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Thisistoeertifythatthe dissertation entitled AN ECONOMIC ANALYSIS OF THE IMPACT OF ACCESS CHARGES ON COMPETITION IN THE INTEREXCHANGE TELECOMMUNICATIONS MARKET presentedby BLAINE CHARLES GILLES has been accepted towards fulfillment of the requirements for PH.D. degree in ECONOMICS Date W MSUI': an Afl'maiw Acfion/Equl Opportunity [m 0-1277! LACE IN RETURN BOX to remove this checkout from your record. or beiore date due. 10 AVOlD FlNES return on ATE DU E DATE ‘ DATE DUE D DUE ,/\_.__/ ,_r— / AN ECONOMIC ANALYSIS OF THE IMPACT OF ACCESS CHARGES ON COMPETITION IN THE INTEREXCHANGE TELECOMMUNICATIONS MARKET BY Blaine Charles Gilles A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 1992 Copyright by BLAINE CHARLES GILLES 1992 ABSTRACT AN ECONOMIC ANALYSIS OF THE IMPACT OF ACCESS CHARGES ON COMPETITION IN THE INTEREXCHANGE TELECOMMUNICATIONS MARKET BY Blaine Charles Gilles Access charges are payments made by interexchange carriers (IXCs), to local exchange carriers (LECs) for use of LEC facilities in originating and terminating toll calls. This dissertation finds that current distance-sensitive access rate levels and structures are discriminatory and yield an input cost advantage to AT&T relative to its competitors which is unrelated to the actual costs of providing access. A theoretical examination reveals incentives for both telecommunications firms and regulators to favor discriminatory access prices. It outlines problems posed by discriminatory prices in intermediate goods markets like the that for access. Discance-sensitive rates which significantly deviate from incremental costs are likely to induce distortions in network configuration and in the relative costs of interexchange carriers. To assess whether such problems exist in the current access price regime, distance-sensitive rates are compared with incremental costs. First, exchange level data on office locations, central office equipment, and access lines served are collected for all Michigan telephone exchanges and combined with location data on all interexchange carrier network nodes in Michigan to assess the relative transport distances involved in serving Michigan’s five largest IXCs. The data reveal that AT&T purchases significantly fewer miles of local access transport per call than any of its competitors, by virtue of its own more extensive network facilities. Cost data from Michigan Bell and traffic engineering methods are then utilized to examine the incremental costs of providing distance. For every type of access technology distance sensitive rates are found to significantly exceed incremental costs. AT&T, since it purchases fewer miles of transport per call, is the competitive beneficiary of such distance-sensitive rates. The current structure of the interexchange telecommunications industry, and the magnitude of this advantage, partially negate arguments which favor deregulation of the interexchange market on the grounds that entrants pose significant competitive threats to AT&T’s market dominance. The discussion concludes with recommendations for an access tariff regime which collects revenues without inducing competitive distortions. For Almira and Matthew ACKNOWLEDGMENTS This research would have proven impossible without the generous assistance of numerous individuals in business, government and academia. Tom Buechel and Rich Florence of Michigan Bell Telephone, in addition to assisting me in gathering cost and pricing data, endured numerous questions and additional requests for information as this research progressed. This work also benefited greatly from conversations with Joe Gillan of Gillan Associates, W. Page Montgomery of Economics and Technology Inc., Kim Horn of Williams Telecommunications Group, and James Sichter of United Telecommunications. I must also acknowledge the patience, insight, and assistance of my dissertation committee: Kenneth Boyer, Bruce Allen, Tom Muth, and Harry Trebing. To Dr. Trebing I owe a special debt of gratitude; the course I took from him sparked my interest in telecommunications regulation and his honesty, clarity and wisdom have been an inspiration throughout my graduate studies. Finally, I wish to thank my wife Almira and my parents for their support and encouragement. Without them this project would never have moved past Chapter 1. vi TABLE OF CONTENTS LIST OF TABLES .......................................... ix LIST OF FIGURES ......................................... X Chapter 1. INTRODUCTION..... ........ ....... ..... ...... ...... 1 Defining Access ................................ 1 The Study.... .................................. 22 Dissertation Format.. ..... . .................... 27 2. PRICING, COSTING AND TELECOMMUNICATIONS REGUMTIONOO0.0000000000000000.00.000.000.00.0. 3o Costing Problems ......... ... ..... . .......... ... 30 Pricing Problems........ ....................... 40 3. HISTORICAL DEVELOPMENT OF THE ACCESS CHARGE SYSTEM ...... . .................................. 45 Exchange Access.......... ..................... . 45 Separations and Settlements ....... . ........... . 48 Breakdown.. .................................... 53 Reformation .................................... 56 Summation ...................................... 62 4. PRICE DISCRIMINATION IN ACCESS MARKETS ...... ..... 64 Defining Price Discrimination .............. .... 65 Application to the Access Market.... ........... 70 Discriminatory Access Charges and Market Performance...... ......... . .................. 79 vi A Simple Model of Network Configuration........ 87 The Effect of Access Price Discrimination on IXC Competition.............................. 93 Input Price Differences and Strategic Behavior. 101 Conclusions and Hypotheses..................... 107 5. ANALYSIS OF RELATIVE DISTANCE SENSITIVE IXC COSTS 109 Overview of the Empirical Study................ 109 IntrOduction O O O O O O O O O O O O O I O O O O O ..... O O O O O O O O O I O 1 1 1 Data.......OOOOOOOOOOOOOOOI... ........ 00...... 112 MethOdOIOgy O O O O O O O O O O O O O O O O O O O O ...... O O O O O O O O O 1 1 4 Results....................................... 117 6. DISTANCE-SENSITIVE ACCESS COSTS................. 134 Technology ................................... 134 Average Incremental Costs...... ...... ......... 138 Data.......................... ...... .......... 139 Cost Estimation............................... 140 7. HYPOTHESIS TESTING: COMPARING RATES WITH LRAIC.. 147 IntrOductionOOOOOOOO0.0... .0... 00...... I. I... O 147 Comparison of Rates and Incremental Costs ..... 149 Competitive Impact.. ............... ........... 150 8. CONCLUSIONSOOOOIOOOO.........OOOOOOOOOOOOOOOO0.0 163 Competition and Access Price Discrimination... 163 The Impact of Current Access Charges.......... 166 The Equal Charge Per Unit of Traffic Rule..... 169 The Impact of Rate Averaging... ..... ..... ..... 170 The Impact of Liberalizing Access Pricing ..... 173 Recommendations........ ..... .................. 176 vii APPENDIX0000000000000 ...... 00000000 ......... 0.00000000 178 BIBLIOGRAPHY00000000000000000 00000 00000000000000.0000. 190 viii Table 5.1. LIST OF TABLES SPECIALACCESS CHMGES0000000000000000000000 WEIGHTED AVERAGE TRANSPORT DISTANCE......... WEIGHTED AVERAGE TRANSPORT DISTANCE......... COMPARISON OF SWITCHED ACCESS TRANSPORT CHARGES00000000000000000000000000000000000 SPECIAL ACCESS DISTANCE SENSITIVE TRANSPORT CHARGES................ .......... A DEMONSTRATION OF ERLANG B......... ........ ESTIMATED MONTHLY MINUTES OF USE BY ACCESS TYPE00000000000000.0.0.0000 00000000 ESTIMATES OF PER MINUTE SPECIAL ACCESS TRANSPORT CHARGES0000000000000000000000000 AVERAGE PER-MINUTE DISTANCE-SENSITIVE COSTS.0000000000000000.000.0000.... 0000000 DISTANCE-SENSITIVE INCREMENTAL COST ANALYSIS000.00000000000000.000000000 000000 MBT’S AVERAGE INCREMENTAL TRANSPORT COSTS... COMPARISON OF MBT’S RATES AND INCREMENTAL COSTS0000000000000.00000000000000000000000 MONETARY ADVANTAGE OF AT&T'S EXTENSIVE NETWORK00...0.000000000000000000000000.000 IMPACT OF SETTING PRICE EQUAL TO DS-l INCREMENTAL COST.................. ......... ix 115 119 119 122 124 128 130 133 133 141 144 151 153 156 LIST OF FIGURES A STYLIZED INTEREXCHANGE NETWORK.... ........ ACCESS ARRANGEMENTS..... ........... ... ...... BYPASS TYPES.00000000000000.0000000. 00000000 LOCATION MODEL OF NETWORK CONFIGURATION ..... MAP OF MICHIGAN LATAS.... 85 89 121 CHAPTER 1 INTRODUCTION Access charges are payments made by interexchange carriers (IXCs), like AT&T, MCI and U.S. Sprint, to local exchange carriers (LECs) for use of LEC facilities in originating and terminating toll callsF.‘This dissertation tests whether current access tariffs, in particular their distance-sensitive rate components, yield undue cost advantages to AT&T over its rivals. It then examines the effect such advantages might have on interexchange competition and social welfare. Acc Access is the physical connection between the facilities of end users and nodes of the interexchange network at each end of a telephone call. However, this physical description belies the complex role played access and access charges in post-divestiture telecommunications. Access is more than a wire between two points, it links two markets-—loca1 exchange and interexchange--subject to differing regulatory philosophies, and conflicting paradigms 1These should be distinguished from ‘local access’ charges paid by end users for connection to the phone network. 1 2 of behavior. Access is generally sold by local exchange monopolies to competing interexchange carriers; its sale provides local exchange firms with a key source of revenues; through its purchase interexchange carriers incur a significant portion of their costs. Firms obtaining access on favorable terms will enjoy higher profits and greater longevity than their high-cost rivals. Delineating the impact of access rate design on interexchange competition requires a comprehensive examination of the multidimensional role of access charges. The section below is therefore divided into three parts, exploring the technical, regulatory and competitive dimensions of access as determinants of interexchange firm behavior. The Technical Dimension: Access and Network Architecture The physical provision of access, at the macro level, involves (a) outside plant: the copper and optical fiber cables, conduit, and ductwork facilities needed to provide trunking between the LEC office and the IXC; and (b) central office equipment: switching, termination, and transmission facilities needed to provide interconnection between these trunks. On a micro level, there are innumerable permutations of equipment type and network configuration which can be used to provide the access link. Ih§_M§§IQ_L§!§l Figure 1.1 presents a stylized depiction of the ‘public network', which is comprised of the linked facilities of private end-users, LECs, and IXCs. Private end-users, in addition to consuming network services provided by outside vendors, may construct their own private network facilities and link them to the network facilities of LECs and IXCs. LECs provide access connections between end users and interexchange carriers, along with most other telecommunications services which originate and terminate within a geographic zone called a Local Access and Transport Area (LATA). LATAs were established during AT&T’s divestiture to define and separate the monopoly markets of LECs from the long-distance market where entry and competition are allowed. The final category consists of the interexchange carriers. IXCs provide long-distance and other services between LATAs, however, they are generally forbidden from transporting intraLATA traffic. The most expensive portion of the network consists of ‘local loops’ which are dedicated connections linking LEC end offices directly with end users, and are used to transport a combination of toll, local, and data traffic. Since direct private connections between end users and IXC POPs can be used only in conjunction with toll services, they are prohibitively expensive for all but the largest end users. thus, rather than undertaking the expense FIGURE 1.1 A STYLIZED INTEREXCHANGE NETWORK LATA BOUNDARY IXC ; IXC LEC ; ............ CENTRAL POP g POP OFFICE LEGEND EU: End User Local Loop: Access: Interexchange Network: A g 5 of connecting the toll network directly to end users, interexchange firms generally purchase access between end users and IXC network nodes, called Points of Presence (POPS), from LECs. To understand the pattern of network design, consider the path travelled by a typical toll call between two end users in different LATAs. The call is initiated and terminated using end-user owned or leased "customer premise equipment"(CPE): the telephone, computer or PBX2 used to send and receive signals over the network. When a call is placed, the CPE originating the call alerts the local exchange central office (CD) that a toll call is about to be made and signals the destination of the call. The connection between the end user and the C0 is usually established via an analog signal carried over a twisted-pair copper circuit. However, larger end-users may utilize high capacity trunks to connect their PBX and computer facilities to the CO. Inside the CO, this connection--the local 100p-- terminates in a "channel bank" which digitizes the analog signal for switching and transport. The local switch then routes this signal through a trunk? to the designated 2PBX:"Private Branch Exchange": a privately owned switch used to interconnect privately-owned lines within a private network or to connect.a private network to the Public Switched Network. 3In telecommunications parlance, a "line" connects and end-user to the network, while a "trunk" is a connection between two switches within the network. 6 IXC’s‘ nearest POP. The signal is multiplexed, enabling'the simultaneous transport of numerous signals over a single circuit. An IXC POP either contains switching equipment or routes the signal to the IXC's nearest switch. POP facilities collect billing information from the signal, concentrate the signal using a multiplexer (MUX) and route the signal over the IXC network to the POP nearest the call’s destination. The process is then reversed, with the multiplexed signal decoded, switched, reconverted to analog, and transported via the local facilities of the recipient's LEC to the recipient’s premises. ° 5 ement Access connections between end-users and IXC POPS are provided through three types of arrangements, distinguished by both network architecture and tariff design: common switched access, dedicated switched access, and special access. These arrangements are detailed below and the architecture associated with them is depicted in Figure 1.2. Switched Access Switched access is the predominant means of connecting residential and small business end users to the interexchange network. Under this arrangement, local loops are used to initiate calls, which are switched by the LEC’s ‘Designated by the end user. 7 C0 facilities to the end-user’s interexchange vendor. There are two varieties of switched access: dedicated and common. Dedicated switched access involves direct, IXC-specific connections linking LEC CO facilities and IXC POPS. When an end-user dials a toll call, the LEC CO switch routes the Signal to the IXC POP via an IXC-specific dedicated connection. Although this connection may pass through other LEC CO facilities (as in Figure 1.2), it is not switched outside of the initial end office. At the time of divestiture AT&T had dedicated links with almost all LEC end offices and, although access arrangements have been altered subsequent to divestiture, it remains the predominant purchaser of dedicated switched access. Common switched access involves the combined trunking of toll calls destined for a number of IXCS from local end offices to a ‘tandem switch'. The tandem switch provides a common interface point for a number of IXCS and routes toll calls to the IXC POP designated by the end user. This arrangement was motivated by the equal access provisions of the Modification of Final Judgement? (MFJ) which set forth the conditions of AT&T'S divestiture. The MFJ mandates that all IXCS be provided with access functionally equivalent to that of AT&T. However, establishing dedicated facilities 5 't t e le a l r , 552 F.Supp. 131 (D.D.C. 1982), aff’d sup ngm, Maryland v. United §§§§§§, 406 U.S. 1001 (1983). 8 FIGURE 1.2 ACCESS ARRANGEMENTS USER OFFICE OFFICE \. A CHANNEL TANDEM BANK SWITCH / I IXC POP IXC POP AQQES§_IXEE§ A: Switched Access (Common) B: Special Access C: Switched Access (Dedicated) 9 from each end office to the nearest POP of every IXC would have proven prohibitively expensive. Transporting access for a number of IXCs along a single route allows the LEC to achieve economies of traffic density between end offices and the tandem, and is thus a mechanism to reduce the costs associated with equal access. Special Access Special access involves the use of dedicated, end-user specific facilities (lines, trunks, terminating equipment, etc.) to connect end users with their IXC. If special access is purchased from an LEC--the most common arrangement--the transport facilities used are nearly identical to those for switched access. However, although the call may pass through LEC CO facilities, technically it is not switched. A network channel is dedicated to the provision of access for a particular end user. When that end user picks up the phone he or she is connected automatically with the interexchange carrier’s switch, receives dial tone from the IXC switch, and places the call through the IXC switch. The LEC does not monitor the call, provide answer supervision, or collect any billing information; it merely transports the signal between the end user and the interexchange carrier. In addition to providing an alternative to switched access for connections between end users and IXCS, special access also provides the final link between the access tandem and the IXC POP. In technical terms, special access is quite similar to 10 dedicated switched access; the facilities used and costs incurred, per mile of transport, are therefore nearly I identical. Both provide a direct, unmonitored, unswitched channel. However, in the case of dedicated switched access this channel terminates at the local end office while special access terminates at the end-user’s premises. The key difference between the two services has nothing to do with technology. Unlike switched access, special access may be provided by vendors other than the LEC‘, allowing the end user to ‘bypass’ the local exchange and avoid the payment of access charges altogether. The potential for bypass has been studied extensively by the FCC, and is cited by the BOCs as their primary impetus for desiring more flexible access pricing arrangements (See Chapter 4). Bypass also underscores the changes in firm behavior induced by the structural and regulatory changes embodied in AT&T’s divestiture arrangements. The Regulatory Dimension II 3 J E E E . . In the post-divestiture regulatory scheme access forms the border separating the "old" regulated local monopoly and the "new" competitive interexchange environment. Consistent with this dichotemized telecommunications network, access 6Some states are now allowing alternative providers to provide forms of switched access as well. At the time of this writing such practices are rare, though increasing in number. 11 pricing is driven by two often competing forces: the promotion of effective interexchange competition, and the pursuit of traditional equity objectives. Access charges comprise a key element in the MFJ scheme to promote a competitive interexchange telecommunications market. In its antitrust prosection of AT&T, the Justice Department contended that internal revenue transfers within the old Bell System could be used to cross-subsidize competitive services with revenues from local exchange monopoly services. Since nearly all interexchange calls, including those of Other Common Carriers (OCCs)’, pass through local exchange facilities, AT&T’s control over these facilities led to a conflict of interest. AT&T was the principle input provider to its competitors and could not be expected to provide these rivals with access arrangements or terms equivalent to those it provided itself. The access charge system permits the arm’s-length financial separation of IXCs from LECs, allowing the division of telecommunications services between monopoly and competition, and alleviating concern over cross- subsidization and anti-competitive business practices. If pursuing effective interexchange competition were the sole focus of telecommunications regulation, then formulating access tariffs would be a rather uncomplicated 7Other Common Carriers (OCCs) is a term used to denote interexchange carriers other than AT&T. 12 issue. However, regulators utilize access charge policy to attain equity objectives as well. Paramount among these are the pursuit of universal service through low end-user charges and nationwide toll rate averaging to ensure that long-distance service in outlying areas remains affordable. The old Bell System attained these objectives through internal transfers of revenues from the interstate services to intrastate services, especially local exchange access. Divestiture, in cutting off revenue flows which could diminish interexchange competition, also cut off the internal flow of revenue needed to keep local rates low and ensure geographically averaged toll rates. The present access charge system replaces internal revenue transfers with a roughly equivalent set of explicit payments, allowing the continuation of pre-divestiture rate structures and levels in the post-divestiture environment. The current system attempts to strike a balance between the goals of equity and interexchange competition. This investigation focuses on the affect which these factors play in determining competitive behavior in the interexchange market. - ° ' e te tr The principle focus of this investigation is on distance-sensitive transport charges for switched and special access. (For a description of the other access. tariff elements see Appendix 1). Distance-sensitive rates 13 for switched access are billed on a per-minute-of—use, per- mile basis, and must be identical for dedicated and common switched transport must be identical under the terms of the Modification of Final Judgement. The ‘Equal Charge Per Unit of Traffic Rule' embodied in the MFJ specifies that: until September 1, 1991, the charges for delivery or receipt of traffic of the same type between end offices and facilities of interexchange carriers within an exchange area, or within reasonable subzones of an exchange area, shall be equal per unit of traffic delivered or received, for all interexchange carriers... ' At the time of this writing, the Equal Charge Rule has been extended for an unspecified time period while the FCC reconsiders access pricing policy. In addition to the Equal Charge Rule, the MFJ also mandates that any IXC POP within five miles of an AT&T Class 4 switch (ie., an AT&T POP) be subject to access mileage charges identical to those applied to traffic emanating from, and terminating at, the AT&T switch. These stipulations were intended to start OCCs off on a common competitive footing with AT&T. Immediately following divestiture, AT&T had facilities collocated in many LEC offices and had inherited dedicated connections to most end offices from the old Bell System, i.e., it inherited a system with very low local transport costs. Special access rates also display distance-sensitivity but, since no usage information is collected, purchasers face a monthly mileage premium. Special access rates vary 8MFJ, Appendix B at B.3. 14 widely from state to state, and the FCC has no specific rules regarding how individual types of special access should be costed and priced. It stipulates only that all access of a specific type be charged a uniform rate within a particular regulatory jurisdiction. There are at least seven varieties of special access, distinguished primarily by signaling speed and optional features. The most important for this investigation are voice grade special access, DS-l access and 05-3 access, since they are substitutes for switched access. Voice grade special access connections are purchased by the circuit with charges based on distance and on transmission features such as line conditioning, signaling and bridging. In addition, there are nonrecurring charges for establishing the dedicated circuit. These non-recurring charges assist the firm in recovering the substantial fixed costs of setting up the necessary facilities and also serve as a disincentive for end-users to migrate between access providers. DS-l access is similar except that it involves the use of multiplexing and higher signaling speeds. Each DS-l channel operates at 1.544 Mbps, also known as the 08-1 rate, and is capable of simultaneously providing 24 voice circuits. On a per-circuit basis, DS-l distance-sensitive rates are discounted below those for individual voice and data circuits. DS-3 channels utilize upgraded central office 15 electronics to provide signaling at 44.736 Mbps allowing simultaneous transmission of 672 voice signals. Per-circuit rates are below those for DS-l and voice-grade service. The Competitive Dimension AT&T's divestiture in 1984 was motivated by the belief that entry into the interexchange (long distance) market would promote technological and service innovation, provide incentives for cost minimization, and result in lower prices than could be achieved by the pre-divestiture constellation of market structure and regulatory regime. This argument was extended to the contention that intra-market rivalry, when sufficiently developed, would obviate the need for continuing a system of complicated and costly regulation9. However, successful long-term entry into the interexchange market, and rivalry sufficient to eliminate the need for continued regulation, necessitates that entrants be able to achieve costs similar to AT&T’s. This cannot be accomplished without regard for access tariffs which comprise the largest single category of IXC costs. In 1989, AT&T paid LECs nearly $15 billion in total access charges. This represents 48% of its total operating expenses and 43% of its total operating revenues (FCC, 1990). The “At the time of this writing, AT&T contends that the interstate interexchange marketplace has already achieved this level of competition and ought to be deregulated. The FCC, - having loosened is control over AT&T between 1989 and 1991 with the implementation of price caps, is considering relaxing its controls still further in CC Docket 90-132. 16 access expenses of MCI, U.S. Sprint, and other facilities- based IXCs comprise similar portions of their respective costs (Ernst & Whinney, 1987). In addition, access charges provide a vast source of revenues for the Bell Operating Companies (BOCs), which are the largest local exchange service providers. In 1989, they earned over 30% of their revenues selling access to interexchange carriers (FCC, 1990). Both the level and structure of access rates are important determinants of competitive behavior in the interexchange market. If distance-sensitive rate levels are inordinately high then only those IXCs with the most extensive network facilities will survive; the cost associated with the relatively long transport distances to smaller IXCS will diminish their ability to successfully compete with larger carriers. Rate structure is the relationship between rates for different types of access customers and different types of access services. If the structure of rates results in input costs for certain carriers which are low relative to those paid by their rivals, then competition will be affected. Rate levels and structures may also induce changes in the physical configuration of the network. If different access arrangements are subject to different rates, IXCs may be motivated to alter the type of access they purchase. If access rates are high relative to the IXC's costs of 17 expanding its own network, then the IXC will benefit by substituting its own transport for that provided by the LEC. W The largest interexchange carriers have the most geographically dispersed networks with the greatest number of network nodes, serving the greatest number of locations. IXCs with relatively small networks make up for this disadvantage in two ways: (a) they lease interexchange facilities from other carriers for the completion of calls to certain locations, and (b) they purchase a relatively great amount of access transport service from LECs, as compared with their larger rivals. Thus, changes in distance-sensitive rates entail relatively greater impacts on the costs of smaller IXCs: they purchase more miles of access per unit of traffic than their larger rivals. Ra u e The structure of rates may also significantly impact competitive behavior and market performance, especially if the structure is such that some carriers are charged lower rates for access than others. Access rate structure is influenced by three often contradictory motivations. First, there is a desire on the part of the FCC and smaller IXCs to promote rates which are roughly equivalent for all carriers, ensuring the ability of AT&T’s rivals to successfully compete. Second, as noted above, the FCC also desires the 18 continuation of toll rate averaging and has enforced rates consistent with that objective. Finally, LECs view access charges as a primary revenue source, and seek to retain their markets and maximize the revenues which accrue from the sale of access services. As Chapter 4 will demonstrate, the latter two motivations are likely to generate a rate structure typified by ‘price discrimination': different IXCs are charged different net prices above incremental cost for access services. Toll rate averaging by AT&T and its rivals, the Other Common Carriers (OCCs), is obtained in part through the averaging of access rates such that the mileage charge incorporated into switched access tariffs is invariant with respect to traffic density, geographic route, or end-user characteristics. In March of 1991, the FCC rejected LEC attempts to charge route and customer specific access rates (FCC, 1991). This means that, on a per-mile basis, access charges are identical in rural and urban areas, thus assisting IXCs in maintaining uniform toll charges between these areas. To the extent that the costs of providing access vary with traffic density, these uniform rates will be discriminatory. LEC interests are also served by a discriminatory access pricing regime. From the LEC perspective, access prices are an important revenue source; however, unlike the old Bell system, end-users have the option of avoiding 19 payments to the LEC altogether. Although the terms of the MFJ preclude IXCs from "bypassing" the local network and connecting directly with end-users, the end-users suffer no such restrictions. Equipment vendors market complete private networks with direct connections to IXC POPs. If LECs charge excessive rates for origination, termination and local transport of toll calls, large end-users will find it advantageous to bypass the local network, cutting off the LEC from a major source of revenues. Therefore, one can expect LECs to push for access tariffs which minimize the potential for bypass. The LECs have repeatedly petitioned the FCC for more flexibility in access pricing”, and seek revocation of the ‘equal charge per unit of traffic rule’. Chapter 4 explicitly demonstrates that the optimal tariff scheme for an LEC attempting to maximize revenues while limiting bypass is discriminatory. Moreover, due to economies of traffic volume in the switching and transport of calls, uniform, averaged, access rates are discriminatory as well. A ' ra IXCs seek the network architecture which minimizes their input costs, including those associated with access. A discriminatory rate structure or high rate levels may induce IXCs to alter their access arrangements or change the mSee comments of NYNEX, Ameritech, and Bellsouth in CC Docket 78 -72, op cit. 20 configuration of their own networks in order to obtain lower access costs. Both of these impacts are versions of bypass. Bypass has been classified into two types: service bypass and facility bypass (GAO, 1986). Service bypass involves the use of special access (private line) service, sold by the LEC, to connect the end-users’ premises directly to an IXC POP. For large end-users this avoids usage sensitive payment for access. However, in a strict sense, this might be termed "service migration"; the revenues from access provision still accrue to the LEC. Facility bypass involves private connections between end users and IXC POPs which avoid LEC facilities altogether. Such connections represent an even more drastic curtailment of LEC revenues. One usually thinks of facility bypass in terms of end users using private facilities to connect with an IXC POP. However, the per-mile charge associated with access, designed to recover a share of traffic sensitive costs, may alter IXC network configuration. If access payments are excessively sensitive to distance, the IXC may attempt to reduce these payments by building more POPs and placing them closer to end users and LEC central offices. The rate structure may also encourage service bypass. An IXC need not construct a major switching center in order to establish a POP. Rather, IXCs can install facilities known as ‘closet POPs'(IXC network access points with no 21 switching capability) by installing termination equipment at a location and then procuring special access transport services to connect this POP with the rest of its transport facilities. If there is a wide differential between the distance sensitive rates for switched and special access, the construction of closet POPs will be encouraged as a method of replacing switched access transport with cheaper special access transport. If termination, switching, and transport are characterized by pervasive economies of traffic density-- presumably the reason that they are regulated as monopoly services--OCC's attempts at lowering transport costs by expanding the number of network nodes will entail a wasteful duplication of services and will raise the social costs of providing network services. It will certainly increase OCC costs. Furthermore, especially in less populous regions, there may not be sufficient traffic to justify the expense of further expanding the network so that additional OCCs have POPs close to the end user. Potential competition in these regions would be sharply curtailed. Moreover, as noted above, LECs attempts at curtailing bypass are likely to involve discriminatory rates which favor larger IXCs, since they are the firms which pose the greater threat of bypass. These motivations and their effects receive further treatment in Chapter 4. 22 Ih§_SLBQ¥ The scope of this study is limited to the distance- sensitive component of access charges; a complete analysis of all access charge components is simply too large a task for a study of this size. The distance-sensitive component is interesting since IXCs may partially or completely avoid by altering their behavior. Therefore, changes in distance- sensitive access rate levels and structure alter the decisionmaking of interexchange firms. Moreover, although the study limits itself to discussing distance-sensitive charges, the intuition regarding LEC and regulatory motivations in formulating access tariffs is generic to all usage sensitive rate elements. Even the somewhat narrow topic of discussion here gives rise to considerable debate over the efficacy of the current access tariff scheme. In addition to questioning the exact formulation of access tariffs, this debate seriously questions the feasibility of fostering effective interexchange competition given the prevailing technological, economic, and political conditions prevailing in the telecommunications. Conflicts Over Access Pricing This study is motivated primarily by the rather quiet but essential debate over the current access charge regime. Although often ignored in debates over the competitiveness of the interexchange market, access charges are a fundamental determinant of competition in post-divestiture 23 telecommunications. Access charges provide a linkage between two contradictory worlds. They are an attempt to simultaneously maintain the traditional goals espoused by regulators--universal service, nation-wide averaged toll rates, and fulfillment of LEC revenue requirements--while at the same time fostering the conditions needed for a competitive long-distance market. On one side of this linkage lies regulated monopoly: on the other side lies a market subject to entry, rivalry, and ever-diminishing regulation. Conflicts between the objectives of the inhabitants of these worlds manifest themselves in the debate over access charges. Most important is the incompatibility between LECs' access pricing objectives and the goals of establishing an effectively competitive interexchange market in which successful entry by smaller IXCs is not precluded. As Chapter 4 demonstrates clearly, those tariffs which act most effectively to eliminate bypass and maximize the revenues obtained from selling access, may also seriously constrain the ability of smaller IXCs to compete: larger IXCs posing greater bypass threats will be charged lower access rates. Conflicts between regulatory equity goals and the objective of interexchange competition must also be considered. Although the interexchange market is subject to entry and rivalry, regulators have attempted to retain many of the pricing characteristics of the old regulated 24 monopoly. Geographic toll rate averaging, a principle equity consideration before divestiture, is still pursued through the averaging of access rates: distance and usage sensitive charges are the same for all cells regardless of the actual facilities used to transport the call. To the extent that access costs vary from location to location, averaged rates are discriminatory. The study below examines whether this type of discrimination, as realized in the structure of access rates, also confers a cost advantage on larger IXCs. Another example of this type of rate averaging is the Equal Charge Per Unit of Traffic Rule. The rule is intended to ensure that all IXCs are able to compete on an equal competitive footing. However, as earlier, the FCC is considering changes in this rule. In fact, its Part 69 costing rules already mandate separate rates and costing procedures for dedicated and common access. Until now, however, these rules have been overridden by the terms of the MFJ. Smaller IXCs have expressed grave concern that potential changes in access tariffs or cancellation of the Equal Charge Rule, could seriously undermine their ability to successfully compete in the future (MCI, 1990; Comptel, 1990). They contend that common and dedicated switched access have very similar costs: expiration of the Equal Charge Rule will simply allow LECs a more effective mechanism for discrimination between large carriers (the 25 purchasers of dedicated switched access) and smaller carriers (which purchase disproportionately large amounts of switched access). Some of AT&T’s rivals also claim that current rates yield unfair advantage to AT&T by virtue of their "excessive sensitivity" to distance. Gillan (1990) investigates the cost advantage due to network size in a study commissioned by Comptel, a consortium of small IXCs. This study appears to show that AT&T has a significant cost advantage over its rivals by virtue of its more far-reaching network. However, although this study is geographically comprehensive, encompassing the 48 contiguous states, it suffers several limitations. First, it did not include all IXC network nodes and made a number of sweeping assumptions about the configuration of interexchange facilities; therefore, the study may not accurately assess AT&T’s distance-sensitive rate advantage. Second, the study includes no cost estimates for the production of access. Thus, the contention that distance-sensitive rates are excessive cannot be supported with the evidence provided in the study. AT&T may pay less than its rivals per minute of access purchased; however, one must also consider the cost of maintaining AT&T’s larger network to determine if the study results are actually indicative of lower input costs. In fact, AT&T countered these arguments by claiming that its 26 access expenses actually exceed those of its rivals“. Despite these limitations, Gillan provides one of the few empirical analyses related to the discussion of access pricing. Moreover, the Gillan study highlights the disparate impact of changes in access rate levels on smaller IXCs. Research Questions To examine the efficacy of the FCC's access charge policy concerning distance-sensitive access rates and its impact on interexchange competition, the economic basis for these contentions needs to be established and tested. This dissertation will therefore focus on two primary research questions: 1. Do different IXC’s pay different distance-sensitive rates for access, and if so, what is the degree of price dispersion? 2. Are distance-sensitive access charges discriminatory, and if so, what are the consequences of this discrimination for competition and efficiency in the interstate interexchange market for telecommunications? The study undertaken here will also shed light on two ancillary questions, though it does not test hypotheses concerning them directly: 3. Does the structure of AT&T's network, in combination with its dominant market share, imply that AT&T will be the lowest cost provider by virtue of lower access costs, even if access tariffs are adjusted to non- discriminatory levels? 4. What is the likely impact of an expiration of the Equal Charge Per Unit of Traffic Rule or other “See "Reply Comments of the American. Telephone and Telegraph Company, CC Docket No. 90-132, September 18, 1990. 27 liberalization of access pricing on interexchange competition and social welfare? 5. Is it possible to collect access revenues in a manner which is less distortionary and promotes greater levels of competition? The remainder of this thesis is devoted to answering these questions and exploring potential dilemmas and conflicts which arise when market participants and regulators espouse goals which are often incompatible. The scope of the study is limited to the distance-sensitive rates and costs of access provision. While this is not a complete picture, the issues raised are relevant to all access charge elements, as are the theoretical and empirical conclusions drawn from the examination. '0 at Chapters 2 and 3 provide background on the economic, historical, institutional and technological aspects of access provision. Chapter 2 is devoted to the economics of pricing and costing network services in a regulated monopoly. It provides a basic overview of economic problems inherent in efficiently pricing telecommunications services as well as addressing the motivations of regulators. Chapter 3 draws upon this development of economic theory to explore the history and development of the current access charge system. Chapter 4 lays the theoretical groundwork necessary for assessing the empirical investigation which follows by investigating the competitive impact of access tariffs 28 schedules which do not result in similar access costs for all interexchange carriers. It first outlines several economic and institutional motivations for pursuing a discriminatory access pricing structure, and uses economic theory to explain why discriminatory prices are a likely outcome in the access market. The second section assesses the impact of discriminatory prices on interexchange firm behavior and competition. First, a simple location model is developed to explore the potential impact of distance sensitive tariffs on network configuration when tariffs differ significantly from incremental costs. Secondly, a definition of price discrimination and its theoretical application to access charges is provided. This analysis reiterates the motivation for regulators and telecommunications firms are likely to pursue a discriminatory access pricing regimes and establishes the potential detriment of this practice in the context of Cournot oligopoly. Finally, a game theoretic analysis of oligopoly behavior under conditions of asymmetric input costs briefly examines the impact of input price discrimination on the strategic interaction of interexchange firms. Chapters 5, 6 and 7 empirically test the first two research questions described above. Chapter 5 provides an empirical analysis of relative access costs of AT&T and its rivals using highly disaggregated data for the state of 29 Michigan. It finds that AT&T enjoys lower access charges by virtue of its greater market share and more extensive network. Chapter 6 utilizes cost data provided by Michigan Bell and United Telecommunications to conduct an engineering study of distance-sensitive access costs. Chapter 7 compares the costs and rate structures delineated in Chapters 5 and 6 in order to test two hypotheses: first, that access charges are discriminatory: and second, that the pattern of access prices yields a competitive advantage to large IXCs which are not due to differences in the costs of providing access. Chapter 8 provides the conclusions of the study, as well as recommendations for future changes in the structure of interexchange access charges. CHAPTER 2 PRICING, COSTING AND TELECOMMUNICATIONS REGULATION The debates surrounding access charges, and virtually all other services provided by the telecommunications network, center on assigning the costs of the network to specific services and establishing rates based-~in some manner--on these cost assignments. This chapter examines the economic problems of pricing and costing within a general network setting. The background materials provided here underscore the chief economic problems underlying the government's attempt at establishing access charge plans conducive to interexchange competition and the public policy dilemmas posed by the division of the telecommunications network into monopoly and competitive sectors. In addition, the cost and pricing concepts described here are used extensively in subsequent chapters, both to describe the development of the current system, and in the theoretical and empirical analysis which follows in Chapters 5 through 7. W Virtually all public utilities provide a number of services, or serve different types of customers, through the 30 31 common facilities of a network. This is true of gas pipelines, electric utilities, and water works as well as telecommunications firms. Although establishing the costs associated with operating the network as a whole is a straightforward accounting exercise, a single network may cross over geographic and legal boundaries, passing through several regulatory jurisdictions, providing a wide spectrum of services to various types of customers. Regulation requires some division or attribution of costs and revenues to specific services within specific jurisdictions, a process which is rarely straightforward. The costs of a network can be grouped into two categories: directly assignable costs and common costs. Directly assignable costs, are costs associated with the production of a particular good or service for which one can establish a direct causal link between production of the service and the cost incurred. A production process displays common costs if two or more distinct outputs share production capacity and the relative utilization of that capacity between the outputs is variable (Kahn, 1971). Most network services are produced in this manner. For example, assume a central office telephone switch provides basic local service (POTSn) and Centrex13 12POTS: plain old telephone service. 1:‘Centrex is a service provided by local exchange carriers to businesses, government agencies, universities and other institutions requiring special intra-institution network 32 switching, and is capable of simultaneously handling 10,000 calls. The proportion of the switch’s capacity utilized by POTS and Centrex may vary greatly with fluctuations in demand for these services. At 8:00 A.M. the switch may handle 1000 POTS calls and 9000 Centrex calls, while at 8:00 P.M. it may handle 2000 POTS calls and no Centrex calls at all.“ One method of apportioning the common costs in this example is by "relative use" of the switch. However, relative use could be measured by access lines served, minutes of use per day, minutes of use during the peak period of the day, or by the revenues accruing to the local exchange firm from each service. These are all, in some sense, measures of the relative use of the switch by POTS and Centrex; however, they yield quite different apportionments of the common costs of the switch. Such ambiguities have led to a long debate over costing methodology and pricing of network services, dating to arguments between Pigou (1913) and Taussig (1913). Sichler (1928) was the first to characterize telephone service as a case of common costs, referring to the production of residential and business services over the same local telephone network. These common cost capabilities. It uses some of the switching and transport capabilities of the public network, to provide the customer with the functionality of a private network. “See Sharkey (1982) for further discussion. 33 characteristics prevail in virtually all services produced by the telecommunications network, unless facilities are dedicated to the production of specific services. Costing Methodologies Where costs are directly assignable there is usually little difficulty in ascertaining them and ascribing them to specific services. However, the prevalence of common costs in telecommunications supply, and the direct bearing of cost estimation upon regulatory proceedings, have made costing methodology a contentious issue. Three basic methodologies, all given to a wide range of variation, have been developed: fully distributed costs (FDC), marginal and incremental costs, and stand-alone costs. Fully distributed costs for specific services are obtained by separating services into categories and assigning a portion of total common costs and overheads to each category (Braeutigam, 1980). The discussion in Chapter 3, which describes the historical development of the access charge system, indicates that changes in service categories, or even relatively small changes in the cost allocation scheme, can trigger large revenue shifts between categories of service and regulatory jurisdictions. The fully distributed costs of a particular unit of service are averages derived from the total costs of the particular category to which that service is assigned. However, as the discussion above indicated, such assignments 34 are necessarily arbitrary . Hence, FDC does not establish causal relationships between those services produced and the costs incurred in their production. For rate-making purposes, an attempt has been made to distinguish between the fully distributed costs of common plant which can be allocated on the basis of relative use15 and the costs of dedicated facilities, namely local loops and the termination equipment in the CO, which are dedicated to particular end users and do not vary with the use of the network. Common-use plant costs are, in the parlance of telecommunications, "traffic sensitive" (TS) costs, while costs associated with dedicated facilities are "non-traffic sensitive" (NTS). One should note the fallacy of associating TS and NTS with the economist’s fixed and variable cost terminology. Telecommunications is an extremely capital intensive undertaking and nearly all of the costs associated with it are fixed. TS and NTS merely distinguish the allocation method used to assign the costs, which may in turn effect the structure of tariffs designed to recover those costs. Even where FDC has been used as the basis for costing, rates have not always borne a close relationship to these measures. As Mitchell (1988, 2) notes: Although FDC costing has guided telephone rates, its 1“There is no strong economic justification for this method of allocating the costs of common plant either-- but at least it is straightforward. 35 formulas are not strictly adhered to for all products. In specific markets, regulators have encouraged telephone companies to charge rates exceeding FDC to guarantee a "contribution" that permits other rates-- particularly for local residential service---to be set below FDC. ‘ Despite these deficiencies FDC continues to provide the basis for most costing in the telecommunications industry. Its primary attributes are its relative simplicity and ease of calculation and the ability of regulators to clearly define procedures for its consistent measurement. The economic literature on public utility pricing emphasizes the inherent drawbacks of the FDC concept and the need to base prices upon marginal costs in order to achieve efficiency in the production and consumption of public utility services (Hotelling, 1938; Baumol and Bradford, 1970: Brown and Sibley 1986: Baumol, Koehn, and Willig, 1987: Wenders, 1987; Berg and Tschirhart 1988). Marginal cost is defined as the additional cost incurred when an additional increment of output is produced. However, in the context of network costing, marginal costs do not change smoothly with changes in output and depend primarily upon the utilization of existing capacity. When existing capacity is uncongested, the network displays marginal costs equal to per-unit operating costs. However, increases in capacity utilization during peak usage periods, or growth in usage over time will cause congestion and necessitate capacity expansion. The costs of this expansion mean that marginal cost will increase whenever congestion occurs and decrease 1'2 36 when it is alleviated. Such discontinuities are amplified by the "lumpiness" of network capacity. For example, if increases in telephone usage necessitate that an additional switching module be added to a digital switch, this added lump of capacity-~and its expense--do not add a one call or one minute increase in capacity. Rather, the module adds the capacity and capital expense of switching hundreds of calls. A solution to pricing in the presence of these cost discontinuities is suggested by Steiner (1957). He formulates a model of "peak load pricing" in which customers during peak usage periods (i.e., those who force capacity expansions) pay higher rates than customers during off-peak periods. However, as Park and Mitchell (1987) indicate for the pricing of local telephone service, establishing economically beneficial peak-load rates for telecommunications services requires an extremely complex tariff structure subject to day-by-day fluctuation. Park and Mitchell conclude that such a practice is not viable because of the expense of collecting and monitoring costs and demand, and the impracticality of complex and varying tariffs. Furthermore, designing peak-load prices still requires that one estimate marginal costs. Since their discontinuous nature renders theoretically defined marginal costs unserviceable as the basis for ratemaking, a useful procedure is to smooth them by taking 37 an average over some increment of output. Long run average incremental cost (LRAIC) is defined as the additional cost of an increment of capacity, divided by the quantity of additional service (lines, minutes of use, etc.) provided by the capacity (Park, 1989). The LRAIC concept is useful for several reasons. First, it establishes a causal link between the service being provided and the incremental costs incurred in its production. Second, this measure represents those costs which would be avoided if capacity expansion were not required. Hence, it is useful for determining cross- subsidization as well a providing a useful comparison measure for determining rates which do not induce inefficient changes in behavior“. Park (1989) establishes that when prices are to be held uniform across varying levels of capacity utilization, average incremental costs provide a relatively efficient basis for setting rates. Thus, if peak-load pricing is not feasible, then LRAIC is an appropriate benchmark for establishing rates. In Chapter 7 the concept of long run average incremental cost is used to estimate the incremental distance-sensitive costs associated with access transport. These costs are used as a basis for determining the efficacy of the current distance-sensitive access tariff regime. “Especially changes in network configuration: see Chapter 38 The most recent addition to the catalogue of network costing methodologies is "stand-alone cost" (Faulhaber, 1975). Stand-alone cost is the cost a firm would incur if it produced a particular service in the absence of any others. For example, the stand-alone cost of producing local telephone service is the cost the phone company would incur if it designed and constructed the phone network solely to provide local service, making no provisions for toll or other services to be produced using the plant of the local network. This method evades the nebulous practice of cost allocation since there are no common or joint costs to be allocated. The stand-alone approach can be used to show that many of the costs of the network normally considered common, actually result from the provision of particular services. For example, Gabel and Gabel (1988) utilize the stand-alone approach to assess the costs of local exchange plant. They find that many of the additions and technological improvements made to local networks were motivated by the need to improve long-distance, data transport, and other enhanced services and that local service has scarcely improved as a result of these innovations. Gabel and Gabel also find that residential customer prices have risen disproportionately to cover the costs of these network 39 improvements”. Stand-alone costs also provide a test for cross- subsidization. A set of prices are said to be "subsidy free" if the revenues recovered from the provision of a service, by a multiproduct firm, are less than the stand- alone coSts of that service to any possible coalition of the firm’s customers (Faulhaber, 1975). Faulhaber and Levinson (1981), Sharkey (1982), and Brown and Sibley (1986) demonstrate that when a multiproduct monopolist is assumed to break even, subsidy-free prices imply that no group of consumers pay more than the stand-alone costs for the services they consume, and each group of customers pays at least its incremental cost. Although estimation procedures for these three cost concepts have been developed, FDC remains the standard despite its deficiencies. Well-established procedures with legal precedence and the relative ease of FDC calculations make FDC well-suited for regulatory proceedings, even if the calculations are economically unfounded. However, as the discussion which follows will make clear, considering incremental costs is imperative if efficiency is to be attained and the problems of bypass and network distortion avoided. ”More questionably perhaps, they use the relative values of stand-alone costs as a mechanism for allocating the remaining common costs of the local network. 40 W The key problem confronting public utilities and their regulators involves determining an appropriate rate structure which satisfies efficiency and equity criteria while allowing the firm to recover its economic costs of production. The network can provide numerous services utilizing common facilities and it is generally thought that the local exchange displays economies sufficient to yield subadditive costs across the entire relevant range of output (Hall, 1975; Public Communication Associates, et. al., 1988). For a multimarket firm selling in K submarkets subadditive costs are said to exist when, for nonnegative output vectors ql. . . , qn such that Q=q1+. . .qn, C(Q)ZS. Costs are a function of distance, and traffic density. Let Z, Z=Z3+ZU be the traffic density between A and B. Then, where no bypass occurs the social costs of access provision between A and B is given by: TC: C(S,Z). (4-2) 3‘This model is a stylized abstraction from actual network configuration. Often, an access tandem might provide service to a number of IXCs from numerous end offices. In addition, the link between A and B may transport other LEC traffic as well, increasing' traffic density along the corridor and lowering the LEC’s per-unit transport costs still further. 90 where C(') is a twice differentiable cost function which displays subadditivity in traffic density between A and B. Therefore, C(S,Z)SC(S,Z°)+C(S,Z1), where z=zd+z,. In addition, C(-) displays an additive property in terms of distance such that, C(T,Z)+C(Y,Z)=C(T+Y,Z). (4.3) Assume that B is located in a position which minimizes the costs of providing access to the large IXC and society”. Thus, B is located where aax, 2,) = aux, Z) ax aX_ .(4.4) Assume also that the small IXC has insufficient traffic to warrant backward integration, or equivalently, that the distance-sensitive price for access set by the LEC is always less than the Small IXC’s incremental distance-sensitive costs. The Firm’s Problem The Large IXC’s location problem involves minimizing its transport charges between A and B. P+(S-X)-t is the LEC’s per-minute charge for access when the IXC has moved its POP X miles closer to point A. P is a fixed per-minute price while t is the per-minute mileage charge. The IXC’s problem in determining its optimal network configuration is: 3”If the large carrier is a dominant firm, point B will then be very close to the social cost minimizing point. 91 min [P+(S-X) t + C(X,z,)], with respect to X. The first order condition reveals that the firm chooses X such that dC(X,zL)/dx=t. Therefore, by Equation 4.4, the IXC chooses the optimal configuration if and only if t=dC(S- x,zq)/dx; social costs are minimized when mileage prices are set equal to the LEC’s incremental costs of providing distance. When the IXC engages in backward integration the social costs of access provision are given by: TC = C(s-x, z,+z,) + C(x,z,) + C(x,z,). (4.5) Because access costs are assumed to be subadditive with respect to traffic density, inspection of Equation 4.4 and comparison with Equation 4.5 reveals that the social costs of access increase when backward integration occurs. In addition, the LEC’s per-unit costs of serving its remaining customers exceed its per-unit costs before backward integration. Cc2. Let s1 and 32 be the market shares of Firms 1 and 2, with 055,51, 055,51, and s,+s,=1. For any given price P, the profits of Firms 1 and 2 are respectively defined as 1r1(P) E (P "CH)Q(P)°SI: and, ”2(P) (P - C2)Q(P)°szr where Q(P) is the industry demand and «3(P) and.n5(P), are strictly concave functions of price. Let.P” be the monopoly 37According to the Folk theorem (Friedman, 1977; Tirole, 1988), there are an infinite number of sustainable equilibria with price falling between the monopoly and perfectly competitive levels. ”Note: This game results in a subgame perfect equilibrium. The threat of retaliatory' price cutting is credible since this is the profit maximizing strategy given that a competitor has begun undercutting the price. 103 price which solves n‘(P) = max[(P - cu)Q(P)]. In Bertrand equilibrium P = c,, since c2 > c,. Therefore, the profit functions for Firms 1 and 2 in Bertrand equilibrium are given by 1r.” = (C. - C.)Q(Cz), and 1r,“ =c2. The individual firm is faced with the choice of supporting the collusive price and perpetually earning 5,-1', or slightly undercutting the price charged by its rival, serving the entire market for one period and earning profits approximately equal to 1r“(P_) = (P. - c,)Q(P.); i= 1 or 2. The short-term gain from cheating for firm i is thus equal to 1r,“ - s,(1r(P_)) = (1-s,)-1r,(P.). The profit maximizing strategy for Firm i is obtained by comparing this short-term gain with the discounted present value of future profits foregone as the result of undercutting the monopoly price. If 66(0,1] denotes the rate at which the firm effectively discounts future earnings”, then the opportunity cost of undercutting the 396 can be defined as 6 = e"*, where r is the rate of interest, and t is the length of time between "periods". However, a broader interpretation of 6 is possible. Other factors, such as the potential for industry growth, the level of uncertainty of future earnings, and even the firm’s stock price may effect the firms time preferences for earnings. 104 price in the present period is given by z 6" [siHm-HB] . k=0 Thus, the collusive price is sustainable if, and only if Eissi[l-Ii(P”')41113]' (4 .6) (1‘51) ”1 (Pm) 5 1 Note that as 6 increases the right side of the equation increases and the potential for successful collusion is increased. If the firm places a high value on future profits, it will not undercut the collusive price. This could be because current interest rates are low and therefore the future is not greatly discounted, the firm may place a high value on its future share of profits because it expects demand, and hence profits, to expand in the future, or retaliation may be swift, so that the chiseling firm earns monopoly profits only for a short time before the Bertrand equilibrium results. To assess the effects of market share and relative costs on the sustainability of the monopoly price, Equation 4.6 can be reformulated for Firm 1 and Firm 2. Firm 1 should not undercut price P_, so long as 6 1-6 (1-sl)rl’f< [sl'Hf-(CZ-C1)'Q(c2)]. (4.7) Here, as 51 increases it becomes less likely that the firm will attempt to undercut the collusive price. The left side of the inequality demonstrates that a firm with a large 105 market share already has a sizable portion of the monopoly profits. Cheating allows it to gain only (1-s,)1r" for a single period and 1-sllapproaches zero as the firm’s market share expands. To examine the potential effect of price discrimination, recall the theoretical result that price discrimination either increases one price and decreases the other--or increases both prices but favors Firm 1 with its greater opportunity for backward integration (Katz, 1987). One clear effect of discrimination therefore, would be an increase in c,. Taking the derivative of the right-hand side of (4.7) with respect to c2 one obtains 25115....11 Q. 20. 602 (1-5) [Q(Cficzac2 C1 C2150.(4.8) The bracketed portion of Equation 4.8 is simply Firm 1’s marginal profit function, dn/dP. By the assumption that w”(P)<0, and the fact that cgfln, one concludes that at c,, profits are an increasing function of price and dnukkx>0. Thus, the right-hand side of Equation 3.4 is a decreasing function of ca. An increase in ca raises the Bertrand equilibrium price and diminishes the penalty to Firm 1 from engaging in a price war. Note also that in a dynamic setting, establishing the Bertrand equilibrium where P=c2:represents simplifying assumptions about firm behavior. It is entirely possible that Firm 1 may pose a credible threat to drive price below 106 (a, especially if the effect is to drive Firm 2 from the market, handicap Firm 2 in the future, or build a reputation in order to sustain collusion in the future (See the discussion below). Finally, although a rise in C5 increases the potential for a price war, it also reduces the positive impact of such a price war on social welfare--price is higher and output lower than when c,==h monumo 03 H440 >-4 Lmucuu at.z mc.>tow zo~h