guidefor pricing policy of public services because in-creasing return technologies are the main reason forregulating the prices of infrastructure services. Thecase for public sector intervention in infrastructureservices is the presence of market failures due toincreasing returns (decreasing average cost struc-tures). In fact, if infrastructure services do not havethese features, regulators should not control prices,but only promote competition.

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5.CAN CROSS SUBSIDIES DESTROY MARKETS?

The above results suggest that one cannot make acase against all price schemes with cross subsidieson a welfare basis. Some schemes may have badproperties, but not all. Even more, cross subsidiesschemes, according to the average cost criterion, area necessary condition for welfare maximizationwhen increasing returns are present and losses areforbidden. Therefore, reasons other than welfareshould be the cause for rejecting price scheduleswith cross subsidies.

One reason for rejecting cross subsidies is that theymay lead overpriced consumers to abandon the regulated firm or force the exclusion of under-priced consumers. Overpriced consumers mayrealize that their payments to the regulated firm arelarger than what they would pay under other ar-rangements. Also, overpriced consumers may noticethat by excluding some underpriced consumers, theymay reduce their payments to the regulated firm.Thus, overpriced consumers may force the splittingof the service and the whole community would losethe benefits of technologies with economies of scale.

The notion of voluntary sustainability characterizesprice schemes under which every group of consum-ers in a community is better off when the publicservice is jointly provided. Therefore, no consumeris willing to change to another provider. A pricediscrimination scheme for a community is voluntar-ily sustainable, if the following two conditions hold:

· Stand-Alone Criterion. Each group of consum-ers pays less for the provision of the servicethan they would pay alone. Thus, separation ofa group will not improve the welfare of mem-bers. This condition sets an upper bound forrevenues from a group of consumers.

· Incremental Cost Criterion. Revenues fromeach group cover the incremental to total costthat occurs when the service is provided to thatgroup as opposed to not being provided at all.This condition sets a lower bound for revenuesfrom a group of consumers.

When the first condition holds, no group will bewilling to separate because doing so will increasetheir payments. However, if the second conditionholds, no group is willing to exclude other groups,since the exclusion of one group will make theremaining consumers worse off.

Some observations on these conditions should bemade. First, a price scheme is sustainable if, andonly if, it is cross subsidy free according to both thestand-alone and the incremental criteria. Second, theincremental cost condition requires that pricesshould be above marginal costs. Therefore, priceover marginal cost should hold for both welfare andsustainability reasons. Third, price schedules meet-ing the conditions for voluntary sustainability mayhave implicit cross subsidies according to the aver-age cost criterion. Therefore, prices with crosssubsidies according to the average cost criterionmay be compatible with both welfare andsustainability requirements. Four, the sustainabilityof a price scheme closely depends upon the alterna-tives for service provision of each consumer orgroup of consumers. That is, checking sustainabilityrequires information about alternative technologiesavailable to every group of consumers. Five, thenotion of voluntary sustainability is strong becauseall groups should be checked. However, in the realworld, it is often difficult for consumers to join in

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order to reach other alternatives of service provisioneven if they can technically reach them.

The example may be used to illustrate these notions.The manager=s proposal is voluntarily sustainablebecause neighborhood c pays its incremental cost.Also, because neighborhoods a and b share thecommon costs, hotel payments are smaller than thecosts of self provision by using wells. Thus, thestand-alone criterion holds. However, the manager=sproposal has cross subsidies according to averagecosts because the price of water for neighborhood cis less than total average costs. By contrast, theconsultant=s proposal is better in terms of welfarethan the manager=s proposal. However, hotels havecheaper alternatives than receiving water from theregulated firm at prices that cover the total cost of tanks and pumps. Therefore, the consultant´sproposal is not voluntarily sustainable and mosthotels separate.

To illustrate that the notion of voluntarysustainability may be too strong, the example ismodified slightly. Assume that the cost of waterprovision for each group of hotels is larger thanpayments to the regulated firm. However, a coalitionof one hotel and a thousand consumers may obtainwater at a cost lower than its actual payments.Assume that the new water supply alternative forthis coalition requires a large initial investment.Assume also that the consumers do not have finan-cial capacity to pay their share of the initial invest-ment. This coalition of a hotel and a thousand con-sumers is technically possible, but the coalitionwould likely not undertake the required investments.By modifying the example, the price schedule of theconsultant is still not voluntarily sustainable ac-cording to the definition of sustainability because itdoes not hold to the stand-alone criterion. However,the separation does not actually occur.

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6.REGULATORY APPROACHES

The economics of regulation deals mainly with threetopics. The first is market failure to reach efficiencyand the corrective actions that regulators shouldundertake to ameliorate them. The second refers toequity issues and the measures for improving in-come distribution. The third, and the more innova-tive, refers to the compatibility between regulatoryframeworks and the behaviors of the economicagents for achieving welfare and equity goals. Forthe issues addressed in this paper, the research foroptimal prices with no-losses condition falls withinthe first topic, while the sustainability of a pricescheme falls within the third. Modern theory drivesregulators jointly dealing with welfare and incentiveissues. In the context of this paper, this means thatregulators should look for prices that are optimaland sustainable. They may follow different ap-proaches to reach this goal.

In one approach, the regulator sets a price schedulethat maximizes welfare subject to a non-negativeprofit restriction. Baumol and Bradford (1970),Boiteux (1971) and Ramsey (1927) follow thisapproach. However, the optimal price schemes mayor may not be voluntarily sustainable.11 If the opti-mal prices are not voluntarily sustainable, then thepublic service may split. With scale economies, thisleads larger social costs. To defend this approachwhile avoiding service splitting, regulators shouldrestrict entry. By doing so, the optimal price sched-ule may be sustainable, but not voluntarily sustain-able. However, it may be difficult to control entry

11 The Weak Invisible Theorem states the conditionsunder which optimal prices are voluntarily sustainable.See Baumol, Baily and Willig, 1977.

effectively since regulators may easily prevent entry into new markets, but may not stop consum-ers from providing their own service. Nevertheless,whatever the reason for splitting, the scale economyadvantages are lost. The case in which optimalprices are not voluntarily sustainable should be quitecommon. The reasons are, as discussed in section 4,that optimal prices depend upon demand elasticitiesand the cost schedule of joint community provision,whereas voluntarily sustainable prices depend uponthe cost alternatives of each group of consumers.

In the example, hotels have a lower price elasticityof demand, therefore, the optimal price schedulesfrom a welfare perspective should set hotel priceshigher than prices for other consumers.Nevertheless, these price schemes are not sustainable because hotels have an alternativesource of water supply: wells. In other words, hotelscan block optimal price policy. The Annex shows anumerical example with no sustainable optimalprices.12

12 Although complete information is not available,figures suggest that optimal prices are not sustainablein the Bahamas because hotels can obtain water fromwells at a total cost close to their payments when priceis set to the average total cost of providing jointly thewhole island. The actual price schedule, which chargesthe hotels over average cost, induces hotels to separate.Most hotels actually do separate.

17

Another approach is for the regulators to choose theprice scheme that maximizes welfare within the setof voluntarily sustainable prices. In this approach,entry may be free because price conditions preventcompetitive entry. If revenues from all groups covertotal costs, then entry would not improve the currentposition of any consumer group. In this approachregulators take into account consumer incentivesand the communities benefit from the advantages ofeconomies of scale through incentives. In the previ-ous approach the economy of scale benefits thecommunity through regulator prohibitions. Thisapproach requires that the regulators have informa-tion on coalitions, and technologies available to eachcoalition. Such information is difficult to gather. Asmanagers often have more information than regula-tors on coalitions and technologies, discriminatoryprice schedules proposed by managers and super-vised by regulators may be appropriate for actuallycarrying out this approach. The regulators check the

optimatility properties of the manager=s proposalthat likely will be sustainable since managers usu-ally wish to avoid separation.

A comparing of the two approaches yields the fol-lowing conclusions. One, the first approach topsefficiency over voluntary sustainability. Second, thefirst approach relies on regulator intervention foravoiding service splitting, while the latter relies onconsumer incentives. Third, for choosing an ap-proach, regulators should balance efficiency gainsagainst the losses of splitting the service that thefirst approach entails. Fourth, the service would beeasier to split when the coalitions among consumersof a community are feasible because the coalitionsmake it easy to share common costs. For example,larger consumers (hotels and big industrial consum-ers) are easy to split because they do not need to joinwith other consumers to share the costs of a pro-vider different from the regulated monopoly.

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7.CONCLUSIONS

This article reaches the following conclusions:

· Schemes with price discrimination and crosssubsidies may be suitable from an efficiencystandpoint. Even more, price schemes withsome prices below average cost and othersabove (that is, with cross subsidies according toone of the many definitions of cross subsidyprices) are a necessary condition for welfaremaximization in public services with increasingreturns and no loss constraints.

· Schemes with price discrimination and crosssubsidies may not be voluntarily sustainable be-cause a group of consumers may be better offby separating from the public service. Theoverpriced consumers may force the communityservice to split and therefore, the overall com-munity would lose the benefits from the in-creasing return technologies.

· If optimal prices are not compatible with vol-untary sustainability, then a choice betweensustainable prices and efficient prices has to bemade. The appropriate choice will dependupon the likelihood that entry will actually

be prevented, the efficiency losses from servicesplitting, and the alternatives for service provi-sion.

These conclusions lead to a final observation: cen-tralized price policy, through regulators, is a com-plex matter because the information required to setthe appropriate prices is often not available toregulators. Therefore, even with increasing returnsand the no loss restriction, the price policy shouldrely, to some extent, on the information provided bymarkets. Market agents, consumers and producers,are better than regulators in gathering the informa-tion13 required to set price discrimination schedulesfor profit maximization without losing customers.Regulators may set limits to these prices, but notforbid them. Finally, if entry is free, the markets willsignal unsustainable pricing policies to regulators.However, restrictions are sometimes required fromprivate operators. In particular, the concessions oftraditional monopolies with large investment re-quirements demand exclusivity of market entry tomake a trade-off. As Friedman, 1962, laments Athereis unfortunately no good solution for technicalmonopoly.@

13 A necessary condition for gathering the appropriateinformation is consumption measurement. However, alarge meter program may be difficult to implement duenot to technical or economic reasons but to the reluc-tance of large consumers to accept to meter consump-tion.

19

ANNEX

OPTIMAL AND VOLUNTARILY SUSTAINABLE PRICE SCHEMES

The following example shows a case in which optimal prices are not voluntarily sustainable. Thus, the Ramseyrule that prices should be lower for high elasticity consumers contradicts the sustainability rule that, in thisexample, would require prices to be lower for low elasticity consumers.

Lets consider two neighborhood 1 and 2. The cost schedules of providing water are the following:

· Neighborhood 1. C(X1) = X1 + 5

· Neighborhood 2. C(X2) = X2 + 4

· Neighborhood 1 and 2. C(X1 + X2) = X1 + X2 + 9

Where X1 and X2 stand for the quantity of water used in each neighborhood.

The demand shedules and consumer surplus for neigborhoods 1 and 2 are the following:

· Indirect Demands: P1 = 2 - 1\5 X1 and P2 = 10 - X2

· Consumer Surplus: S(X1)= 2X1 - 1\10 X12 and S(X2)= 10X2 - 1\2X2

2

Where P1 and P2 stand for prices in each neighborhood.

Optimal prices are obtaining by solving the following optimization problem:

Maximize: l1 S(X1) + l2 S(X2) - X1 - X2 - 6

Subject to: P1 X1 + P2 X2 - X1 - X2 - 6= 0

Where l1, l2 are consumer surplus= weights.

First, lets consider the solution for l1, and l2 equal to 1. That is, the case in which the welfare of both neighbor-hoods are equally weighted. A pair (X1, X2) solves the above problem if and only if 9 X1 = 5 X2. This equationimplies the following relationships between prices:

P1 = 2-1\9 X2 and P2 = 10 - X2 which in turn implies that P1 = 1\9 P2 + 8\9.

The figures corresponding to the solution of this problem are summarized in table 1:

20

Table 1

Optimalprices

QuantitiesUnder optimal

prices ElasticityPayments underoptimal prices

Currentcosts

Alternativecost

Neighb. 1 1.0755 4.6225 1.1633 4.9715 - 9.6227

Neighb. 2 1.6791 8.3206 0.2018 13.9716 - 12.3209

Total - 12.9431 - 18.9431 18.9431 21.9256

Notice that the payments of consumers of neighborhood 1 are 4.9715 units and the payments of consumers ofneighborhood 2 are 13.9716 units. Payments of neighborhood 1 cover the marginal and variable costs for thisneighborhood (i.e., 4.6225 units) and a small part of the common costs. Payments of neighborhood 2 also coverthe marginal and variable costs (i.e., 8.3206 units) and a large part of the common costs.

It should be noticed that this solution is in accordance with the elasticity rule of Ramsey prices because the pricefor neighborhood 1 is lower than the price for neighborhood 2 and the price elasticity of neighborhood 1 is largerthan the price elasticity of neighborhood 2. This solution, which that is optimal from a welfare standpoint, is notsustainable because neighborhood 2 would be better off separating and providing service with its own company.The cost of water consumption for neighborhood 2 would be 12.30 units (the new company cost schedule is C(X2) = X2 + 4). Thus, if the new producer reduces the price for neighborhood 2 to 1.5, the revenues will be enoughto cover total cost and produce some profits.

21

REFERENCES

Baumol, W.J. and D.E. Bradford. 1970. Optimal Departure from Marginal Cost Pricing. AmericanEconomic Review, 60: 265-283.

Baumol, W.J., E.E. Bailey and R.D. Willig. 1977. Weak Invisible Hand Theorems no theSustainability of Prices in a Multiproduct Monopoly. American Economic Review, 67: 350-365.

Boiteux, M. 1971. On the Management of Public Monopolies Subject to Budgetary Constraints.Journal of Economic Theory, 3: 219-240.

Braeutigam, R. R. 1989. Optimal Policies for Natural Monopolies. In Handbook of Industrial Or-ganization. Elsevier Science Publishers, Smalensee and Willig, Vol. 2: 1289-1343.

Faulhaber, G.R. 1975. Cross-Subsidization: Pricing in Public Enterprise. American Economic Review,65 : 966-977

Friedman, M. 1962. Capitalism and Freedom. Chicago: University of Chicago Press.

Panzar, J.C. 1989 Technological Determinants of the Firm and Industry Structure. In Smalensee andWillig, Handbook of Industrial Organization. Elsevier Science Publishers, Vol 1: 4-56.

Ramsey, F.P. 1927. A Contribution to the Theory of Taxation. Economic Journal, 37:47-61.

Willig, R.D. 1978. Pareto Superior Nonlinear Outlay Schedules. Bell Journal of Economic, 9: 56-59.