How Market Regulation A¤ects Network and Service Quality in Related Markets Justus Haucap
Gordon J. Kleiny
University of Erlangen-Nuremberg
ZEW Mannheim
April 2008 Preliminary Version. Please do not cite!
Abstract This paper analyzes the e¤ect regulation of network infrastructure has on complementary service markets. In particular, the paper proposes a theoretical model that explains the interactions of regulation in a network sector with investement in network infrastructure and investements in complementary markets. As we will show access regulation negatively a¤ects the network operator’s incentives to invest into network quality, but this may be more than compensated by the increase in investment incentives for providers of complementary services so that access regulation may actually increase the perceived overall quality level for …nal consumers. JEL Classi…cation: D43, L13, L51.
University of Erlangen-Nuremberg, Department of Economics, Lange Gasse 20, D-90403 Nuremberg, Germany; e-mail:
[email protected]. y Centre for European Economic Research (ZEW), Research Group Information and Communication Technologies, L7,1 D-68161 Mannheim, Germany; e-mail:
[email protected].
1
1
Introduction
How to regulate access prices in network industries has been one of the major themes of debate in academic circles and among policy makers and regulators alike over the last 10 to 20 years. While most of the academic literature has initially focused on pricing issues in a static context (see, e.g., Armstrong, 2002; La¤ont and Tirole, 1998), more recent contributions have also analyzed the relationship between access regulation and investment (see, e.g., Gans and King, 2004; Foros, 2004; Kotakorpi, 2006; Vareda, 2007).1 This literature shows that stricter access price regulation usually has a negative impact on investment, even though Vareda (2007) …nds that the negative relationship between access price level and investment level only holds for quality enhancing investments, but not for cost-reducing investments. Common to all of these papers is that the focus is on the incumbent’s investment incentives, i.e. the investment incentives faced by existing infrastructure owners. Another stream of literature has argued that tighter access regulation encourages competitors to invest into complementary infrastructure in order to slowly build up an alternative network. This idea, which has gained enormous support among regulators and policy makers in telecommunications markets, has been coined the "ladder of investment" (see Cave & Vogelsang, 2003; Cave, 2006). This idea is related to our paper which focuses on investment incentives for …rms who o¤er complementary services to the regulated infrastructure. An important example may be the (potential) regulation of broadband access markets which also a¤ects investment incentives for …rms providing Internet services. Similarly, in railway markets the investment incentives for train operating companies (into rolling stock and services) are also in‡uenced by the regulation of access to the rail network (i.e., the tracks). The same holds for airlines whose investment incentives are at least partially determined by airport regulation (slot allocation, landing fees, etc.). As is obvious now, our focus is related, but still di¤erent from the "ladder of investment" perspective, as we analyze strictly complementary services which cannot substitute the original infrastructure, but rather have to rely on access to this infrastructure. Empirically the relationship between access price regulation and investment is also unclear. While a study by London Economics (2006) on behalf of the European Commission has tried to establish a positive link between regulation and investment, most other empirical studies come to ambiguous …ndings.2 Unfortunately though, the empirical studies available rely on aggregate data so that they cannot distinguish between investment undertaken by incumbent operators and entrants’investment. Relatedly, there is no distinction between investment into complementary assets versus investment into alternative infrastructures. as we will argue in this paper, this is a crucial distinction for empirical research, as the e¤ects of access regulation on investment are fundamentally di¤erent for network operators and for …rms that provide complementary services. 1 For 2 For
an overview also see the contributions in Dewenter and Haucap (2006). a survey see Andersson, Bohlin & Garrone (2004).
2
As we will show access regulation, for example of broadband Internet access, negatively a¤ects the network operator’s incentives to invest into network quality, but this may be more than compensated by the increase in investment incentives for providers of complementary services, to stay in the example of Internet services, so that access regulation may actually increase the perceived overall quality level for …nal consumers. In addition, we relax the assumptions regarding the strict complementary relationship. This allows to expand the framework from complementary between network access and network services to complementarity between goods and services on a network that exhibit complementarity on each other. This is scenario is important for a lot of cases occurring on Internet service markets. For instance, online webstores and price searching websites or online music stores and digital music players are relevant cases. 3 Regulation is not usual in these markets. However, due to the importance of network e¤ects, market concentration (e.g. companies as amazon.com, ebay.com etc. dominate their market segments) might rise the possibility of antitrust enforcement. We show in an adjustment of the model that the same as in the previous section holds: Antitrust action negatively a¤ects the regulated providers incentives to invest into quality, but this may be more than compensated by the increase in investment incentives for providers of complementary services such that antitrust enforcement may actually increase the perceived overall quality level for …nal consumers. The remainder of this paper is organized as follows: Section 2 introduces and analyses the model when goods are perfect complements. In section 3 we then analyze a case with partial complements before we draw out conclusions and summarize our main results in section 4.
2
Investment Incentives with Perfect Complementarity
This section analyzes a setup where two markets are in a complementary relationship. To consume one good of market A another good has to be purchased of market S. The focus of analysis is on the qualities provided under a regulatory regime. The section describes …rst the model setup, second the outcome considering three benchmarks and third a comparison of the outcome.
2.1
Model Setup
Let us consider an industry with two related markets, where one speci…c product is provided in each market, but the two products are jointly consumed. Examples are airline tickets and airport fees or Internet access and Internet services. 3 Utility is generated by use of online webstores as well as by the use of price searching websites as they inform people to enhance their purchasing decisions. On the one hand the more people use online webstores, the utility of price searching websites increase. On the other hand the more people have information about o¤ers of webstores the more probable is their purchase there.
3
That means, the speci…c products are complements, which makes each markets outcome dependent on the other markets’outcome. We assume that both markets are monopolized, i.e. the two markets are served by two monopolists. Moreover, we allow one market to be regulated. The two markets outcome is determined in a sequential game. We allow for three di¤erent setups of this game. Let us denote the two markets by i = A, S, where market S is supposed to be a retail good or service xS . We assume that each unit of service xS requires exactly one unit of an input xA (so that xA = xS ), which is provided in market A. This input may be Internet or airport access. Both …rms charge endcustomers for consumption pi . For simplicity we assume that the two companies do not face any marginal costs and that …xed costs are already sunk. Moreover, both companies can invest into a quality upgrade qi of their good or service. Investment incurs costs of 12 ki qi2 : Consumer intend to buy retail goods or services. To do so they must consume the input jointly with the retail good. The input itself does not generate utility. However, its quality upgrade has an e¤ect on consumers’ utility. Consumers inverse demand is given by pS = aS + qS + qA xS pA 4 , where aS > 0 is the basic utility of the service taken into account the present quality of the two inputs. The variables qS and qA describe a quality upgrade in the respective markets. To allow for a di¤erent valuation of the quality upgrade the quality upgrade by the input market is multiplied by 2 [0; 2]. Moreover, customers inverse demand is decreasing in quantity xS and price incurred for the input pA . The outcome is determined in a sequential game. We allow for three di¤erent variations regarding the timing and the players involved. First only the two monopoly companies interact. In the second and third variation we introduce a welfare maximizing regulator. The three relevant setups are: 1. Firms freely set their output without regulatory intervention. 2. The regulator sets a price for market A and can commit to it during the game. 3. The regulator sets a price for market A, but cannot commit to it during the game. First there is the case without any regulation. This consists of two stages. The only players are the two monopoly companies. In the …rst stage …rms decide about quality investment and in the second they decide about prices. In games 2 and 3 we introduce a regulator as a third player, who can decide about companies A price. There are two relevant setups for regulation. First there is the commitment case, which means that a regulator can commit to its price setting behavior before investment occurs and then during all the game. In this 4 Utility is given by a representative consumer model according to Bowely (1924), which is widely used in Industrial Economics, for instant Singh and Vives (1984): U = (aS + qS + 1 2 qA ) xS (pA + pS )xS x 2 S
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case, there are three stages. 1) The regulator sets the price 2) Firms in both markets invest 3) The …rm in the unregulated market sets its price. The second possibility is that the regulator cannot commit to its price setting behavior and changes its initial decision after investment occurred. The game will change as follows. 1) Firms in both markets invest 2) The …rm in the unregulated market invests. 3) The regulator sets the price in the regulated market. Importantly, the regulator attempts to maximize the overall welfare which is the sum of the pro…ts and consumer surplus. W =
1
+
2
+ CS
(1)
The pro…t functions of the …rms are
2.2 2.2.1
S
= pS xS
1 kS qS2 2
(2)
A
= pA xS
1 2 kA qA 2
(3)
Outcomes of the Model Firms Determine Output Freely Without Regulation
The outcome without regulation is determined in a two stage game as pointed out before. In each stage the …rms decide independently about their decision variables for each necessary input and retail good. The game is solved by backward induction. The second stage is solved by maximizing pro…ts for the two …rms to derive the best response functions and the according equilibrium prices: 1 (aS + qS + qA ) (4) 3 The two …rms anticipate the resulting equilibrium prices and take them into account when they chose their pro…t-maximizing quality upgrades, which yields the best response functions in qualities and the according equilibrium qualities: pA = p S =
qA = qS =
2 aS kS 9kA kS 2kA 2
2k S
2aS kA 2kA 2
2k S
9kA kS
Assumption 1: We assume that (kA + quality upgrades non-negative.
5
2
(5) (6)
kS )=(kA kS ) < 9=2 holds so that
2.2.2
Regulation with Commitment
Corollary 1 If a regulator imposes a price on one …rm and can commit to it during the game the quality level in this market will decrease, but the quality level in the unregulated market increases if the quality spillover is su¢ ciently low. The solution of the game follows the three stages pointed out above. It is solved by backward induction to identify subgame perfect equilibria. In the third stage, the unregulated company optimizes its pro…t function, equation (2), regarding prices, which yields its best response function regarding : pS =
1 (aS + qS 2
pA + q A )
(7)
In the second stage both …rms anticipate this best response function and take it into account when they choose their pro…t maximizing quality. The resulting equilibrium qualities are: 1 pA 2 kA
(8)
2kA (aS pA ) + 2 pA 2kA (2kS 1)
(9)
qA =
qS =
Assumption 2: To ensure that the quality upgrade qS is non-negative than zero we assume that kS > 12 Assumption 2 implies that costs for investment in quality are su¢ ciently high. We also assume that the numerator is positive. Both quality levels are depend on the level of the regulated price pA . It is easy to see that the in‡uence of pA on quality is linear and positive (equation 9). The quality of the unregulated market is a¤ected twofold in the price (equation 9). It is negative in the investment cost factor for market A; kA and positive in the quality spillover : To analyze the in‡uence of a price regulation, which decreases the price in the market for the essential input, both equations (8 & 9) are di¤erentiated regarding pA . The derivative shows the e¤ects price changes have on quality in the regulated market. @qA 1 = @pA 2 kA
6
(10)
As both factors and kA are only de…ned for positive values, the derivation of market A’s quality is positive. This means that a decreasing price decreases the quality provided in this market. The derivative of quality in market S with respect to pA is: 1 2 2kA @qS = @pA 2kA 2kS 1
(11)
As the denominator is always positive as long as kS > 12 ; which is assured by assumption 2 the sign of equation (12) depends on the numerator, which changes for: p (12) 7 2kA If the quality spillover is su¢ ciently large and the costs for investment in the regulated market are su¢ ciently small than the impact of regulation in the regulated market leads to a quality reduction in the service market. If, however, the e¤ect is not su¢ ciently large this leads to an increase in the unregulated markets quality. Now, the question arises how this a¤ects the overall quality? Of course, a measurement of overall quality is di¢ cult as it is a comparison of di¤erent things. To measure the overall quality we use a concept of perceived quality, which is derived from the consumers’ utility function. This concept should re‡ect the quality parameters as they a¤ect the consumers utility function. Corollary 2 If a regulator imposes a price on one …rm and can commit to it during the game the quality level in the regulated market will decrease, but it increases the overall quality level in both markets if investment costs for quality in the unregulated market and the quality spillover are su¢ ciently small. The overall quality is de…ned as: Qges = qA + qS
(13)
It is the sum of the qualities, equation (8 & 9) corrected for the consumer’s valuation of the access quality . The derivative of the user’s quality with respect to pA is analyzed regarding its sign: kS 2 kA ?0 kA (2kS 1)
(14)
The derivation of equation (14) is smaller than zero if kS > 21 , which is ensured by assumption 2, and kS 2 kA < 0; which is 2 < kA =kS . Therefore
7
the switching level of the overall derivations’sign is determined by the ratio of both investment cost factors kA and kS . r kA @Qges > ! >0 (15) kS @pA r kA @Qges < ! 0 s2 )
(28)
Taking into account the variable de…nitions, numerator and denominator of the derivation shown in equation (29) are negative for the relevant values. The overall term is therefore positive. This implies that a price decrease forced by regulation leads to a decrease in markets A quality. To analyze the relationship in the second market, we derive qS given in equation (27) to pA . 2 + 2 s2 s + 2AkA s + 2 @qS = @pA 2AkA (2AkS + 1)
(29)
The derivation indicates that regulation can have a negative as well as a positive impact on the provided quality of the unregulated market S. The sign of the term is de…ned by numerator and denominator. The numerator ( 2 + 2 s+2 +2 s2 1 kA s s3 ) can be either positive or negative. Hence kA is not too large, it is positive for all relevant values. The denominator is positive q for quantity spillover lower than s < 1 2k12 and negative afterwards. If the costs for quality in market A; kA are not too high, the derivation is negative which means that regulation in market A increases investment in market S. The same question as in the previous setup arises: How does regulation a¤ect the overall investment? Corollary 4 If a regulator can commit to a price in the regulated market there are solutions where the level of the quality perceived by the consumer can increase through regulation. It is necessary that the quantity spillover is high enough to reach this solutions.
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To analyze the impact of regulation on the overall quality, we use the perceived quality, which is quality in market A; equation (27), multiplied by its in‡uence in the demand functions and quality in market S, equation (28): Qreg = (1 + )q1reg + q2reg
(30)
To focus on the importance of the spill-over e¤ects we assume aA = 5 and aS = 5 as a representative value. Moreover, we normalize the cost factors to kA = kS = 1: Deriving the quality perceived Qreg to the regulated price pA gives the impact of a price change. Derivation of Qreg to pA is: 3s2 @ Qreg = @pA
4
2s + 2s3 2s 2 + 2s3 4s2 2s + 4s3 2
5s
2s2
2
2
(31)
The sign is de…ned by numerator q and denominator. The denominator 2kA (1+
s)(1 + 2kS (s2
1)) > 0 if s >
1 2 .The
numerator (2 + s( s + 2(1 + s) + ) +
2(1 + s)(1 + )( 2 + s s ))) is always negative7 . Therefore, it is possible that if the quantity spillover is high enough, regulation leads to an increase in the perceived quality. Solving the welfare maximizing regulators’stage yields the welfare maximizing access price: reg preg 0, which The welfare optimized price is: preg A A = pA (s; ). It is pA means it is bounded by the monopoly price and price equal to marginal costs. Pricing at marginal costs is the smallest price possible that enables, under the assumption of no …xed costs, the regulated company to stay in the market. 2
3.2.3
Regulation without Commitment
As in section 2.2.3 we analyze the case of a regulator that is not able to commit to an announced policy. Solution is achieved by backward induction to …nd subgame perfect Nash equilibria. A regulator that cannot commit to a regulatory policy will solve a welfare optimization without taking into account investments. As this needs pricing at marginal costs, which are zero in our model, prices are also pA = 0. Although the incumbent cannot make any pro…t, we assume that he just stays in the market. However, this no pro…t condition leads to zero investments in quality qA = 0. The optimization of equation (2) …rst regarding prices and then anticipating the price to optimize equation (2) regarding quality yields: pS =
1 1 (aS + qS ) + saA 2 4
(32)
2aS + aA s kS (4 s2 ) 2
(33)
qS = 7 Result
derives by numerical analysis.
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3.3
Comparison of Quality Levels
The distribution of the price level is equal as in 2.3. The unregulated price is the highest, followed by the price level resulting from regulation with a regulator that is able to commit himself. The lowest price is the one of a regulator that cannot commit to a price level. pA_N R > pA_RC > pA_RN C The comparison of the quality level has to be divided into the quality in market A and in market S as well as the overall perceived quality Qreg . Equal to setup 2.3 quality in market A is the highest if there is no regulation. It is followed by the regulation under commitment case and the regulation without commitment case: qA_N R > qA_RC > qA_RN C To interpret the quality of the unregulated market S, one has to consider that if the quantity spillover is high enough and the costs for investment in quality are not too high, a price regulation on market A always increases the quality in the unregulated market S. As the zero price is the limit, this means that a welfare maximizing price somewhere above zero (in the commitment case) results in a quality level, which is higher than in the unregulated case, but lower than in the no commitment case. To analyze the investment level of the no commitment case we can assume that a regulator can at least commit to optimize prices to marginal costs, which are in our setup zero. In this case commitment to zero price is equivalent to no commitment. qS_N R < qS_RC < qS_RN C The same order is true for the perceived quality. QN R < QRC < QRN C If the spillover is not high enough and the costs for investment are too high than this relationship turns out to be the opposite.
4
Conclusion and Discussion.
Our paper contributes to the existing literature on regulation regarding incentives for investments in quality by introducing a model analyzing the e¤ects on complementary markets. We show that taking into account complementary service markets it can be that regulation of access markets can have a positive e¤ect on the quality provided on the unregulated service market. However, this e¤ect depends on the spillover constellation. The quality on the access market is always negatively a¤ected by regulation. Considering both e¤ects, it is possible that this positive e¤ect on the unregulated market outweights the negative e¤ect on regulated market regarding the quality perceived by the consumer. These e¤ects depend on the constellation of spillover e¤ects. Applied to broadband Internet access, it can be that regulation of a broadband Internet access market has a positive e¤ect on the overall perceived quality of Internet service consumption, which consists of the quality of both: Internet access and Internet services.
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Moreover, relaxing the assumptions on strict complementarity we can show that the observed e¤ects are also relevant in a setup of partial complementarities and therefore on a large range of other scenarios. The results can be summarized in the corollaries we were able to proof. First we can state for the case of perfect complementaries with regard to the …rst setup that if a regulator imposes a price on a market and can commit to it during the game the quality level in this market will decrease, but it might increase the quality level in the unregulated market if the quality spillover is not too high. As the second corollary states, If a regulator imposes a price on a market and can commit to it during the game the quality level in the regulated market will decrease, but it might increase the overall quality level in both markets if costs for quality investment in the unregulated market is not too high and the quality spillover is not too high. This results are comparable to those in the second setup. The third corollary says for the case of partial complementary relationship that if a regulator imposes a price on a market and can commit to it during the game the quality level in this market will decrease, but it might increase the quality level in the unregulated market if the quantity spillover is high enough and the investment costs for investment in the unregulated market is not too high. The fourth corollary shows in addition that if a regulator can commit to a price in the regulated market there are solutions where the level of the quality perceived by the consumer can increase through regulation. It is necessary that the quantity spillover is high enough to reach this solutions. Fifthly, as the comparisons of the output levels have shown the results of the four corollaries do not only hold for regulation of a regulator that can commit to a regulatory policy, but also for a regulator that cannot commit to a regulatory policy. Our results imply that regulatory and antitrust authorities should take complementarities between markets into account when analyzing the e¤ects of possible regulation or antitrust enforcement.
References [1] Andersson, E., E. Bohlin & P. Garrone (2004), Investment, Innovation and Telecommunication Regulation, IMIT Report prepared for the Swedish Communications Authority: Stockholm. [2] Armstrong, M. (2002), The Theory of Access Pricing and Interconnection, in Cave,M. S. Majumdar, I. Vogelsang (eds.) Handbook of Telecommunications Economics, Amsterdam, 295-384. [3] Cave (2006), Encouraging Infrastructure Competition via the Ladder of Investment, Telecommunications Policy 30, 223-237.
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[4] Cave, M. & I. Vogelsang (2003), How Access Pricing and Entry Interact, Telecommunications Policy 27, 717-727. [5] Dewenter R & J. Haucap (2006), Access Pricing: Theory & Practice, Amsterdam. [6] Gans, J. & S. King (2004), Access Holidays and the Timing of Infrastructure Investment, Economic Record 80, 89-100. [7] Bowley, A.L. (1924), The Mathematical Groundwork of Economics, Oxford. [8] Foros, O (2004), Strategic investments with Spillovers, vertical integration and foreclosure in the broadband access market, International Journal of Industrial Organization 22, 1-24. [9] Kotakorpi, K. (2006), Access price regulation , investment and entry in telecommunications, International Journal of Industrial Organization 24, 1013-1020. [10] La¤ont J., P. Rey & J. Tirole (1998), Network Competition: Overview on Non-Discriminatory Pricing, Rand Journal of Economics 29,1-37. [11] London Economics (2006), An Assessment of the Regulatory Framework for Electronic Communications Growth and Investment in the EU eCommunications Sector, Final Report to the Commission DG Information Society and Media. [12] Singh, N. & X. Vives (1984), Price and quantity competition in a di¤erentiated duopoly, Rand Journal of Economics 15, 546-554. [13] Vareda (2007), Unbundling and Incumbent Investment in Quality Upgrades and Cost Reduction, FEUNL Working Paper 2007.
Appendix Welfare maximizing price in the perfect complementary setup: We regulator is denoted to maximize welfare, which is the sum of consumer surplus (CS) and and overall pro…ts (producer surplus) de…ned as: W = CS +
A
+
S
Maximizing W regarding the price pA yields the …rst order condition: pA =
2 k 4kA S
3
2 2 2 4aS kA kS 6 2 aS kA kS +2 2 aS kA kS 4 k 2 +4k 2 k 2 + 2 k + 4 k 2 k k +8 A S 4 A S S A S
To simplify we choose kS = 1 which yields
pA =
4aS kA 2
2 kA 5kA 2 2
16
2k
2 A kS
To ensure that pA is larger ful…lled:
kA
0 the following condition must be
< 52 kA
Assumption i : The welfare maximizing price is non-negative and therefore condition kA < 2 < 25 kA holds In addition the second order condition must hold. Second derivation of the welfare function yields: d2 W dp2A
=
1 2 8kA
4
4
10
2
kA < 0
The price maximizes welfare if the above condition is below zero. Therefore, the condition 2 < 52 kA must hold, which is assured by assumption i. Welfare maximizing price in the partial complementary setup: A regulator is denoted to maximize welfare, which is the sum of consumer surplus (CS) and overall pro…ts (producer surplus) de…ned as: W = CS +
A
+
S
Maximizing W regarding the price pA yields the …rst order condition, which must be set to zero and solved to pA . The welfare maximizing price is therefore: p1 = 2 (A) k1 (D) a1 + (D) 4 + 3s2 s a1 (s + )a2 k2 2 (D) 4+s 3s a1 3(s + )a2 + 2 + (A) k22 4 (A) 2s (A) (sa1 + a2 ) k1 k12 1 + 4 + 3s2 k2 (1 + (A) k2 ) 2
+k1 (D) + 4
2
1 + s2 k2 (D)
(2 + s( s + ))2 1 + k2
2 (A) (A) (1 + s )k2
+ (A)
4 + (s )(3s + ) 4 + s2 6s 3 2 k2
It is assumed that the second order condition holds.
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