> ![](media/image1.wmf){width="1.1416666666666666in" height="2.0in"}
>
> Federal Communications Commission
>
> Office of Plans and Policy
>
> 445 12^th^ Street, SW
>
> Washington, DC 20554

OPP Working Paper Series

A Competitively Neutral Approach To Network Interconnection

> **December 2000**
>
> Jay M. Atkinson
>
> Christopher C. Barnekov

**A Competitively Neutral Approach to Network Interconnection**

Jay M. Atkinson\*

Christopher C. Barnekov\*

December 6, 2000

OPP Working Paper No. 34

\*The authors are Economists in the Competitive Pricing Division, Common
Carrier Bureau, Federal Communications Commission. We wish to
acknowledge very helpful comments from Bill Sharkey, Keith Brown, Don
Stockdale, and Paul Zimmerman. We especially wish to thank Jane Jackson
for ordering us to \"think about a general theory of everything,\" and
for giving us the time to carry out her wish. We also thank Robert
Pepper for graciously offering to elevate the work of two Common Carrier
economists to the status of an OPP working paper. The views expressed in
this paper are those of the author and do not necessarily represent the
views of the Federal Communications Commission, any Commissioners, or
other staff.

This document is available on the FCC's World Wide Web site at
<http://www.fcc.gov/>.

Table of Contents

Executive Summary ii

I. Introduction [1](#introduction)

II\. Efficient Inter-Carrier Compensation as the Focus for
Interconnection Policy
[3](#efficient-inter-carrier-compensation-as-the-focus-for-interconnection-policy)

III\. Two Criteria for Interconnection Regimes
[7](#two-criteria-for-interconnection-regimes)

IV\. Efficient Interconnection Rules in a simplified network
[9](#efficient-interconnection-rules-in-a-simplified-network)

A. A simplified measure of facilities: *urlinks*
[9](#a-simplified-measure-of-facilities-urlinks)

B. Adding subscribers in a linear network
[12](#adding-subscribers-in-a-linear-network)

C. Assigning the incremental cost of interconnection
[13](#assigning-the-incremental-cost-of-interconnection)

D. Networks should recover from their own subscribers all costs not
incremental to interconnection: the "BASICS" rule
[15](#networks-should-recover-from-their-own-subscribers-all-costs-not-incremental-to-interconnection-the-basics-rule)

E. Interconnection among more than two networks
[16](#interconnection-among-more-than-two-networks)

V. Distinguishing costs incremental to interconnection from
intra-network costs
[16](#distinguishing-costs-incremental-to-interconnection-from-intra-network-costs-interconnection-of-less-than-fully-provisioned-networks)

A. Interconnection between networks of differing service quality levels
[16](#__RefHeading___Toc500040871)

B. Does the BASICS Rule resolve quality of service externality problems?
[20](#does-the-basics-rule-resolve-quality-of-service-externality-problems)

C. Can Networks resolve the Network Externality under BASICS?
[20](#can-networks-resolve-the-network-externality-under-basics)

VI\. Can these results be Generalized?
[21](#can-these-results-be-generalized)

A. Does BASICS work for networks of other than linear form?
[21](#does-basics-work-for-networks-of-other-than-linear-form)

B. What if the subscribers are actually central offices?
[23](#what-if-the-subscribers-are-actually-central-offices)

C. What if the networks have differing link costs, or subscribers have
differing preferences?
[24](#what-if-the-networks-have-differing-link-costs-or-subscribers-have-differing-preferences)

VII\. Interconnection with a dominant carrier
[25](#interconnection-with-a-dominant-carrier)

VIII\. A Brief Comparison of BASICS To current interconnection Regimes
[26](#a-brief-comparison-of-basics-to-current-interconnection-regimes)

IX\. Policy considerations that precluded BASICS-like proposals in the
past may no longer apply
[29](#policy-considerations-that-precluded-basics-like-proposals-in-the-past-may-no-longer-apply)

Executive Summary

This paper develops a consistent, competitively neutral regulatory
regime for interconnection between telecommunications networks. It
proposes a default bill and keep solution under which carriers split
equally those costs that are solely incremental to interconnection, and
recover all remaining costs from their own customers. The analysis
differs from previous work primarily in that it distinguishes the costs
incremental to interconnection from those incremental to increased
traffic volume. The paper demonstrates for several basic network types
that this default rule is competitively neutral and encourages efficient
subscription and interconnection decisions. This default rule resolves
serious common cost allocation, externality and gaming problems that
arise under current interconnection regimes and under other proposed
resolutions.

The key finding is that it is essential to isolate those costs
incremental to interconnection *per se*. Local networks are assigned the
costs of handling all the possible traffic that their subscribers
generate in making or receiving calls. The additional facilities
necessary to allow interconnection of two such fully provisioned
networks can then be defined as the incremental cost of interconnection.
Splitting these latter costs equally between the two networks produces
competitively neutral results for basic network types. The paper argues
that these results can be generalized to more complex network forms.
These results do not depend on the technology used by the networks, on
the balance of traffic between them, or on the level of termination
costs.

The rapid pace of change of telecommunications market conditions
requires a regime that is largely self-administering. As new entrants
appear and new types of networks arise, current interconnection regimes
become increasingly difficult to administer. This is because they
involve intractable problems of allocating substantial common costs
among services and among users. The best economists can offer under
current approaches is a "second-best" solution that produces significant
inefficiencies. This solution also creates opportunities for gaming and
regulatory arbitrage that produce more inefficiencies. Furthermore, this
solution requires much more information than regulators can acquire, and
even the most diligent and clever regulator cannot make necessary
adjustments at the pace at which market conditions are changing. The
rule proposed here is a largely self-administering scheme that relies
primarily on market mechanisms. It also enables efficient outcomes,
rather than "second best" solutions attempted under current
interconnection regimes.

This proposal resembles other "bill and keep" proposals in that it
offers a structural solution to the intractable problems of allocating
substantial common costs among services and among users that hamper
current interconnection regimes. The FCC has successfully resolved
similar problems in recent decades by separating more and less
competitive segments of the market. The market for consumer premises
equipment (CPE) was separated from that for local service. Enhanced
services, particularly computer services, and long distance services
were also separated from local service. This structural approach has
generally enhanced competition and produced desirable results.

A Competitively Neutral Approach to Network Interconnection

# Introduction

1.  As both the number and the variety of telecommunications networks
    continue to multiply, interconnection is becoming increasingly
    important. As the number of controversies over network
    interconnection rises, it becomes increasingly useful to reconsider
    current regulatory approaches. It is not clear that these approaches
    can accommodate the new types of interconnection that are appearing
    or keep pace with market developments. We develop below a simple set
    of principles of interconnection and apply them to current and
    proposed interconnection regimes.

2.  How would we know a good interconnection regime if we saw one? We
    propose that a good regime should result in a competitively neutral,
    economically efficient inter-carrier compensation and minimum
    regulatory intervention. By competitively neutral, we mean that the
    interconnection regime itself confers no special advantage or
    disadvantage on any carrier or technology.[^1] Whatever advantages
    or disadvantages existed prior to interconnection remain undistorted
    by the interconnection regime. For several basic types of networks,
    we demonstrate below that competitively neutral interconnection is
    achieved by a simple rule: networks should share equally those costs
    that are solely incremental to interconnection and bear individually
    all costs that are not incremental to interconnection. We argue
    below that this result can also be generalized to more complex
    networks. We believe this rule is the minimum feasible regulation,
    and we argue below that it provides a competitively neutral and,
    with respect to interconnection, efficient outcome.

3.  Our approach to the problem of interconnection differs from the
    usual treatment in the economics literature. The most fundamental
    difference is that the interconnection literature typically accepts
    existing institutional arrangements as given, then attempts to find
    pricing rules to navigate the morass of problems that arise from
    these arrangements.[^2] In contrast, regarding institutional
    arrangements we begin *tabula rasa*, with a blank whiteboard, and
    consider whether alternative arrangements might lead to a simple,
    competitively neutral, efficient result. [^3]^,^ [^4]

4.  Our differing approach is largely motivated by the rapidity with
    which new forms of interconnection are developing and market
    conditions are changing. This contrasts to the necessarily glacial
    pace at which even a supremely competent regulator can regulate in a
    society that values due process, eschews arbitrary and capricious
    exercise of power, and in which regulators have limited specific
    knowledge of market conditions.[^5] From this perspective,
    reexamining the institutional arrangements seems the only workable
    approach to untangling the current inconsistent assortment of
    interconnection rules that have been crafted over recent decades for
    various telecommunications sectors to meet various policy
    objectives.[^6] Despite this somewhat radical approach, we believe
    our analysis is generally consistent with previous analyses, in the
    sense that differences in results stem primarily from differences in
    assumed institutional arrangements. We also find that solutions
    similar to those we propose have been suggested previously by
    others, but were not adopted for reasons that apparently no longer
    apply.[^7] We discuss briefly below, mainly in footnotes, how our
    analysis relates to the previous literature.

# Efficient Inter-Carrier Compensation as the Focus for Interconnection Policy

5.  We believe it has become useful to depart from tradition by focusing
    on inter-carrier compensation rather than on end user charges. Until
    fairly recently, the primary focus of interconnection policy has
    been the distribution of costs among end users, and the literature
    has focused on end user pricing. More recently, interconnection
    policy has also been seen as a means of promoting competition.[^8]
    Today, however, the public switched network has become a network of
    networks. As a result, interconnection's importance is no longer
    simply as a mechanism for transferring subsidies from certain
    carriers (or end users) to others. If the national economy is to
    continue to grow and prosper, it is increasingly important that
    interconnection be economically efficient. We therefore propose to
    redirect the focus of interconnection policy to inter-carrier
    compensation.

6.  In the past, legislatures and regulators have shaped interconnection
    regimes to further a variety of policy goals. Universal service, the
    cross-subsidization of high cost users by low cost users,[^9] was
    typically the driving policy consideration.[^10] With the
    Telecommunications Act of 1996, Congress fundamentally altered this
    landscape. Regulated monopolies were to be supplanted by competitive
    markets, and cross-subsidization was to be replaced by explicit,
    "specific, predictable, and sufficient ... mechanisms to preserve
    and advance universal service."[^11] Universal service
    considerations are no longer to dominate interconnection policy.

7.  We assert that competitive neutrality and inter-carrier economic
    efficiency should now become the primary interconnection policy
    consideration. There exists an economically efficient, competitively
    neutral solution if the problem is formulated in terms of
    inter-carrier compensation.[^12] The economic efficiency of
    inter-carrier compensation affects both the structure of the
    industry and, more importantly, the contribution the
    telecommunications sector makes to the nation's economic growth and
    productivity. Because inefficiency in this increasingly important
    sector can substantially degrade overall national output,
    interconnection policy should now focus on inter-carrier efficiency.

8.  An alternative way of stating this last point is that competitive
    neutrality has become increasingly important in interconnection.
    Current interconnection rules have distorted production and output
    in telecommunications. Rates that diverge greatly from true economic
    costs, and rate *structures* that diverge from true cost structures,
    have resulted in inefficient production and behavior that is
    rational only because of artificial rules.[^13] The industry has
    reshaped itself extensively to respond to artificial incentives that
    are often an unintended consequence of artificial rules.[^14] This
    often diverts traffic from the public switched telephone network
    onto such alternatives as private lines, competitive access
    providers, and, perhaps next, Internet telephony. Regulators and
    parties have expended much energy in erecting artificial boundaries
    to maintain artificial distinctions and artificial prices. The
    market relentlessly undermines these regulatory walls,[^15]
    particularly when inconsistent rules encourage parties to adopt
    avoidance strategies.[^16] The regulatory walls eventually crumble,
    but in the meantime efficiency suffers. We may have reached the
    point at which telecommunications has become so important that our
    society can no longer afford such inefficient policies. It may be
    time for a competitively neutral interconnection rule that does not
    distort choices among technologies or among firms.

9.  Focusing on inter-carrier compensation enables us to avoid two
    serious stumbling blocks. The first is that the traditional end user
    focus requires viewing inter-carrier calls (local or long distance)
    as services among many others that carriers market to end users.
    This makes most network costs, particularly loop costs, common costs
    to be allocated among these various services. Only markets can make
    such an allocation correctly. Regulators cannot possess the
    requisite specific knowledge.[^17] The problem is intensified
    severely by the institutional rule that the calling party's network
    pays the entire cost of the call. Because this cost includes an
    allocation of common costs, the calling party's network ends up
    paying a share of the common costs of the called party's network.
    There is no perfect solution to these cost allocation problems,
    largely because regulators cannot know how benefits are distributed
    between the parties. That is, regulators cannot see individuals'
    demand functions. Any allocation a regulator can make is arbitrary
    (in the economic sense), yet even a small allocation error can
    produce massive distortions.[^18]

10. The second stumbling block we avoid is that, under current
    institutional arrangements, end users have no direct control over
    access arrangements. Under the access charge regime, interexchange
    carriers (IXCs) must purchase access from local exchange carriers
    (LECs) on both the originating and terminating end of calls. By law
    and FCC interpretation,[^19] IXCs must average the access charges
    they pay across all LECs, so that IXC customers pay the same rate
    whether they call to (or from) a high cost or a low cost LEC. IXCs
    are not permitted to pass through the access charges incurred on a
    particular call to the end user who makes that call.[^20] Thus, even
    if an omniscient regulator existed who could discern the correct
    (i.e., socially efficient, incorporating all externality effects)
    inter-carrier cost allocations, these would not necessarily result
    in correct end user rates. The parties to a call are not empowered,
    under current arrangements, to choose the lowest cost means of
    completing a call of the quality and other characteristics they
    prefer. Therefore even correct inter-carrier cost assignments cannot
    assure efficient outcomes under current arrangements.

11. By focusing on inter-carrier compensation, we avoid these two
    inter-related problems entirely. We will show that the efficient
    allocation of interconnection costs between carriers is independent
    of how the calling and called parties bear the cost of a call. Nor
    does the balance of traffic between networks affect the efficient
    allocation of interconnection costs. It does not matter which
    network's subscriber caused a call by initiating it.[^21] The
    carriers' retail rate structures, the ways they recover their costs
    from their end users, are not our focus.[^22] We are concerned here
    with inter-carrier compensation rather than end user charges.

12. Brock (1995) makes the important point that the FCC's 1980 *Computer
    II* decision to deregulate customer premises equipment (CPE) was
    equivalent to mandating interconnection with customer-owned CPE and
    setting a zero interconnection rate for CPE. That is, local carriers
    could no longer charge for or control end users' purchase or use of
    CPE that met FCC technical standards. Prior to 1980, CPE had been a
    profitable venue for LEC price discrimination. LECs priced CPE usage
    as many discrete services. LECs could, and did, charge usage fees
    for every jack and every piece of equipment the customer wished to
    attach. The resulting common cost allocation problems were insoluble
    and pricing was based primarily on marketing estimates of demand
    elasticities for particular services.[^23] The *Computer II*
    decision gave customers complete control of (and responsibility for)
    the wiring and equipment on their side of the network interface
    device (NID). In a somewhat analogous manner, we are suggesting
    that, just as CPE was separated from local service, inter-network
    interconnection can also be separated from local service in a manner
    that empowers end users.

13. It is difficult to overestimate the impact of *Computer II'*s
    decision to give customers the right to purchase CPE outright,
    rather than only to buy discrete CPE services from the LEC. We will
    not attempt to prove this assertion here, but we believe that the
    recent development of the Internet, and of much of Information
    Technology, would not have happened if CPE (for example, modems)
    were still marketed only by LECs. The blossoming of the CPE market
    into a highly competitive industry offering a wide variety of choice
    at low cost and rapid technological advances, and enabling
    previously unknown possibilities such as the increasingly numerous
    Internet services, is arguably a direct consequence of the
    deregulation of CPE.

14. We are suggesting that, in a manner similar to CPE, interconnection
    can be separated from local network services. At present, LECs
    retain access rights to their customers lines. They sell discrete
    access services to IXCs and other interconnecting carriers, who in
    turn sell individual calls to individuals. Instead of this
    arrangement, subscribers could directly purchase unlimited access to
    their own lines. Although this paper does not address the manner in
    which carriers retail their services, we do not exclude any
    particular arrangements. Our point is that the best way to achieve
    efficiency may be first to "get inter-carrier compensation
    right,"[^24] then to address the end user market separately.

15. Getting inter-carrier compensation right does not guarantee that end
    user charges will also be right, but it is a major step in that
    direction. Interconnection policy alone cannot cure underlying
    problems, such as possible dominance in local exchange markets,[^25]
    but it can limit the harm generated by such dominance and thus
    contribute toward achieving solutions. Efficient interconnection
    policy can prevent a dominant carrier from using its control over
    interconnection to extend its market power to other markets, to
    leverage its market power to extract monopoly rents from
    interconnectors, or to erect artificial barriers to competitive
    entry.[^26] That is, interconnection policy can restrict a dominant
    LEC to exploiting only its own customers. If a dominant carrier does
    try to exploit its own customers, the chances that a competitor can
    contest the market are improved. Regulators may wish to influence a
    dominant carrier's end user charges, but interconnection policy is
    not the correct tool for this purpose. By focusing exclusively on
    inter-carrier compensation here, we assert that the first step in
    getting end user charges right is to achieve efficient inter-carrier
    compensation, and that this is the proper focus of interconnection
    policy.

# Two Criteria for Interconnection Regimes

16. As long as there are dominant local networks, it may be necessary to
    mandate and regulate interconnection. A dominant network may be able
    to disadvantage a competitor by either of two basic strategies. It
    may simply refuse interconnection and thereby force subscribers of
    other networks to subscribe to it in order to connect to its
    subscribers.[^27] Or it may impose (discriminatory) charges on calls
    to or from subscribers of other networks, thereby inducing these
    customers to join its network or taxing, in the economic sense, the
    other networks. [^28] Neither of these strategies could be
    effective, and no network would have an incentive to refuse
    interconnection,[^29] if no single network held a commanding market
    share, but they become increasingly attractive as the largest
    network approaches market dominance. In the presence of a dominant
    carrier, a regulatory remedy may be necessary.

17. If a regulatory remedy is necessary, it should minimize the extent
    of regulatory intervention. Absent regulation, a dominant network
    may be able to impose crippling disadvantages on potential
    competitors. The result may be exploitation of customers and
    potential competitors as well as inefficiencies that inflict
    significant net losses on society. But will a regulatory remedy do
    more good than harm? The problem is that regulation itself can also
    impose significant costs.[^30] This is particularly problematic when
    regulators "get it wrong," an outcome which is hardly unprecedented
    and the more likely the more information is required to "get it
    right." An ideal solution, therefore, should minimize the
    information regulators need.

18. So we propose two criteria by which to judge potential mandatory
    interconnection regimes. Do they result in economically efficient
    inter-carrier compensation? And are regulators likely to get it
    right? The first criterion means that the correct pricing signals
    are sent to networks making investment and make/buy decisions, and
    thus potentially also to consumers making subscription
    decisions.[^31] The second criterion means that regulators do not
    need many facts or much data to administer the regime. Ideally,
    regulators could limit themselves to stating fairly simple
    principles or rules and allow the parties to negotiate efficient
    solutions suited to their particular circumstances. In such a
    regime, disputes would be resolved primarily through ordinary
    commercial procedures such as negotiation and arbitration.[^32] We
    propose that an interconnection regime that meets these two
    criteria, efficiency and simplicity, would permit an efficient and
    competitive telecommunications system to develop and enable it to
    adapt rapidly and smoothly to changing technologies and market
    conditions.

19. In proposing these two criteria, we should note that our goal is
    relatively modest. We do not seek an interconnection regime that
    will resolve all the problems of telecommunications. It would be a
    significant improvement to discover one that, unlike the current
    regimes, does not add new or compound old problems. We do assert,
    however, that inter-carrier and retail rate structures can be
    addressed separately, just as CPE problems were resolved by treating
    CPE separately. In fact, we believe these problems can be solved
    only if inter-carrier and retail issues are addressed separately.

# Efficient Interconnection Rules in a simplified network

20. Real world networks are by nature so complex that it is very
    difficult to analyze them. Economists have always developed their
    principles by abstracting from real world complexities to capture
    essential features, and we resort to that technique here. We begin
    with a simplified, highly abstract representation of a network to
    demonstrate the principles of economically efficient
    interconnection. In the text, we attempt to develop these principles
    through simple, graphical illustrations employing a stylized linear
    network. Footnotes present a more general mathematical derivation.
    In a later section, we derive the same principles mathematically for
    each of two other fundamental types of networks.[^33] Although we do
    not attempt to prove these results for the completely general case,
    real networks can be represented reasonably well as a composite of
    these three fundamental building blocks. We therefore believe the
    principles apply to the more complex forms.

21. We make a number of simplifying assumptions in order to clarify the
    exposition. Later we will discuss the extent to which we can
    generalize these insights when some of these assumptions are
    relaxed. For now, our networks ignore scale economies, trunking
    efficiencies, and the many other engineering considerations that
    shape any real network. We thus abstract from the particular
    technology used to solve the problem of connecting any group of
    customers. We focus instead on the fundamental, underlying
    facilities requirements faced by each network in serving its
    subscribers. We assume that each network has access to the same
    technology set and employs brilliant engineers who select the most
    cost-effective means of provisioning the underlying facilities
    requirements. But we are not concerned with how the engineers work
    their magic, only with the abstract, underlying facilities
    requirements.

## A simplified measure of facilities: *urlinks*

22. Let us begin by imagining a small network with four identical
    subscribers. We want to determine what facilities are necessary to
    meet the following two requirements: First, any two subscribers to
    the network should be able to connect with each other. Second, there
    should be no call blocking. This means that any subscriber can
    always complete a call to any other subscriber who is not already
    engaged in a conversation. The call will not be blocked by
    inadequate facilities.[^34] Put differently, the network has
    sufficient facilities to enable all possible simultaneous
    conversations to take place.

23. The most primitive network imaginable would meet our two
    requirements simply by using a separate line to connect each pair of
    subscribers. With four subscribers, each depicted by an X, we would
    need six lines, as shown in Figure 1. Note that this network
    consists entirely of lines and has no switching capability at all.
    For five subscribers, we would need ten lines, for six we would
    need 15. In general, for n subscribers, this type of network
    requires (n^2^-n)/2 lines.

24. We use this facilities requirement for this primitive network as an
    abstract measure of required facilities. Engineers, of course, do
    not construct real networks by stringing a line between each pair of
    subscribers. As soon as n gets very large, the number of links
    required becomes astronomical (and subscribers would find it
    annoying to have n-1 separate lines). Engineers, therefore, use
    various technological devices to reduce costs. One basic method is
    to substitute switching capabilities for some of the links.
    Switches, multiplexers, and other line concentration devices may
    provide these substitutes for links. We are not concerned with
    precisely how the engineers provision the network. Regardless of the
    particular combination of links and switching actually used, we can
    think of the basic facilities requirement as a combination of links
    and switching that is equivalent to (n^2^-n)/2 links for a network
    of n subscribers. We coin the term ***urlink*** to indicate the
    facilities required to enable one direct connection between one pair
    of subscribers, noting that urlinks may be supplied by various
    combinations of links and switching. Thus, we can say a network of
    four subscribers has an underlying facilities requirement of six
    urlinks. A network of five subscribers requires ten urlinks, and a
    network of n subscribers requires (n^2^-n)/2 urlinks.The mesh
    network is a basic network form similar to our primitive network, in
    that it uses the same number of lines; but it adds a switch at each
    node. The mesh network provides added reliability because there are
    multiple paths between each pair of subscribers. If one link fails,
    a call can be routed over alternative links. The mesh also requires
    (n^2^-n)/2 links. We extend our interconnection principles to mesh
    networks later, but base our initial discussion on the even simpler
    linear network form, because a mesh becomes very difficult to depict
    graphically as n increases.

25. For our graphical depictions in the text, we use a linear network.
    To determine the facilities required, we write down all the possible
    simultaneous two-party conversations. We use a long dash to
    represent a unit of transport *and related facilities* that we will
    again call an urlink.[^35] Using upper and lower case to distinguish
    between calls, there are three possibilities for two simultaneous
    2-party conversations, as shown in Figure 3.

26. In words, Combination A needs only two urlinks since there is only a
    left side and right side conversation. The remaining possible
    combinations need these plus two in the center, since both the
    conversations cross the center of the network. In Combination B, the
    center parties (x-x) require one urlink and the outside parties
    (X--X) require three. In Combination C, each conversation requires
    two urlinks. We can denote the facilities needed for our four-party
    network to meet our two requirements as in Figure 4.

27. In words, a network of four parties (subscribers) can have a maximum
    of 2 simultaneous two-party conversations (the number of dashes in
    the center) and requires 4 urlinks (the sum of all the dashes) to
    allow every possible two-party conversation to take place.

28. This diagram is a deliberate abstraction that does not specify the
    network architecture or technology that is used to meet the
    requirements that any two parties can connect and that there is no
    call blocking. In the real world, a network could meet these
    requirements with a ring, star, mesh or any other imaginable
    architecture; wireline or wireless links; and circuit or packet
    transmission. We are also abstracting from cost-saving techniques
    that real networks use to economize on links.[^36] We ignore
    possible scale economies or trunking efficiencies and assume
    initially that the network is engineered for zero call blocking.
    Finally, this simple network does not have any redundant links to
    improve reliability.[^37] In other words, we are focusing on the raw
    capacity required and abstracting from engineering techniques used
    to provision this raw capacity (urlinks) economically.

29. We can generalize this depiction to any number of parties. For a
    linear network of n subscribers, the maximum number of simultaneous
    two-party conversations is n/2. (Logically, each party can engage in
    only one conversation at a time.) To ensure that any combination of
    n/2 conversations can occur simultaneously[^38] requires (n/2)^2^
    links.[^39]

## Adding subscribers in a linear network

30. We are now almost ready to explore interconnection between two
    networks; but first we need to consider what happens as additional
    parties subscribe. We make two more initial assumptions to simplify
    the analysis. Later we relax these. We assume all parties are
    identical (and choose their initial network randomly). We also
    assume for now that each urlink has the same cost.

31. If two more parties subscribe to the X network, then a six-party
    network in our notation would be diagrammed as in Figure 5. Three
    simultaneous calls are possible, so three urlinks are needed across
    the center of the network. This network meets our two requirements,
    that any two parties can connect and that there is no call blocking.

32. Notice that the original four-party network had an average of one
    link per party, but adding the two new parties requires five more
    links. The parties benefit equally from the network (in the sense
    that each can call any of the others), so instead of making the new
    parties pay for all the additional links, every subscriber pays a
    proportionate share of the additional links.[^40] The average number
    of links per party rises from 4/4 = 1 per subscriber to 9/6 = 1.5
    per subscriber. As more subscribers are added, the benefits of the
    network increase, but the number of links needed per subscriber also
    rises.[^41] The network will add new parties until there are no more
    potential subscribers or the price (average cost) rises to the point
    at which some subscribers begin dropping off the network.

## Assigning the incremental cost of interconnection 

33. What is the incremental cost of interconnection? Suppose the two
    parties who joined Network X in Figure 5 had instead already
    subscribed to another network, Network O? Comparing Figures 6a and
    6b, we see that to meet our two requirements, interconnection
    requires four additional links (dotted in Figure 6b).[^42] This is
    the incremental cost of interconnection.

34. It is worth noting that the interconnected network of Figure 6b has
    precisely the same facilities requirements as the six party network
    of Figure 5. In this case, interconnection is precisely equivalent
    to subscription. Ideally, our rule for allocating responsibility for
    the incremental interconnection links should not give parties an
    incentive to masquerade as networks[^43] or as subscribers, or to
    rearrange calling patterns,[^44] in order to exploit the rules. That
    is, an ideal rule will not distort decisions.

35. How should responsibility for these four incremental links be
    assigned? Suppose each network were assigned a share proportional to
    its number of subscribers. The X network would pay for two-thirds of
    the four incremental links (2.67 links), and would have a new
    average of (6.67)/4= 1.67 links per subscriber. The O network would
    be responsible for 1.33 additional links, raising its average to
    2.33/2 = 1.17 links per subscriber. However, a subscriber to either
    network receives precisely the same benefits: non-blocking access to
    the same subscriber list. Therefore, subscribers to the X network
    would be better off if they switched to the O network. As the O
    network grew, its links per subscriber would increase (and losing
    subscribers would reduce links per subscriber on the X network). The
    artificial price wedge created by this interconnection cost
    assignment would only disappear when the networks became equal in
    size. Eventually, subscribers would migrate until each network would
    have 1.5 links per subscriber.

36. The discussion in the previous paragraph suggests a surprising
    result, that dissimilar-sized networks must share equally the
    incremental cost of the facilities required to interconnect them.
    Under this "Split the Incremental Cost of Interconnection" rule, the
    O network, with only two subscribers, must pay for the same number
    of incremental links as the X network, even though X has twice as
    many subscribers. This means, of course, that the cost *increase*
    faced by O subscribers is greater (from 0.5 to 1.5 links per
    customer) than that faced by X subscribers (from 1.0 to 1.5 links
    per customer). This seems reasonable, because the O customers are
    gaining access to four additional parties, while the X subscribers
    are gaining access to only two more parties.[^45] Following this
    rule yields the same number of links per subscriber for each
    network.[^46] That is, the raw capacity burden per subscriber is the
    same on each network. Since full, non-blocking interconnection
    allows subscribers to either network precisely the same benefits,
    failure to balance links per subscriber does not produce a stable
    outcome. The burdened network will lose subscribers and the favored
    network will gain subscribers until the burden is equalized.

37. When we compare Figures 6a and 6b we can see that interconnection
    does not increase the maximum number of simultaneous calls (the
    number of links in the center of the combined networks). Prior to
    interconnection, three simultaneous calls are possible: two on the
    (four party) X network and one on the (two party) O network. The
    interconnected six-party XO network also accommodates three
    simultaneous calls. Thus interconnection only increases the number
    of parties it is possible to call, not the number of simultaneous
    calls. This point will prove significant later, when we drop the
    assumption of no call blocking.

38. Note that we have achieved this efficient allocation of costs
    between networks without any reference to how the calling and called
    parties bear the cost of a call, to which network caused a call by
    initiating it, or to the balance of traffic between networks. We
    thus avoid the intractable common cost allocation problems
    encountered in the traditional approach.

## Networks should recover from their own subscribers all costs not incremental to interconnection: the "BASICS" rule

39. Our analysis suggests a second principle, that *only* the costs
    incremental to interconnection should be split. Therefore, all
    remaining network costs should be recovered from the network's own
    subscribers. In our example in Figure 6b, dividing the total
    links (9) equally between the networks would give the X network
    4.5/4 = 1.125 links per subscriber. In contrast, the O network would
    have 4.5/2 = 2.25 links per subscriber.[^47] Even if the networks
    were the same size, but dissimilar in cost, including the internal
    network costs would create an artificial cost difference. We
    consider this point more fully and distinguish more clearly between
    internal network costs and interconnection costs in the next
    section.

40. We can now combine our two principles to form a rule we will name
    "Bill Access to Subscribers, (Incremental) Interconnection Costs
    Split," or "**BASICS**." The second half of this acronym is the
    rule, developed in the previous section, that the costs incremental
    to interconnection should be split equally between the two
    interconnecting networks. The first half refers to the requirement
    that each network collect all remaining costs (those not incremental
    to interconnection) from its own subscribers. In particular, access
    rights to subscribers' lines are not sold to interconnecting
    networks on a per minute basis, as under current access rules.
    Instead, all access rights are sold directly to the subscribers
    themselves. We confess that our name for this rule is somewhat
    awkward, and freely admit that the name was crafted primarily for
    the sake of its acronym.

## Interconnection among more than two networks

41. In the case of more than two networks, the BASICS rule would apply
    *seriatim*. That is, the initial interconnection forms an
    interconnected network. As additional networks join, each would do
    so on a BASICS basis. In each case, the network joining would bear
    half the incremental costs of the new interconnection. The networks
    previously interconnected would bear the remaining incremental
    costs, which would be distributed among these networks on a per
    subscriber basis. This allocation would produce the same results as
    above, and the result would be the same (an equal urlinks per
    subscriber burden) regardless of the order in which networks joined.

# Distinguishing costs incremental to interconnection from intra-network costs: Interconnection of less than fully provisioned networks 

42. If the BASICS Rule is to be implemented, it is essential to identify
    those costs that are incremental to interconnection *per se*. It is
    particularly important to distinguish costs incremental to
    *interconnection* from costs of improving service quality *within* a
    network. An especially difficult issue is distinguishing costs
    incremental to interconnection from those incremental to increased
    traffic volume. We believe the correct approach to resolving this
    problem is to recognize that the level of call blocking that
    subscribers experience is a key element of service quality.
    Increased traffic volume increases call blocking unless the network
    is adequately provisioned to be non-blocking. In order to
    distinguish between costs incremental to interconnection and costs
    incremental to intra-network service quality, we must now drop our
    assumption that all networks are fully provisioned to be
    non-blocking.[]{#__RefHeading___Toc500040871 .anchor}

## Interconnection between networks of differing service quality levels

43. In Figure 7a, we show two networks that offer differing service
    quality levels. The X network offers a lower quality of service. It
    is not fully provisioned, having provided only one urlink across its
    center. As a result, call blocking will occur whenever more than one
    X subscriber attempts a call across the X network's center. Network
    X is offering something loosely resembling old-fashioned party line
    service, serving four subscribers using only three urlinks at an
    average cost of ¾ urlink per subscriber. The O network, in contrast,
    is fully provisioned. O has an average cost of 1 urlink per
    subscriber and offers completely non-blocking service. In a
    competitive market, we can presume Network X's lower quality is
    offered at a lower price.[^48]

44. To see the incremental cost of interconnection in this case, it is
    helpful first to see what should *not* be included. In Figure 7b,
    the networks have interconnected *and* the X network (perhaps for
    competitive reasons) has added its missing link to become fully
    non-blocking. The total number of urlinks added is nine (and the
    maximum number of possible simultaneous calls across the centers of
    the networks has increased from three to four). If all nine added
    links were considered incremental to interconnection, then the X
    network would have 3 + 4.5 = 7.5 urlinks, or 1.875 per subscriber.
    The O network would have 4 + 4.5 = 8.5 urlinks, or 2.125 per
    subscriber. This cost assignment gives X an artificial advantage
    because one of its intra-network links is being included in the cost
    of interconnection. X can now offer the same calling list and the
    same quality of service as O, but at a lower price. O subscribers
    are paying a "tax"[^49] of 0.125 urlinks in order to subsidize X
    subscribers. Recognizing that X added this second link across its
    center to upgrade its intra-network service quality, rather than for
    interconnection *per se*, eliminates this artificial advantage.

45. As a further illustration of this point, suppose the X and O
    networks want to maintain their differing grades of service. In this
    case, only six incremental links (dotted in Figure 7c) are needed to
    maintain the O network's non-blocking grade of service while not
    reducing blocking (upgrading service) between X network subscribers.
    The other two interconnection links in Figure 7b can never be needed
    as long as X has only one link across its own center, because there
    can never be enough XO traffic to require their use.

46. Now we are ready to illustrate our point about distinguishing
    between interconnection and intra-network service quality. After
    interconnection in Figure 7c, the maximum number of possible
    simultaneous conversations possible between pairs of X network
    subscribers is unchanged. As before interconnection, only one
    conversation can cross X's center. Applying the BASICS Rule to the
    incremental links (there are six more urlinks than before
    interconnection in Figure 7a) assigns three more urlinks to X, for a
    total of six urlinks for four subscribers, or 1.5 urlinks per X
    subscriber. The four O subscribers now have 4 + 3 = 7 urlinks, or
    1.75 per subscriber. Note that the O network again has more links
    per customer and a higher quality of service (zero intra-network
    call blocking) than the X network (where there is some
    blocking).[^50] The point is that interconnection under the BASICS
    cost-assignment rule has not distorted the relationship between cost
    and service quality for the two networks.

47. Comparing Figures 7b and 7c also enables us to distinguish clearly
    between costs that are incremental to interconnection *per se* from
    those that are incremental to improving service quality *within* a
    network. In both cases, the O network is fully provisioned and will
    not experience any blocking whatsoever on O-O calls or on any calls
    that arrive from X. In 7c, however, the X network remains less than
    fully provisioned and does experience some internal blocking. Some
    calls from O subscribers to X subscribers may also be blocked, but
    blocking can only occur on calls to or from X subscribers. Costs of
    upgrading service quality for these X subscribers are not
    incremental to interconnection *per se*.

48. Figure 7c also helps highlight the distinction between
    interconnection and intra-network quality of service.
    Interconnection increases the number of parties that each subscriber
    is able to call. It does not directly affect possible call blocking
    *within* the interconnecting networks. Thus costs incurred to reduce
    call blocking that occurs entirely on one network are not costs
    incremental to interconnection, and would not be split between the
    networks. We are thus distinguishing between costs incremental to
    *traffic* and costs incremental to *interconnection*. We believe
    this analysis demonstrates that to achieve efficiency the former
    should be assigned to the separate networks and only the latter
    should be split (equally) between the two interconnecting networks.

49. Because this is such an important and potentially controversial
    point, let us illustrate the distinction between costs incremental
    to interconnection and those incremental to intra-network service
    quality from yet another perspective. It is possible that after
    interconnection X subscribers may wish to make more calls than
    before, because they can now reach more parties.[^51] If this
    increased demand causes X to provision its internal links fully (by
    adding the second link across its own center), the total number of
    possible calls across X's center increases from one to two. Thus
    Network X becomes fully non-blocking. If it adds this second
    center-link, Network X has the same cost (7/4 = 1.75 links per
    subscriber) and the same quality of service as O. The added link may
    be seen as incremental to *traffic volume*, or to service quality
    within X, but it is *not incremental to interconnection per se*. We
    believe this is a highly significant distinction that is essential
    to getting interconnection policy right, that is, to finding an
    efficient rule for assigning interconnection costs.

50. Notice, furthermore, that once X has fully provisioned its internal
    network, the networks may now want to add two more interconnection
    links (dotted in Figure 7d). These two links would have been
    redundant without the second link across X's center, but they now
    improve quality of service (reduce blocking) on inter-network calls.
    Note also that these two links are needed only to preclude blocking
    of inter-network, not intra-network, calls. They can never be needed
    for intra-network calls.[^52] Under BASICS each network would pay
    for half these additional inter-network links, and each would end up
    with 8/4 = 2.0 urlinks per subscriber. Thus, once both individual
    networks are internally non-blocking, fully non-blocking
    interconnection means adding a total of eight links (the six dotted
    in Figure 7c plus the two dotted in 7d). These eight links are
    incremental to interconnection, but the second link across the
    center of X is not incremental to interconnection.

51. We should also note at this point that, although our diagrams do not
    make this obvious, the interconnection links differ from the
    internal links in that they are needed only to carry inter-network
    traffic. They can never be needed for intra-network traffic. More
    importantly, they are inter-office links rather than loops (links
    between end offices and end users). This distinction may be
    significant when networks use differing loop technologies.
    Inter-network links today, and almost all inter-office links, are
    likely to be optical fiber links.[^53] If one or both of the
    individual networks uses a different technology, for example,
    wireless, its *internal* links may be more expensive. The analysis
    we have developed thus far suggests that only the costs of the
    (fiber) inter-network urlinks[^54] should be split equally between
    the two networks.[^55]

## Does the BASICS Rule resolve quality of service externality problems?

52. Does a network's decision to offer a lower quality of service impose
    an externality on the interconnecting network? The answer, no, is
    already implicit in the discussion above comparing Figures 7b and
    7c. This is such an important point, however, that it seems
    worthwhile to make it explicit. Figure 7c shows that any call
    blocking that results from under-provisioning links will occur on
    the network that under-provisions, not on the interconnecting
    network.

53. If we made some simple assumptions regarding calling preferences, we
    could calculate the expected call blockage suffered by subscribers
    to the degrading network and subscribers to the interconnecting
    network. Assuming that each subscriber is equally likely to try to
    call each other subscriber, we could show that the bulk of the call
    blockage would occur on the network that degrades its internal
    links. [^56] The only blockage experienced by subscribers to the
    fully provisioning network is on inter-network calls to customers of
    the under-provisioned network. The network that under-provisions
    bears the main impact itself, and the other network is affected only
    on some inter-network calls.

## Can Networks resolve the Network Externality under BASICS?

54. By focusing on inter-carrier compensation, we can also resolve
    serious externality problems and thus transform telecommunications
    markets into normal markets in the sense used by Brock,[^57] that
    is, markets without externality problems. The current rules, in
    effect, create externalities, because buyers and sellers do not see
    the networks' actual costs, only averaged rates. If we can resolve
    these externalities, we share Brock's view that networks can
    successfully internalize the fundamental network externality that
    other subscribers also benefit when an additional party subscribes.
    The BASICS rule of splitting equally only those costs incremental to
    interconnection *per se*, internalizes those externalities caused by
    current institutional arrangements.

55. In less regulated telecommunications markets, such as for internet
    service provider (ISP) and wireless services, we frequently observe
    networks offering inducements to attract new subscribers. Because
    the network becomes more attractive as more subscribers sign up, we
    believe networks can successfully internalize the network
    externality, at least where regulatory restraints on pricing do not
    preclude this.

56. In unregulated communications markets, firms do use pricing
    strategies that seem to internalize the network externality.
    Newspapers and magazines, for example, face something similar to the
    network externality because their attractiveness to advertisers and
    even to other potential subscribers depends to a great extent on
    their number of subscribers. For this reason, newspapers often offer
    subscriptions at rates that appear to be below average cost and
    perhaps even below marginal cost, sometimes barely covering delivery
    cost.[^58] This strategy seems to be profitable because it increases
    advertising revenues. Similarly, many ISPs offer below cost
    subscription or free E-mail service, apparently in order to increase
    sales of advertising. Web sites and broadcasters pursue a similar
    strategy of offering free information or entertainment in order to
    attract advertising revenues. These unregulated firms[^59] appear to
    be using retail pricing strategies successfully to internalize
    externalities. Although we do not attempt to prove this formally, we
    believe networks may succeed in internalizing the network
    externality through similar strategies.

# Can these results be Generalized?

## Does BASICS work for networks of other than linear form?

57. We believe these results can be generalized, although we must offer
    an important caveat. In our analysis above, we abstracted from such
    engineering considerations as scale economies and trunking
    efficiencies. We believe this is a reasonable abstraction because,
    as noted above, we assume that each network has access to the same
    underlying technological possibility set and to equally skillful
    engineers. Although we express our results in terms of cost per
    subscriber, it would be more accurate to say "urlink burden per
    subscriber," referring to our abstract measure of interoffice link
    or switching capacity. A more general expression of our results
    would not be that the BASICS rule equalizes per subscriber *cost*,
    but rather that it equalizes the raw, underlying per subscriber
    burden due to interconnection. Our point is that interconnection
    does not distort the underlying, pre-interconnection cost
    relationship. Each network enjoys whatever scale or scope economies
    its engineers can find, employs whatever technology it chooses, and
    faces the resulting costs. A BASICS rule simply does not distort
    whatever cost relationships would have existed without
    interconnection, and does not distort carrier decisions. In this
    sense, BASICS is a competitively neutral cost allocation rule.

58. The key mathematical relationship upon which our results above
    depend is that, for the simple networks we examined, splitting
    equally the incremental costs of interconnection yields the same
    cost per subscriber for each of the interconnecting networks. With
    the caveat noted above, we believe that if this relationship holds
    for other network forms, then our other results also follow.

59. The BASICS results do hold for mesh type networks. Unfortunately, a
    graphical depiction of a mesh of more than a very few subscribers or
    nodes exceeds our skill level. Fortunately, the algebra is no more
    complex than that for linear networks, so we can show this result
    algebraically.[^60] The basic difference is that the number of
    urlinks required for a mesh network is (n^2^-n)/2 (the standard
    formula for combinations of two in a population of n) rather than
    the n^2^/4 of a linear network.

60. The BASICS rule also holds for a network composed of a fiber optic
    ring connecting central offices, if we make a simplifying
    assumption. It does not matter how the various central offices are
    configured, other than that each network should have the same
    average number of subscribers per central office. We address the
    reasonableness of this assumption below. Once again the algebra is
    fairly simple,[^61] and the BASICS rule produces the same burden (in
    urlinks per subscriber) for each network after interconnection.

61. Viewed with a reasonable degree of abstraction, almost any network
    configuration can be resolved into a combination of the linear, mesh
    and ring forms.[^62] Although we do not attempt here a formal proof
    of this point,[^63] we argue that one can make a strong intuitive
    case that our results can be extended to most if not all real world
    network configurations. We conclude tentatively that, arguing by
    analogy, the basic principles we have discovered here are robust.
    That is, the BASICS rule is administratively simple and produces an
    efficient assignment of interconnection costs between the two
    networks.

## What if the subscribers are actually central offices?

62. The assumption immediately above for ring networks that both
    interconnectors have central offices of the same average size seems
    rather strong, but we believe it is not nearly so unreasonable as it
    may first appear. This point is worth exploring, because it applies
    to other network forms as well. Even our simple linear networks
    implicitly assume that, if the Xs and Os are actually central
    offices rather than individuals, they are of the same size.

63. We believe our equal average size assumption is reasonable because
    our analysis depends on viewing interconnection at the same level of
    line concentration. All our analyses take place at the same lowest
    common denominator, in the sense that we analyze a very large switch
    as a combination of smaller ones. That is, we view a large central
    office as equivalent to several smaller ones that are linked
    together. Thus a large central office requires internal links among
    its components. We think this is a network topology question for
    engineers to optimize, not a question of underlying urlink burden.
    The engineers determine the optimum combination of switching and
    links to meet the urlink requirement. We recognize that scale
    economies and network efficiencies occur, but we assume that each
    network does have access to equally brilliant engineers and to the
    same technology set. We are only concerned that each interconnecting
    network bears the same "urlink burden," that is, the same underlying
    raw capacity requirement per subscriber, not with the manner in
    which its engineers provision this burden.

64. We could allow subscriber (i.e. central office) sizes to vary. The
    mathematical treatment would become much more complex. Urlinks would
    become erlangs, that is, we would have to take explicit account of
    circuit demands. The analysis would become much more complex, but we
    believe the essential results would not change. We do not, however,
    attempt to prove this assertion formally in the present paper.

## What if the networks have differing link costs, or subscribers have differing preferences?

65. The case of differing link costs is the exception that proves the
    rule. Here, the BASICS rule will not produce equal urlink/subscriber
    burdens, but rather preserves the pre-interconnection relationship.
    It does not distort subscriber choices.

66. As a simple illustration, let us recall the interconnection example
    of Figure 6; but in Figure 8 let the heavy O-O link cost as much as
    10 ordinary links. O offers premium service characteristics (perhaps
    mobility) at a premium price. Before interconnection, the average
    cost for Network X is 1.0 (urlinks per subscriber). O's average cost
    is 5.0 (one expensive link shared by two subscribers).
    Interconnection requires four incremental links, which are ordinary
    links.[^64] After interconnection, each network is responsible for
    two (half of four) incremental links. X's average cost rises to (4 +
    2)/4 or 1.5. O's rises to (10 + 2)/2, or 6.0. The
    pre-interconnection cost relationship remains: O offers a premium
    service at a higher price. The BASICS rule has not distorted this
    relationship.

67. It is useful to break down the costs in this illustration between
    intra-network and interconnection services. X subscribers pay[^65]
    1.0 urlink each for access to other X subscribers and 0.5 (0.25 x 2)
    for access to the two O subscribers. O subscribers pay 5.0 for
    premium access to other O subscribers and 1.0 (0.25 x 4) for access
    to the four X subscribers. Each X or O subscriber pays (in this
    example) ¼ urlink in interconnection costs for each additional party
    it can call as a result of interconnection. X subscribers do not pay
    any more or less for access to other X subscribers than before
    interconnection. The same is true for O subscribers. The point is
    that neither network subsidizes the other. BASICS does not distort
    subscriber choices.

68. In a world in which various types of networks are possible, it is
    important that each network recover its intra-network costs from its
    own subscribers. Not all subscribers have identical preferences
    regarding technology, service quality, additional features, price
    and other aspects of network offerings. A single package is not
    likely to be optimal for every individual subscriber. Some
    subscribers may place a premium on very high reliability while
    others may accept occasional blockage, reduced voice or data
    quality, or even occasional outages in exchange for a lower price.
    Likewise, some subscribers may be willing to pay for the benefits of
    mobility offered by certain technologies, while others may forego
    mobility in return for a lower price. Some subscribers may choose a
    lower monthly charge plus a usage charge, while others may prefer a
    higher monthly charge that includes unlimited usage. Splitting
    equally the costs that are purely incremental to interconnection and
    requiring each network to recover its intra-network costs from its
    own subscribers permits each network to offer retail packages and
    each subscriber to choose the combination of features and price that
    best suits her preferences without distortions caused by
    cross-subsidization.

# Interconnection with a dominant carrier

69. Interconnection with a dominant carrier is the one case in which we
    need to discuss retail pricing arrangements in the present paper.
    Where there is no dominant carrier, we have argued that retail
    pricing can (and in fact must) be treated separately from
    interconnection, and that a regulator need not be concerned with the
    manner in which carriers structure their retail offerings. In such a
    case, competitive market forces will assure efficient results.[^66]
    As discussed in Section III above, however, a dominant carrier may
    be able to exploit its market power by discriminating between
    on-network and off-network calls. Such discrimination might enable
    the dominant carrier either to deter competitive entry or to exploit
    a network in a related market. It may therefore be necessary to
    prevent a dominant carrier from engaging in such discrimination.

70. We believe the remedy for possible discrimination by a dominant LEC
    is to grant interconnectors a right to non-discriminatory treatment
    within whatever local calling area the dominant LEC has established.
    An interconnecting LEC located within the dominant LEC's local
    calling area, upon fulfilling the BASICS requirement of splitting
    incremental costs of interconnection, would have the right to have
    its traffic treated on the same basis as the dominant LEC's own
    local traffic. That is, the dominant LEC could not discriminate
    between on-net and off-net calls within its local calling area.

71. Similarly, an out of area carrier (a LEC or an IXC) would be
    entitled to non-discriminatory treatment if it provides all the
    transport to (and from) a point within the local calling area of the
    dominant LEC plus the usual BASICS requirement of half the (local)
    incremental interconnection costs. If the out of area carrier bears
    these costs, a local dominant LEC would be obligated to treat
    inter-carrier calls in the same manner as it treats other local
    calls. The out of area carrier would, of course, be free to charge
    end users (but not other carriers) for the transport into the local
    area in any manner it chose, as long as it is not a dominant
    carrier.

72. Interconnecting networks in different local calling areas could also
    agree to split the cost of the transport between their local calling
    areas. If they did so, both networks would remain free to impose a
    toll (per-minute fee) or other fee on end users for their use, if
    they chose to do so. If the networks do not agree, however, a
    non-dominant carrier would have the right to demand that a dominant
    LEC allow it to provide the transport into the local calling area,
    interconnect on a BASICS basis, and have its traffic be treated on a
    non-discriminatory basis.

73. We do not discuss in this paper the separable question of whether
    recovery would be from calling parties, called parties, or both.
    What BASICS would preclude, however, is one network charging the
    other network for local interconnection, except to the extent that
    they split capacity costs incremental to local interconnection (or
    mutually agree to another arrangement).

# A Brief Comparison of BASICS To current interconnection Regimes

74. A bill and keep regime patterned after the BASICs rules solves
    several problems that are inherent in access charges, reciprocal
    compensation and international settlements. First, such a regime
    eliminates the ability of a network to shifts costs from its
    subscribers to another network. A network can recover its costs from
    another network\'s subscribers only to the extent each of those
    subscribers is willing to accept its charges. By eliminating the
    intrinsic monopoly of access, reciprocal compensation and
    settlements, it also eliminates the chief theoretical justification
    for rate-regulating inter-carrier compensation.

75. Second, forcing networks to bear their own costs has many efficiency
    ramifications. Subscribers and networks, through their subscription
    and entry decisions, control the costs they bear. Under access
    charges a network recovers only a fraction of its costs from its own
    subscribers. Under reciprocal compensation and international
    settlements, a network\'s costs are an average of many networks.
    Under bill and keep, a network\'s costs are determined by its own
    decisions.

76. Third, a bill and keep regime greatly reduces the artificial
    arbitrage opportunities by giving customers the correct market
    signals about whether to build a network and interconnect, or to
    subscribe to an existing network. Under access charges, much traffic
    has moved off the public switched network on to private special
    access networks. The ESP exemption allows enhanced service providers
    to interconnect with local networks as subscribers and thus avoid
    being penalized by the high access charges imposed on IXCs.

77. Fourth, by eliminating the emphasis on the direction of the flow of
    traffic between networks, bill and keep reduces the incentives of
    customers to artificially organize traffic into one-way flows. For
    example, under reciprocal compensation, new networks had a strong
    incentive to seek out customers that only received calls. Under
    settlements, call-back schemes proliferated.

78. Finally, although access, reciprocal compensation and settlements do
    not necessarily lead to artificial per-minute costs being created on
    interconnecting networks, as a practical matter they have inevitably
    transmuted what are capacity costs on one network into real
    per-minute costs on interconnecting networks. It seems fair to say
    that the Internet would not be what it is today if Internet service
    providers had had a per-minute cost structure imposed on them.

79. The access charge regime, of course, was not intended to achieve
    economic efficiency. It was designed to transfer subsidies from IXCs
    (or their customers) to local carriers, in order to reduce local
    rates.[^67] The stated primary purpose was to increase penetration,
    i.e. the percentage of the population that subscribed to telephone
    service, and thus promote universal service. Today, penetration is
    very high except in certain very limited areas.[^68] More
    importantly, the Telecommunications Act of 1996 directed that
    support for universal service no longer be provided through
    cross-subsidies.[^69] Now that the statute has directed that its
    primary purpose should be accomplished by other means, there is no
    longer an over-riding justification for enduring the inefficiencies
    of the access charge regime.

80. The reciprocal compensation regime differs from the access charge
    regime in degree rather than in principle. It may be thought of
    simply as symmetric access charges. The principal difference is that
    reciprocal compensation rates are not explicitly intended to
    transfer substantial subsidies to the terminating carrier, thus they
    tend to be much lower than access charges. On the other hand,
    reciprocal compensation applies to local rather than long distance
    traffic, so these rates are applied to many more minutes than are
    access rates. From a BASICS viewpoint, the costs of terminating
    calls should not be included in reciprocal compensation rates.
    Furthermore, as with access charges, direction of traffic flow is
    irrelevant from a BASICS perspective. The BASICS rule would yield
    much greater efficiency than a reciprocal compensation system.

81. The current system of international settlements is based on the same
    broad approach as access charges. That is, the terminating carrier
    is compensated not only for the incremental costs of
    interconnection, but also for local termination of international
    calls. The monopoly carrier in other countries often sets the
    settlement rates at very high levels, thus aggravating the resulting
    inefficiency.

82. Of the current access regimes, the ESP exemption is the closest to
    BASICS in that it allows Enhanced Service Providers to interconnect
    with LECs by subscribing as end users. Under the right
    circumstances, as noted above, (mutual) subscription is
    approximately equivalent to a BASICS solution.[^70] This solution to
    potential carrier market dominance in these potentially competitive
    markets was generated in the FCC's Computer Trilogy orders. Allowing
    carriers to interconnect on a subscription basis appear to be a
    useful approximation to a BASICS solution.

83. Technological developments are making it more attractive and easier
    for subscribers to exploit arbitrage opportunities offered by the
    differences among these various interconnection regimes. The use of
    Internet-based E-mail has already enabled many users to avoid
    (bypass) use of long distance voice services that are priced
    substantially above costs by substituting a similar, though not
    identical, service. The ESP exemption and reciprocal compensation
    rules favor flat rated (unlimited usage) pricing of ISP
    services.[^71] At the same time, Internet interconnection closely
    resembles a BASICS rule. These factors already make E-mail a very
    low cost alternative to voice services and thus encourage customers
    to substitute away from long distance calls.

84. The ongoing improvement of the quality of Internet Protocol (IP)
    Telephony may greatly exacerbate the trend away from traditional
    long distance voice services. For the same reasons described in the
    previous paragraph, users are able to exploit the arbitrage
    opportunities offered by the differences among the access charge,
    reciprocal compensation and ESP exemption regimes. As IP telephony
    improves, this movement away from long distance can be expected to
    intensify.

85. These developments make the replacement of inconsistent
    interconnection regimes very desirable from the viewpoint of
    economic efficiency and regulatory simplicity. They may also be
    desirable to firms that cannot be sure how future developments will
    interact with the inconsistent regimes. Other future technological
    developments, whose natures are unknown at this time, may have
    substantial additional impacts as long as there are several
    inconsistent interconnection regimes. E-mail and IP Telephony are
    technological developments that have appeared suddenly, having
    become significant only in the past five years. Other problems are
    arising as the concept of access charges is extended to carriers
    with very different costs. Substantial "arbitrage opportunities"
    generated by differences in current interconnection regimes are
    inducing inventors and entrepreneurs to find new ways of providing
    services. These developments can be highly beneficial. To the extent
    they are motivated by differences in regulatory rules applying to
    various types of interconnection, however, they can also result in
    substantial inefficiencies and disruptions. A BASICS interconnection
    regime could replace all current interconnection regimes with a
    simple, efficient solution and offer the benefits of consistent
    treatment of all inter-network interconnection.

# Policy considerations that precluded BASICS-like proposals in the past may no longer apply

86. The history of interconnection policy suggests that a BASICS rule is
    not a radical departure from precedent, and that considerations that
    precluded its adoption in the past may no longer hold. As Brock
    explains, the very first competitive entry into retail long distance
    service relied on interconnection on a basis that is very close to a
    BASICS rule. In the mid-1970s, MCI initially obtained
    interconnection by subscribing to local business line service on
    both ends of MCI's inter-city transport link.[^72] As we noted
    above, at least for simple networks, subscription is equivalent to a
    BASICS interconnection rule.[^73] AT&T responded by creating
    special, higher, interconnection rates, which regulators permitted
    in order to protect the subsidies included in long distance
    rates.[^74]

87. When AT&T began implementing discriminatory rates for
    interconnection, the interim rates were capacity based.[^75] This is
    a rough approximation to a BASICS rule, under which carriers split
    incremental capacity costs equally, although the rates were set
    above cost to preserve the subsidy.

88. DOJ considered long distance service analogous to CPE. When the AT&T
    Divestiture was being negotiated, DOJ's theory was that long
    distance (i.e. interconnection) should be separated from local
    service.[^76] This is our conclusion as well. In discussing
    financial arrangements between the new companies, Brock notes that
    "the simplest solution \[to interconnection\] would have been to
    follow the CPE model and allow any long distance company to connect
    to any local service with no payment other than the established
    local service charge."[^77] This is, of course, equivalent to
    interconnection by subscription, thus very similar to the BASICS
    proposal. This proposal was not adopted because it would have
    "eliminated the complex set of payments among telephone companies
    ..."[^78]

89. In his 1995 paper, Brock also points out that a BASICS-like rule
    would resolve interconnection problems and produce an efficient
    solution compatible with competition. Brock's results, however,
    depend on balanced traffic or negligible termination costs. Our
    analysis above extends this proposal more generally by showing that
    traffic flow and termination costs are irrelevant.

90. BASICS resembles previous proposals and the earliest experience with
    competitive interconnection. The primary reason that these previous
    proposals were not adopted was the driving policy objective of
    protecting subsidy flows to local carriers. This objective has been
    removed by the 1996 Act. BASICS should now be considered as a
    replacement for all current interconnection regimes.

Recent Working Papers Series

Office of Plans and Policy

Federal Communications Commission

A Competitively Neutral Approach To Network Interconnection by Jay M.
Atkinson and Christopher C. Barnekov, Working Paper #34, December 2000,
pp. 30

Bill and Keep at the Central Office As the Efficient Interconnection
Regime by Patrick DeGraba;

Working Paper #33, December 2000, pp. 37

The Digital Handshake: Connecting Internet Backbones by Michael Kende;
Working Paper #32, September 2000, pp. 46

The FCC and the Unregulation of the Internet by Jason Oxman; Working
Paper #31, July 1999, pp. 26

Internet Over Cable: Defining the Future In Terms of the Past, by
Barbara Esbin, Associate Bureau Chief, Cable Services Bureau; Working
Paper #30, August 1998, pp. 130

Digital Tornado: The Internet and Telecommunications Policy, by Keven
Werbach;

Working Paper #29, March 1997, pp. 98

Putting It All Together: The Cost Structure of Personal Communications
Services by David P. Reed;

Working Paper #28, November 1992, NTIS PB93 114882, pp. 86

Changing Channels: Voluntary Reallocation of Television Spectrum by Evan
R. Kwerel and

John Williams; Working Paper #27, November 1992, NTIS PB93 114874, pp.
146

Broadcast Television in a Multichannel Marketplace, by Florence Setzer
and Jonathan Levy;

Working Paper #26, June 1991, NTIS #PB91 201749; \$23.00; pp. 180

What Makes the Dominant Firm Dominant?, by John Haring and Kathy Levitz;
Working Paper \# 25,

April 1989, NTIA PB89 190425; pp. 29

Through the Looking Glass: Integrated Broadband Networks, Regulatory
Policy, and Institutional Change, by Robert Pepper; Working Paper #24,
November 1988, NTIS #PB89 136923; pp. 106

Loosening the Ties that Bind: Regulating the Interstate
Telecommunications Market for the 1990's by Kathleen B. Levitz; Working
Paper #23, February 1987, NTIS #pB87 220265; pp. 52

Competition Policy in the Post-Equal Access Market, by John R. Hering
and Evan Kwerel;

Working Paper #22, February 1987, NTIS PB87 220257; pp. 31

Private Frequency Coordination in the Common Carrier Point-To-Point
Microwave Service, by

John Williams; Workikng Paper #21, September 1986, NTIS PB87 118188/AS;
\$13.95; pp.77

Alternatives for Improved Personal Communications, by James E. McNally,
Jr.; Working Paper #20, August 1986, NTIS #PB87 118170/AS; \$18.95; pp.
92

Promoting Competition Between International Telecommunication Cables and
Satellites by

Evan R. Kwerel and James E. McNally, Jr.; Working Paper #19, Jauary
1986. NTIX #PB86 156288/AS; \$11.95; pp. 75

RECENT WORKING PAPERS ARE AVAILABLE AT [http://www.fcc.gov/](). IN
ADDITION, ABOVE PUBLICATIONS MAY BE ORDERED BY MAIL OR TELEPHONE. PLEASE
INCLUDE NTIS NUMBER (SEE ABOVE) WHEN ORDERING.

International Transcription Services

1231 20^th^ Street, NW

Ground Floor

Washington, D.C. 20036

Telephone Number 202/857-3800

[^1]: This corresponds to the definition of competitive neutrality
    adopted by the FCC for Universal Service purposes. See *In the
    Matter of Federal‑State Joint Board on Universal Service*, CC Docket
    No. 96‑45, 12 FCC Rec'd 8801, ¶47.

[^2]: A recent state of the art presentation of this approach is found
    in Jean-Jacques Laffont and Jean Tirole, *Competition in
    Telecommunications*, MIT Press, 2000. An earlier example is Robert
    D. Willig, "The Theory of Network Access Pricing" in *Issues in
    Public Utility Regulation*, H. Trebing, editor, Michigan State
    University Press, East Lansing, 1979.

[^3]: This is not our only departure from the customary approach. Very
    briefly, our main focus is on cost, rather than demand, and we
    distinguish costs incremental to interconnection from those
    incremental to traffic. We also depart from the typical view of the
    "network externality" problem, as discussed below. We develop these
    points more fully below.

[^4]: Our willingness to consider alternative institutional arrangements
    is uncommon, but not unique. For other recent examples, see Gerald
    W. Brock, "The Economics of Interconnection," Teleport
    Communications Group (1995). The three component articles in this
    publication were placed in the record in CC Docket No. 95-185 as
    attachments to comments by Comcast Corporation, Teleport
    Communications Group and Cox Communications. See also, Patrick
    Degraba, "Bill and Keep at the Central Office As the Efficient
    Interconnection Regime," Office of Plans and Policy, Federal
    Communications Commission, OPP Working Paper No. 33 (December 2000).

[^5]: See Friedrich A. Hayek, "The Use of Knowledge in Society,"
    *American Economic Review*, XXXV, No. 4; September, 1945, 519-30,
    reprinted at
    <http://www.virtualschool.edu/mon/Economics/HayekUseOfKnowledge.html.>

[^6]: Recent history has demonstrated that in the current climate firms
    have difficulty predicting accurately what institutional rules will
    be in their interest in even the relatively short term. For example,
    reciprocal compensation arrangements that incumbent LECs believed
    were favorable to their interests have proved extremely costly. Over
    a span of three or four years, incumbent LECs claim that rapid
    growth in dial up Internet access traffic raised their payments to
    competitive LECs from small amounts to over \$2 billion \[Letter of
    W. Scott Randolph, Verizon Communications, to Magalie R. Salas,
    Secretary, FCC, November 1, 2000 in CC Docket No. 99-68\]. This
    development took incumbent LECs utterly by surprise. At present,
    there is widespread uncertainty about such unknowns as the future
    impact of Internet telephony, broadband markets, changes in
    reciprocal compensation rules, various court rulings, and many other
    factors. This uncertainty seems greater than in the past, making it
    more difficult for firms to be sure what specific rules might later
    turn out to have been in their interest. This may make a general
    reexamination of basic institutional arrangements more feasible than
    usual, because no party can quite be sure what rule it would prefer
    in tomorrow's market. These conditions invite something of a
    "Rawlsian constitutional convention" \[John Rawls, *A Theory of
    Justice*, The Belknap Press of Harvard University Press, 1971\] in
    which parties seek a "fair game" because they do not know what their
    future interests will be.

[^7]: For the history and background of the development of current
    institutional arrangements, see Gerald W. Brock, *Telecommunication
    Policy For the Information Age: From Monopoly to Competition,*
    Harvard University Press, 1994.

[^8]: Interconnection can be viewed as the means by which nascent
    competitive networks obtain vital inputs from dominant, incumbent
    networks. *See generally* *In re* Implementation of the Local
    Competition Provisions of the Telecommunications Act of 1996, CC
    Docket No. 96-98, *Report and Order*, 11 FCC Rcd. 15,499, 16,012-13
    (1996) (Local Competition Order), *rev'd in part on other grounds*,
    Iowa Utilities Board v. FCC, 120 F.3d 753 (8th Cir. 1997), *rev'd*,
    AT&T v. Iowa Utilities Board, 119 S. Ct. 721, 733, 738 (1999).

[^9]: The economics literature generally does not address this type of
    cross-subsidization. It focuses, rather, on "Ramsey pricing," which
    seeks to minimize the inefficiency caused by recovering common costs
    through prices above marginal cost. The Ramsey solution raises
    prices most on those customers who have low demand elasticity. For a
    typical application, see Laffont and Tirole, fn 2 *supra.*

[^10]: Much of the economics literature of interconnection expresses
    this universal service policy as correcting a network externality.
    That is, all users benefit when another user is added to the
    network, because they all have access to the new user. The potential
    new user, however, compares the price she is required to pay only to
    her private benefits, ignoring the "external" benefits to other
    users. This is the theoretical basis for advocating a subsidy that
    lowers the price in order to correct for the externality. For
    typical treatments, see Robert D. Willig, , fn 2 *supra,* and
    Laffont and Tirole, fn 2 *supra*.

[^11]: Codified at 47 USC 254(b)(5).

[^12]: As a bonus, this solution eliminates the danger of a dominant LEC
    extending its market power to monopolize interconnected markets.
    This is a major concern in the literature, and a very difficult
    problem under the access charge interconnection regime. See, e.g.,
    Gerald W. Brock, "Interconnection and Mutual Compensation with
    Partial Competition," in Brock (1995), fn 4 *supra*; Laffont and
    Tirole, fn 2 *supra,* especially chapter 5.

[^13]: For illustrations see the background and discussion sections of
    *Access Charge Reform* *First Report & Order*, FCC 97-158.

[^14]: Perhaps the most vivid current example is the phenomenal growth
    of CLECs specializing in terminating ISP-bound traffic. See comments
    submitted in *In the Matter of Inter-Carrier Compensation for
    ISP-Bound Traffic*, CC Docket No. 99-68 and CC Docket No. 96-68.

[^15]: Robert Frost may have dabbled in economics on the side. See
    *Mending Walls*, reprinted at
    <http://www.english.upenn.edu/~afilreis/88/frost-mending.html>

[^16]: This process used to be called "bypass," meaning that a customer
    avoids paying an above-cost subsidy by finding an alternative means
    of interconnecting. The currently more fashionable term is
    "arbitrage," which encompasses more broadly numerous methods of
    exploiting differences in regulation among alternative services. A
    current example is the concern of many that advances in "Internet
    telephony" will encourage callers to avoid the entire "access"
    regime.

[^17]: Even if they could gather the data, it would be out of date
    before they could assemble it. The genius of markets is their
    ability to make rapid, decentralized decisions that are efficient.
    See Hayek, fn 5 *supra*.

[^18]: The recent rapid growth in ISP minutes subject to reciprocal
    compensation agreements between incumbent LECs and competitive LECs
    is a compelling illustration of the result of a "small" error in
    setting compensation rates and structure.

[^19]: See 47 USC 254(g) and *Implementation of Section 254(g) of the
    Communications Act of 1934, as amended*, CC Docket No. 96-61 (FCC
    96-331).

[^20]: In effect, such policies give every LEC a monopoly over access to
    and from its end users. *See LEC Pricing Flexibility Order and
    NPRM*, 14 FCC Rcd at 14316-17, para. 186.

[^21]: In fact, the entire concept of the "directionality" of a call is
    rapidly becoming highly ambiguous, if not entirely meaningless. In
    international telephony, for example, the prevalence of arrangements
    such as "call-back plans" make it very difficult to identify "true"
    causation. Similarly, what is the direction of causation when a
    person returns a call in response to an answering machine message
    (or an E-mail)? This point is discussed in Degraba, fn 4 *supra*.
    For an Internet-related analysis, see Michael Kende, \"The Digital
    Handshake: Connecting Internet Backbones,\" FCC Office of Plans and
    Policy Working Paper No. 32, September, 2000, p. 36ff.
    <http://www.fcc.gov/Bureaus/OPP/working_papers/oppwp32.pdf>.

[^22]: We do address below an end user pricing problem related to
    interconnection with a dominant LEC.

[^23]: This is discussed in considerably greater detail in Brock (1994),
    fn 7 *supra*, Chapter Six.

[^24]: The term "right," as used in this paper, should be understood as
    shorthand for socially efficient, that is, economically efficient
    taking into account any external costs or benefits.

[^25]: Other analysts have also noted this problem. "The twin objecives
    of allocative and productive efficiency cannot both be attained by
    the single instrument of the access price, so the aim is to achieve
    the optimal tradeoff." Mark Armstrong and John Vickers, "The Access
    Pricing Problem with Deregulation: a Note," *The Journal of
    Industrial Economics*, XLVI, March 1998, p. 116.

[^26]: Gerald W. Brock, "Price Structure Issues in Interconnection
    Fees," in Brock (1995), fn 4 *supra*.

[^27]: Brock (1994), fn 7 *supra,* discusses how AT&T successfully used
    this strategy in the early 1900s to build a monopoly.

[^28]: See Brock (1995), fn 4 *supra,* for an extensive discussion of
    these problems, particularly in an access charge regime.

[^29]: Kende (2000), fn 21 *supra,* discusses these incentives in the
    context of a competitive market, i.e. the Internet.

[^30]: Among these are litigation expense, delay, uncertainty,
    opportunities for "rent-seeking" behavior by interested parties, and
    the real possibility of error, even assuming regulators are both
    highly intelligent and benevolent.

[^31]: Competition forces carriers to price according to their costs and
    cost structure. See Gerald W. Brock, "Price Structure Issues in
    Interconnection Fees," in Brock (1995), fn 4 *supra,* illustrates.
    If a carrier is market dominant, of course, it may not pass correct
    pricing signals to its customers. As discussed above,
    interconnection policy alone cannot cure underlying market structure
    problems such as dominance, but it can be an important step toward
    resolving such problems. An inefficient interconnection policy, in
    contrast, virtually guarantees that customers will face incorrect
    pricing.

[^32]: The Coase Theorem states that parties will negotiate efficient
    solutions to rights allocation problems, so long as the rules are
    clearly stated and transactions costs are low. Coase's Theorem was
    foreshadowed in Ronald H. Coase, "The Federal Communications
    Commission," *Journal of Law and Economics*, v.2 (1959), pp. 1-40,
    and then made explicit in his \"The Problem of Social Cost ,\"
    *Journal of Law and Economics* v. 3, no. 1 (1960), pp. 1-44. Coase
    won the Nobel Prize in Economics in 1991 "for his discovery and
    clarification of the significance of transaction costs and property
    rights for the institutional structure and functioning of the
    economy." \[Press release of The Royal Swedish Academy of Sciences,
    October 15, 1991, at
    <http://www.nobel.se/economics/laureates/1991/press.html> .\]

[^33]: In addition to the linear network, we examine a mesh network and
    a fiber optic ring connecting central offices of any configuration.

[^34]: We relax this "non-blocking" assumption later. We will also relax
    the assumption that the "subscribers" represent individuals rather
    than, say, central offices.

[^35]: We use this term here as shorthand to represent the facilities
    (link and switching) needed to route one conversation between two
    adjacent subscribers. The astute reader will soon note that for
    linear networks we are using a slightly different definition of
    urlink that now includes some switching capabilities, enough to
    route calls. We think it less confusing to recycle the term than to
    invent another, and we use the term only for counting basic
    facilities requirements, not for comparisons between different
    network topographies.

[^36]: One such technique is engineering to accept more than zero call
    blocking. We address this possibility below, but for now maintain
    the zero blocking assumption.

[^37]: Mesh and ring networks, of course, have built-in redundancy for
    improved reliability.

[^38]: That is, a call attempt might fail because the called party's
    line is already busy, but not because of circuit blockage.

[^39]: A mathematical proof is fairly simple. In the "worst case," which
    requires the most links, the parties in the center of the network
    call each other, then the next nearest pair, continuing until the
    pair at the extreme ends of the network call each other. The
    "center" call requires one link, the next requires three, and the
    *i*th call requires (2*i*-1) links. For a network of n subscribers,
    in which the maximum number of possible calls is n/2, the "extreme"
    call requires 2(n/2) --1 = n-1 links. The sum of all the required
    links is
    $\sum_{}^{}{(2i - 1) = 2\sum_{}^{}{i - \frac{n}{2}}} = 2\left\lbrack \frac{\left( \frac{n}{2} \right)^{2} + \left( \frac{n}{2} \right)}{2} \right\rbrack - \frac{n}{2} = \left( \frac{n}{2} \right)^{2}$.

[^40]: The network is unable to discriminate among subscribers, because
    any subscriber could drop from or join the network. Thus each is
    potentially a "marginal" subscriber.

[^41]: More generally, because the number of links is (n/2)^2^ = n^2^/4,
    the average number of links per subscriber is always n^2^/4/n = n/4.
    As the number of subscribers increases, each subscriber benefits
    from being able to call more people, but the "raw" capacity needed
    per subscriber rises. We are abstracting from the engineering
    techniques that can offset this diseconomy of scale in real
    networks.

[^42]: More generally, if a linear network with *a* subscribers
    interconnects with a linear network of *b* subscribers, the number
    of incremental links required is *ab*/2. Recall that the total links
    needed to meet our two requirements (enabling all possible
    connections and the maximum possible number of simultaneous
    conversations) is n^2^/4. If the size of the interconnected network
    is n = *a* + *b* , the total links requirement is (*a* + *b*)^2^/4 =
    (*a*^2^ + 2*ab* + *b*^2^)/4. Before interconnection, the two
    separate networks needed *a*^2^/4 and *b*^2^/4 respectively. Thus
    the number of incremental links required for interconnection is the
    difference, 2*ab*/4 or *ab*/2.

[^43]: A difficult problem in access regimes, and even in some forms of
    bill and keep proposals, is that, when traffic is primarily
    "inbound," an end user may have an incentive to claim it is a
    network in order to avoid bearing transport costs. If traffic is
    primarily "outbound," a network may wish to claim it is an end user
    for the same purpose. See Degraba, fn 4 *supra*.

[^44]: Networks or users can often arrange their traffic flow to make it
    appear mainly inbound when doing so is advantageous. See fn 21
    above.

[^45]: A bit of simple algebra shows that, for linear networks, the
    average cost increase for subscribers to one interconnecting network
    is always equal to ¼ link per subscriber on the other network.
    Splitting the incremental cost of interconnection equally, each
    network would be responsible for an additional *ab*/4 links (half
    the total increment of *ab*/2). For network X, the average cost
    rises by *ab*/4*a* = *b*/4. Similarly, the average cost on O rises
    by *ab*/4*b* = *a*/4 links per subscriber.

[^46]: This result also generalizes to interconnection between two
    linear networks of any size. Recall from the previous footnote that
    the number of incremental links necessitated by interconnection of a
    network of *a* subscribers with a network of *b* subscribers is
    *ab*/2. If this increment is assigned equally to the two networks,
    their respective *total* numbers of links will be *a*^2^/4 + *ab*/4
    and *b*^2^/4 + *ab*/4. To obtain their average links per subscriber,
    we divide each network's total capacity by its number of
    subscribers. We obtain, respectively, (*a*^2^ + *ab*)/4*a* and
    (*b*^2^ + *ab*)/4*b*. Each of these expressions reduces to (*a* +
    *b*)/4. Thus if the incremental links are split equally, each
    network ends up with the same average number of links per
    subscriber, regardless of their respective sizes. No other
    allocation of incremental links will produce this equality. This
    equality of links per subscriber also results if this rule is
    applied to mesh networks or to fiber optic rings (see Section \[VI\]
    below).

[^47]: More generally, because the previous footnote demonstrated that
    splitting incremental links equally produces equal average burdens
    regardless of the sizes of the separate networks, adding any
    additional costs would produce an unstable outcome.

[^48]: If we relax our assumption that all subscribers are identical,
    this result could be a stable outcome in that Network X attracts
    those who are willing to accept lower quality service in return for
    a lower price.

[^49]: This term is used here not in its legal sense, but in the
    economic sense of a price above marginal cost.

[^50]: In fact, the average cost (price) difference is 0.25 urlinks,
    precisely as before interconnection. This can be understood as the
    premium O subscribers pay for a higher (non-blocking) quality of
    service. The fact that the difference is precisely unchanged depends
    on the assumption that the two networks are of equal size. In the
    more general case, the magnitude of the difference might change, but
    the direction would not (the more expensive network would remain
    more expensive, thus a quality premium would remain).

[^51]: That is, we would expect the demand for calls to be a function
    of, among other things, the number of parties who can be called.

[^52]: Recall that we are abstracting from designed redundancy in our
    simple network.

[^53]: Some "legacy" copper or microwave links have not yet been
    replaced.

[^54]: Recall that our urlinks include a bit of incremental switching
    capability. We believe this would amount only to a modest increase
    in switch memory (to accommodate larger look-up tables) and possibly
    a dash more processor. Our understanding is that rates for transport
    links (trunks) and entrance facilities include the switch
    rearrangements necessary to enable the switch to recognize and route
    calls to and from the links. In a dispute resolution, we would
    suggest that a regulator or arbitrator adopt the incremental-only
    costing approach that FCC applied in the Local Number Portability
    proceedings, which would explicitly reject any allocation to
    interconnection of the "common costs" of a switch. See In the Matter
    of Telephone Number Portability, Cost Classification Proceeding, CC
    Docket No. 95-116, In the Matter of Telephone Number Portability,
    *Third Report and Order*, 13 FCC Rcd 11701, 11740 (1998).

[^55]: We consider the case of differences in link costs in the next
    section.

[^56]: The algebra is reasonably straightforward, but somewhat tedious.
    That is, an economist with low opportunity costs could work it out
    on the back of a very large envelope, but few lawyers would be
    willing to follow it. These results do depend on making a strong
    assumption that expected call attempts are uniformly distributed. On
    the other hand, the most likely alternative to this assumption would
    be that subscribers are, if anything, somewhat more likely to call
    others on their own network. This is because networks are more
    likely than not to be formed initially among subscribers who share
    some community of interest (if only location). To the extent that
    intra-network calls are more prevalent, our results are
    strengthened.

[^57]: That is, markets without externalities. Gerald W. Brock,
    "Interconnection and Mutual Compensation with Partial Competition,"
    p. 10, in Brock (1995), fn 4 *supra.*

[^58]: "Introductory" rates for new subscribers are often even lower. In
    this case, however, the firm may hope to retain the new subscriber
    as a long term customer, a slightly different motivation.

[^59]: Broadcasters are, of course, regulated in several ways, but their
    pricing is generally unregulated.

[^60]: Using the same variables and approach as for the linear network
    in footnotes \[42ff\] above, we find that the incremental urlinks
    required to combine a network of *a* subscribers with a network of
    *b* subscribers is, for mesh networks, *ab*. So each network would
    be responsible for half, *ab*/2. Network X starts with
    (*a*^2^-*a*)/2 links and adds *ab*/2. Dividing by *a* subscribers
    produces an average urlink "cost" of (*a*^2^ -- *a -- ab*)/2*a*,
    which reduces to (*a + b* - 1)/2. Similarly, Network O begins with
    (*b*^2^-*b*)/2 urlinks and adds *ab*/2. Dividing by *b* subscribers
    produces (*b*^2^ -- *b + ab*)/2*b.* This reduces, again, to (*a + b*
    -- 1)/2.

[^61]: Imagine a constellation of central offices connected by a fiber
    optic ring. The total number of subscribers (sum of all central
    offices) is n. The average size of a central office is s
    subscribers. In order to be non-blocking, the \"width\" of the ring
    has to be n (a ring has built-in redundancy for reliability). Thus
    the number of central offices is n/s. The number of urlinks needed
    to make up the ring is (n)(n/s) = n^2^/s.

    Now suppose two networks of central offices interconnect. The total
    numbers of subscribers on the networks are *a* and *b*,
    respectively. Assuming s is the same for each network, the networks
    begin with *a*^2^/s and *b*^2^/s links respectively. The incremental
    ring-links are the difference between the requirement before and
    after interconnection, or (*a+b*)^2^/s -- *a*^2^/s -- *b*^2^/s =
    2*ab*/s. If we split this number equally, each network is
    responsible for *ab*/s additional ~ur~links. So the number of
    ~ur~links for the first network is now *a*^2^/s + *ab*/s and its
    average ~ur~links per subscriber is (*a^2^ + ab*)/*a*s = (*a +
    b*)/s. For the second network, the number of ~ur~links is now
    *b*^2^/s + *ab*/s and its average ~ur~links persubscriber is
    (*b*^2^ + *ab*)/*b*s. This reduces again to (*a + b*)/s.

[^62]: Another common network form is the "star," in which there is one
    link (loop) from each subscriber to the central office. We view this
    simply as an engineering solution that provisions the basic,
    underlying urlink requirement by employing more switching and fewer
    links. All the switching is concentrated in the central office. Star
    networks have desirable efficiency properties under some
    circumstances, but their geographic size is limited by their need
    for longer links as the service area expands. As "constellations" of
    stars are linked into a larger network, the results resemble a
    linear, mesh or ring network, depending on just how they are linked.

[^63]: The problem is that, while we can represent urlink requirements
    for simple network types mathematically, we are not sure how to
    represent the requirements for a generalized network.

[^64]: Recall that virtually all inter-network transport today is
    provisioned by optical fiber, regardless of the technology of the
    interconnecting networks. Even between two wireless networks,
    interconnection is generally via fiber links. Thus the costs that
    are purely incremental to interconnection are generally independent
    of the internal technologies of the interconnecting networks.

[^65]: For convenience we assume here that the networks are pricing at
    average cost, even though it would be more accurate to say that the
    networks are bearing these per-subscriber burdens and recovering
    them in some unspecified manner.

[^66]: See Gerald W. Brock, "Price Structure Issues in Interconnection
    Fees," in Brock (1995), fn 4 *supra*; and *Policy and Rules
    Concerning Rates for Competitive Common Carrier Services and
    Facilities Authorizations Therefor*, First Report and Order, 85 FCC
    2d 1, 31-35 (1980) (discussing reasons it is unnecessary to regulate
    the rates of non-dominant carriers).

[^67]: See Brock (1994), fn 7 *supra*, especially chapter ten.

[^68]: See FCC, *Universal Service Monitoring Report*, CC Docket No.
    98-202, September 2000, Section 6.

[^69]: 47 USC 254(b)(5).

[^70]: See paragraph 35 above.

[^71]: The ESP exemption prevents carriers from charging per minute
    access charges on ISP traffic. The reciprocal compensation rules
    encourage competitive LECs, in particular, to offer attractive terms
    to ISPs who will attract large volumes of terminating traffic, and
    thus large amounts of revenue, from incumbent LECs.

[^72]: Brock (1994), fn 7 *supra*, pp. 124-127.

[^73]: See discussion at paragraph 35 above. This is a bit of an
    oversimplification, of course, in that subscription typically
    includes services that may be bundled and that may not be useful to
    an interconnecting carrier.

[^74]: This is a highly simplified summary of a rather complex
    discussion in Brock (1994), fn 7 *supra*, chapter 8.

[^75]: These were the initial Exchange Network Facilities for Interstate
    Access (ENFIA) rates. See Brock (1994), fn 7 *supra*, p. 142.

[^76]: Brock (1994), fn 7 *supra*, p. 175.

[^77]: Brock (1994), fn 7 *supra*, p. 176.

[^78]: Brock (1994), fn 7 *supra*, p. 176.