Quality Regulation without Regulating Quality

Transcription

1 1 Quality Regulation without Regulating Quality Claudia Kriehn, ifo Institute for Economic Research, Germany March 2004 Abstract Against the background that a combination of rice-ca and minimum uality regulation is social otimal but hard to imlement the aim of this aer is to develo an alternative otimal regulatory mechanism that involves lower administrative costs. In a modelling framework which adeuately describes the behaviour of market articiants in network industries we found that return-on-cost regulation has (aroximately) the same effects on rice, uality and welfare than minimum uality regulation. If it is the aim of the regulator to achieve the welfare maximum under the zero rofit constraint, we show that a combination of rice-ca and return-on-cost regulation leads arbritrarily close to this oint and can thus be alied instead of the rice-ca lus minimum uality regulation. JEL classification: L51, L98 1 Introduction Since the 1980s, many countries have introduced economic reforms and cometition laws that have involved rivatisation, demonoolisation and regulatory reform in major network industries, such as electricity, gas, railroads and telecommunications. These initiatives have created a business environment conducive to cometition. It must, however, be recognised that some arts of network industries still have natural monooly roerties. In articular the rovision of the network itself involves high fixed sunk costs and is best left to a single firm subjected to regulation. Claudia Kriehn, ifo Institute for Economic Research, Branch Dresden, Einsteinstr. 3, D Dresden, Germany. Phone: , Fax: , kriehn@ifo.de.

2 2 To regulate a natural monooly, many regulators have alied rice-ca regulation as roosed by Littlechild (1983). It allows the regulated firm to increase its overall level of ricesbythereviousyear srateofinflation in the economy, as measured by the Retail Price Index, moderated by a ercentage that reflects the real cost reduction which the regulator exects. The firm can retain any further cost savings in form of extra rofit. Without any doubt, rice-ca regulation has a number of desired roerties including that it can easily be imlemented at least comared to other regulatory regimes such as rate-of-return regulation, and that the regulated firm minimises costs. However, a major drawback of rice-ca regulation is its ossible adverse effect on infrastructure uality. Booz Allen & Hamilton (1999), for examle, state that uality deterioration is a major concern in rice-ca regulation for Railtrack, which is the monoolistic rovider of the railway network in the UK. In a situation where the unregulated monoolist sets uality below the social otimal level, uality deterioration under rice-ca regulation imlies that the maximum welfare is not obtainable. The roblem is well known in the theory of monooly regulation. White (1972), Sence (1975), and Sheshinski (1976) show that a rice regulation can reduce the uality and can even result in a welfare loss. Recently, Kidokoro (2002) concludes that rice-ca regulation increases investment related uality, but decreases effort related uality. As both rice and uality enter the decision of the monoolist, the obvious solution to the roblem of uality deterioration is to combine rice-ca with minimum uality regulation. It can easily be shown that under this regime the monoolist still minimises costs and that any rice-uality combination including those which maximise welfare is achievable. But measuring uality is a difficult task, so that the successful imlementation of minimum uality regulation involves high administrative costs. The object of this aer is to develo an alternative regulatory mechanism which has (aroximately) the same effects of rice, uality and welfare than the combination of rice-ca and uality regulation but involves less administrative costs. For this urose we introduce a modelling framework which includes the following major characteristics of a network industry. First, total costs consist of substantial fixed costs but almost negligible variable costs; to simlify, we assume that variable costs are eual to zero. Second, the monoolist can choose among various uality levels, but the ossibility of uality discrimination is excluded. A uality level refers to certain hysical roerties of the network, and it is lausible to assume that they are uniform for all network users. Third, fixed costs are endogenous; they

3 3 increase with uality and thus shae the rofit maximising behaviour of the monoolist. Within this framework we find that minimum uality regulation can be relaced by an average cost ricing rule. If the monoolist is regulated such that he is allowed to earn a strictly ositive rofit, we show that a rice regulation which allows the regulated firm a roortional mark u on the average costs thisregulationisalsoknownasreturn-on cost regulation has the same effects on rice, uality and welfare as a minimum uality regulation. Return-on-cost regulation further leads arbritrarily close to the solution under minimum uality standards when the rofit is restricted to zero. If it is the aim of the regulator to achieve the second-best social otimum in which welfare is maximised under the restriction that the rofit is nonnegative, the use of the second-best rice as rice ca, together with a maximum allowable return on cost set slightly above zero leads arbritrarily close to the second-best outcome. That means, uality can be regulated without restricting the level of uality and minimum uality regulation can be relaced by return-on-cost regulation to achieve aroximately the social otimal outcome. Under both regimes the monoolist has no incentive to use an inefficient inut combination or to waste inuts. The cost advantage of the return-on-cost regulation is obvious: the imlementation reuires only information on reorted total costs and rofit. The aer is organised as follows. In section 2 we resent the modelling framework and comare the second-best otimum with the monooly solution. The monoolist s rofit maximising decision always deviates from the second-best otimum, which rovides the justification for regulation. In section 3 we study the effects of rice-ca, mimum uality, and return-on-cost regulation. We use the results to comare the effects of a combined rice-ca and uality regulation with those of a combination of rice-ca and return-on-cost ricing in section 4. We conclude in section 5. 2 Second-Best Otimum and Monooly Euilibrium Cost and Demand Conditions Two decision variables enter our model: rice, anduality. Quality is treated as a scale index, with larger values corresonding to higher uality. Total costs are given by C() with C 0 > 0 and C 00 > 0. (1)

4 4 The monoolist chooses and such that the rofit Π(, ) =R(, ) C(). (2) is maximised, where R(, ) =D(, ) defines the revenue function, with demand D(, ). We assume that each consumer buys zero or one units of the good, and has a maximum willingness to ay for one unit given by V (θ,)=θg() with g(0) = 0, g 0 > 0, g (3) The arameter θ > 0 measures the intensity of a network user s taste for uality and is distributed with a density function f(θ) > 0 over the intervall θ, θ. The distribution function F (θ) is assumed to be twice continuously differentiable and strictly increasing. Let N be the total number of otential network users. An individuum buys one unit if the rice is below or eual to his willingness to ay, that is if V (θ,) or, euivalently, /g() θ. For any 0 and >0, totaldemandcan then be written as D(, ) =N ³ 1 F ( b θ), (4) where b θ = /g() denotes the taste arameter of the individuals who are just willing to buy one unit. Partial derivation of (4) leads to D < 0 and D > 0. 1 A network user s benefit is given by the difference of willingness to ay and rice, and consumer surlus is defined as the sum of the individual benefits, CS(, ) =N Z θ b θ (θg() ) f(θ)dθ, (5) with CS < 0 and CS > 0. SocialwelfareW is defined as the sum of consumer surlus and rofit. Second-Best Otimum Socialwelfareisgivenby W (, ) = CS(, )+Π(, ) = Ng() Z θ b θ θf(θ)dθ C(), (6) 1 Describingthedemandinthiswayiscommoninthefield of roduct differentiation (see e.g. Mussa and Rosen (1978), and Besanko and Donnenfeld (1988)) and has been used in network economics as well (see e.g. Economides (1999), and Lambertini and Orsini (2000)).

5 5 Maximisation of W with resect to and yields a rice eual to marginal costs, which means =0. Thus, in the first-best solution, the monoolist makes losses eual to total costs. If the aim of regulation is to achieve the first-best solution, it follows that the network rovider has to be subsidised. But in ractice, regulators are usually restricted to subsidy free regulatory mechanisms. Therefore the second-best otimum, defined as the solution of max W (, ) s.t. Π(, ) 0, (7), is often used as reference oint in the theory of otimal regulation. Let (, ) be the solution to roblem (7). From the first-order conditions we obtain Π =0.Wealsohave Π > 0 and Π < 0. (8) Starting from the second-best oint the monoolist could increase rofit by increasing the rice and lowering the uality. We follow Sheshinski (1976: 129) and assume that the secondorder conditons hold. It can be shown that it is sufficient to assume W < 0, which imlies strict concavity of W as well as strict concavity of Π. Monooly Euilibrium Without regulation, the monoolist maximises rofit as given by (2). The first-order conditions are Π M =0and Π M =0, (9) where M, M denotes the solution to this roblem. (9) is necessary and sufficient, given W < 0 since this imlies strict concavity of the rofit function (see above). The comarison of (8) and (9) leads to the conclusion that the monooly solution deviates from the second-best otimum, W (, ) >W M ( M, M ), (10) which is analysed more detailed in the following subsection. Comarison of second-best otimum and monooly euilibrium The second-best otimum and the monooly euilibrium can be deicted in a (, )-diagram. The sloe of an iso-w -curve is d = W, (11) d W =const W

6 6 and the sloe of the zero-rofit curveis d = Π. (12) d Π=0 Π By (12), it can be seen that the curve Π =0is vertical in oints with Π =0, and horizontal where Π =0holds. ThesloeofthecurveΠ =0is d d Π =0 = Π Π, (13) and the sloe of the curve Π =0is d d Π =0 = Π Π. (14) From W > 0 it can be derived that Π < 0, Π < 0, Π > 0, andπ Π Π 2 > 0. Hence, both exressions are ositive and the curve Π =0is steeer than the curve Π =0. It can also be shown that the curve Π =0and the iso-demand curve D = D M are identical (see Kriehn (2004)). Conseuently, for any oint left to the curve Π =0,demandishigher than in the monooly solution. The rofit is maximised where both curves intersect. In the second-best otimum, the iso-w curve is tangent to the curve Π =0and thus we have Π Π = W W = CS CS > 0. (15) The sloe of both curves is ositive, so that the oint (, ) must be in the increasing and concave section of the curve Π =0. Therefore (, ) lies on a higher iso-demand curve than the monooly solution, or euivalently, D(, ) >D( M, M ). (16) Comaring both oints in figure 1, we see that M maybelargerorsmallerthan,and M maybelargerorsmallerthan. From Result 1 it follows that we have either < M and M, (17) or R M and > M. (18) Figure 1 shows a situation in which the monooly rice is higher and the monooly uality is lower comared to the second-best values. 2 2 W.l.o.g., we assume that the curves Π =0, Π =0, and the iso-demand curves are linear.

7 7 W* D=D * П =0, D=D M W M * П =0 M П=0 * M Figure 1: Monooly vs. Second-Best Solution 3 Price-Ca, Minimum Quality, and Return-on-Cost Regulation Price-Ca Regulation (PCR) The PCR constraint is given by with < M. (19) As it is well known, under this regime the monoolist minimises costs and chooses = (see e.g. Kriehn (2004)). Therefore, the first-order conditions for the constrained rofit maximum can be written as Π PC where PC, PC denotes the solution. > 0 and Π PC =0, (20) Since the sloe of the curve Π =0is ositive and the oint PC, PC is on this curve, PCR always leads to a decrease of uality and an increase of outut. The second-best outcomecannotbeachieved,becausethiswouldreuireπ PC < 0. The effects of PCR are illustrated in figure 2. The monoolist chooses PC = and sets PC such that an iso-rofit curve is tangent to the vertical rice restriction. We draw a situation in which PCR leads to a welfare increase, which is not always the case. 3 3 A counterexamle is given in Kriehn (2003).

8 8 D = D PC W PC W M П =0 M PC П PC П=0 PC M Figure 2: Effects of Price-Ca Regulation Minimum Quality Regulation (MQR) Under MQR the constraint is given by with > M. (21) Let MQ, MQ be the solution to the rofit maximisation roblem under MQS. Similar to PCR, it is easy to show that the monoolist does not waste ressources, chooses MQ = and sets such that Π MQ ( MQ,)=0. (22) Since the sloe of the curve Π =0is ositive and the oint MQ, MQ lies on this curve, MQR increases both rice and uality such that demand is eual to D M. From Π MQ =0 we know, that the second-best otimum cannot be achieved. In figure 3, we illustrate a MQR that increases welfare. The monoolist chooses the oint MQ, MQ on the curve Π =0where an iso-rofit-curve tangents the horizontal uality restriction.

9 9 П =0 W MQ W M MQ П =0 M П MQ П=0 M MQ Figure 3: Effects of Minimum Quality Regulation Return-on-Cost Regulation (ROCR) We consider a rice regulation, that allows the monoolist to mark u rice over average costs by the roortion δ, that is (1 + δ)c() with δ > 0. (23) (23) can be written as R(, ) δ with δ > 0, (24) C() which means that the roortional average cost ricing rule is euivalent to return-on-cost regulation (ROCR) which restricts the roortion of costs the firm is allowed to retain as rofit. 4 From Train (1991, ch. 2) we know that it deends on the sign of the marginal revenue whether the monoolist has an incentive to waste ressources or not under ROCR. Our model can be seen as a secial case of Train s aroach in which the marginal revenue is eual to zero in the monooly solution and remains zero under regulation (see below). For this case it is known that the monoolist does not waste. Conseuently, the monoolist minimises costs. This together with a binding restriction allows us to write the rofit maximisation 4 The roortional average cost ricing rule is also formally euivalent to the return-on-sales regulation which allows the monoolist to earn a certain amount of rofit on each unit of revenue, that is R(,) C() R(,) ζ. Setting δ = 1 1 ζ 1 in (24) leads to the return-on-sales restriction.

10 10 roblem as max Π(, ) s.t.π(, ) =δc(). (25), From the first-order conditions we obtain Π ROC =0, which means that ROCR has no effect on total demand. It also follows that the curve ROC = δ tangents the curve Π =0in the solution oint ROC, ROC. Comarative statics yield and d ROC dδ d ROC = 1 H δcroc C ROC0 Π ROC < 0 (26) = 1 dδ H δcroc C ROC0 Π ROC < 0, (27) where H is the bordered Hessian matrix. A stronger regulation leads to an increase of both rice and uality such that total demand remains constant. Again, with Π =0we can exclude that welfare is eual to W. The effects of ROCR are illustrated in figure 4. The sloe of an iso-roc curve is given by d = CΠ d ROC=const CΠ ΠC, (28) 0 and is thus eual to zero where the curve intersects the curve Π =0. Conseuently, in ROC, ROC the curve ROC = δ tangents the curve Π = Π ROC. П =0 ACP П =0 M W ACP W M П=0 ROC=δ П= П ACP M ACP Figure 4: Effects of Return-on-Cost Regulation If we comare figures 3 and 4, it is obvious that the effects of MQR and ROCR are identical as long as the rofit is strictly ositive. Both regulations result in a oint on the

11 11 curve Π =0in the northeast of the monooly solution. Any oint achieved by MQR can also be achieved by ROCR, excet the intersection oint of the curves Π =0and Π =0. But by lowering δ toward zero the regulator can induce the monoolist to choose an outcome arbitrarily close to the intersection oint. Thus we obtain Proosition 1 For all with Π MQ () > 0 there exists an δ > 0 such that W ROC (δ) =W MQ (). (29a) If is given such that Π MQ () =0,wehave lim δ 0 W ROC (δ) =W MQ (). (29b) 4 Combined Regulations Price-Ca lus Minimum Quality Regulation If the regulator restricts only one decision variable (rice or uality), the second-best otimum cannot be achieved, as it was shown in the last section. It is intuitively clear that the simultaneous restriction of both rice and uality by the second-best values leads to the second-best outcome, which is illustrated in the following figure. The monoolist is allowed to choose the second-best oint or any oint in the grey area including the borders. As the second-best oint is the only oint in which the rofit is nonnegative, the monoolist sets the second-best rice and uality. W MPC =W* П =0 * П =0 M П=0 * M Figure 5: Effects of PC lus MQ Regulation

12 12 Though the combination of PC and MQ regulation is otimal, its imlementation might involve high administrative costs, because it reuires the estimation of the current and otimal levels of uality which usually is a difficult task. Proosition 1 asserts that PCR could be combined with ROCR instead of MQR such that welfare is arbritarily close to the second-best welfare. The effects of the PC-ROC regulation are analysed in the following. Price-Ca lus Return-on-Cost Regulation If PCR and ROCR are combined such that both regulations are binding, the rofit maximising roblem can be written as 5 max Π(, ) s.t. δc() Π(, ) =0. (30) Let POC, POC be the solution oint to roblem (30). From the first-order conditions to this roblem it follows that the monoolist chooses one of the two intersection oints of the vertical rice restriction = and the ROC = δ-curve. As we have Π POC = δc( POC ) in both oints, the monoolist chooses the oint with the higher uality. The roblem is deicted in figure 6. П =0 ROC POC M A П =0 ROC=δ П= П ROC П=0 B POC M ROC Figure 6: EffectsofPClusROCRegulation The oints in the grey area including the border are allowed. From the first-order conditions we know that the monoolist chooses either oint A or oint B. As Π A = δc( A ) > 5 It is shown in Kriehn (2004), that the monoolist chooses the maximum allowable values of rice and return on cost and does not waste ressources.

13 13 δc( B )=Π B, the monoolist chooses oint A in which we have Π POC as in the second-best solution. > 0 and Π POC < 0 As the monoolist chooses a oint such that the rice euals the rice ca and Π POC < 0 holds, we suggest that a oint arbitrarily close to the second-best oint can be achieved by setting = and lowering δ toward zero. In fact, this can easily be shown. Comarative statics yield d POC C POC =, (31) dδ Π POC δc POC0 and from the first-order conditions we know that the denominator is negative. Hence, d POC < 0. For a given rice restriction a stronger ROCR increases uality. As a conseuence, if the regulator sets = and lowers δ toward zero, POC increases. But dδ uality cannot reach a level above, and thus costs are below C( ), which means that the roduct δc( POC (, δ)) converges to zero, and also does the rofit Π POC = δc( POC (, δ)). Hence, the oint ( POC, POC ) converges to the oint (, ) on the zero-rofit curve and we obtain: Proosition 2 With = the following holds: The result is illustrated in figure 7. lim δ 0 W POC (,(, δ)) = W. (32) With the second-best rice as rice ca and a maximum allowable ROC close to zero, welfare is slightly below the second-best welfare. By reducing δ further toward zero, welfare could be increased further. W* W POC П =0 * POC П =0 ROC=δ П=0 POC =* Figure 7: PC lus ROC Regulation and Second-Best Solution

14 14 With the combined PC-ROC regulation we have develoed a regulatory mechanism that leads arbitrarily close to the second-best solution but is easier to imlement than the combination of PC and MQ regulation, because it only reuires information on total costs and rofit and no information on the comlex asects of uality. 5 Conclusion Against the background of the subotimality of rice-ca regulation and the difficult imlementation of a combination of rice-ca and minimum uality regulation the aim of this aer was to develo an alternative regulatory mechanism that leads (aroximately) to the second-best outcome and involves relatively low administrative costs. In a modelling framework which adeuately describes the behaviour of market articiants in network industries we found that both minimum uality and return-on-cost regulation have identical effects on rice, uality and welfare as long as the allowed rofit is strictly ositive and have aroximately the same effects if the regulator wishes the rofit to be eual to zero. In our oinion, return-on-cost regulation is an attractive alternative to minimum uality regulation in terms of administrative costs, so that the first should be referred byregulatorsto the latter and a rice-ca lus return-on-cost regulation should be alied instead of a rice-ca lus minimum uality regulation. References Besanko, D. and S. Donnenfeld (1988): Rate of Return Regulation and Product Variety, Journal of Public Economics 36: Booz Allan & Hamilton (1999): Railtrack s Performance in the Control Period : Final Reort. London, UK: Booz Allan & Hamilton Ltd. Economides, N. (1999): Quality Choice and Vertical Integration, International Journal of Industrial Organization 17: Kidokoro, Y. (2002). The Effects of Regulatory Reform on Quality, Journal of the Jaanese and International Economics 16:

15 15 Kriehn, C. (2003): Network Provision, Quality, and Price-Ca Regulation, Discussion Paer No Bochum, Germany: Ruhr-University Bochum. Kriehn, C. (2004): Price, Quality and ROR Regulation in Network Industries, mimeo. Dresden, Germany: ifo Institute for Economic Research. Lambertini, L. and R. Orsini (2000): Monooly, Quality, and Network Externalities, Discussion Paer. Bologna, Italy: University of Bologna. Littlechild, S. C. (1983): Regulation of British Telecommunications Profitability, Reort to the Secretary of State, February London, UK: Deartment of Industry. Mussa, M. and S. Rosen (1978): Monooly and Product Quality, Journal of Economic Theory 18: Sheshinski, E. (1976): Price, Quality and Quantity Regulation in Monooly Situations, Economica 43: Sence, A. M. (1975): Monooly, Quality and Regulation, Bell Journal of Economics 6: Train, K. E. (1991): Otimal Regulation. Cambridge, USA and London, UK: MIT Press. White, L. J. (1972): Quality Variation When Prices Are Regulated, Bell Journal of Economics and Management Science 1972: