ASCAP VERSUS BMI (VERSUS CBS): MODELING COMPETITION BETWEEN AND BUNDLING BY PERFORMANCE RIGHTS ORGANIZATIONS.

KLEIT, ANDREW N.

ANDREW N. KLEIT [*]

Bundling has been a long-standing issue in industrial organization. In recent years, bundling has gained renewed controversy as it has been employed by computer software manufacturers. This article examines BMI v. CBS (1979), which dealt with bundling by performance rights organizations (PROs). A model of competition between PROs using blanket licenses is presented. The usage of blanket licenses is shown to generate both higher profits for PROs and higher costs for the users of musical compositions when there are a small number of competing PROs. In addition, the model explains why blanket licenses are observed in unregulated PRO markets. (JEL L41, K21)

I. INTRODUCTION

The question of bundling has been a longstanding issue in industrial organization economics, dating back at least to Stigler [1963]. This article looks at bundling in the context of the famous antitrust case, BMI v. CBS, 441 U.S. 1 (1979). The defendants in the case were two performance rights organizations (PROs), the American Society of Composers and Publishers (ASCAP) and Broadcast Music, Inc. (BMI). PROs monitor the usage of copyrighted songs by users of music, collect fees from those users, and pay member composers whose songs are played. PROs have historically offered "blanket licenses" where, for a certain fixed fee, a station can use all the music in a PRO's catalog. Blanket licenses are thus equivalent to "bundling," or "block booking." At issue in the case was CBS's petition to require PROs to switch from offering blanket to per-use licenses, where a station would pay per usage for each composition.

Here I will model competition between PROs using either blanket or per-use licenses. PROs will compete against each other, both for the compositions of songwriters and for offering their products (licenses for compositions) to producers of television programs. I will show the circumstances under which the usage of blanket licenses generates higher profits for the PROs and/or higher costs for the users of musical compositions. I will also show which license is likely to arise in equilibrium, helping explain why CBS felt compelled to sue BMI, of which it was a part owner, as well as the reluctance of ASCAP to issue attractive "per-program" licenses, as an antitrust consent decree nominally requires it to do.

Bundling in general and the economic questions raised by the BMI case are staples in the economics of industrial organization and antitrust (see, for example, Kaserman and Mayo [1995, 173-4]). Yet up to this time there has apparently been little modeling of bundling of several products by competing firms. In addition, there has been little written on competition between PROs, an important exception being Besen et al. [1992]. Even that article does not formally examine the competition between PROs and the differentiated products they sell to their users. This article attempts to fill this void.

The remainder of the article is organized as follows: Section II briefly describes the origins of the major PROs and the questions raised by the BMI litigation. Section III generates a market equilibrium for PROs using blanket licenses. Section IV generates an equilibrium using per-use licenses and compares that equilibrium to the one derived in section III. Section V discusses which form of license will arise in equilibrium, and section VI contains some concluding remarks.

II. THE ORIGINS OF PROS AND THE CBS LITIGATION

The Origins of PROs

PROs exist because of the following problem: Copyright owners of compositions have property rights to their material, and therefore no one is allowed to use that material without the payment of agreed-on fees. Thus, any time a copyrighted song is played for commercial purposes the copyright owner is entitled to compensation. But it would be very costly for live theater owners, and later radio and television stations, to locate and pay the copyright owner of each score, just as it would be very difficult for copyright owners to monitor users to determine if their compositions are being played. PROs have copyright owners as their members (or clients), and such owners rely on PROs to collect revenues on their behalf.

PROs monitor musical productions and issue licenses to broadcasters and other users. Composers are paid based on observed usage in the monitoring process at a similar rate. The fees paid by users are not a function of the identity of the composer, and PROs do not allow composers to offer different rates for compositions licensed through a PRO. [1] Generally, composers belong to only one of three competing PROs. [2]

The Copyright Act of 1897 gave composers the right to charge for the public performance of their music. However, no mechanism was established to collect fees for such performances. ASCAP was born in 1913 from the desire of a group of Broadway composers to collect fees when their songs were performed on "Tin Pan Alley." The initial group of ASCAP customers--theaters, dance halls, hotels, taverns, and later radio stations--were usually unaware of which songs would be performed in their venues; if they were, it was only with a limited amount of notice. To solve this problem, ASCAP created blanket licenses. Traditionally, blanket license fees have been set to be a percentage of the gross revenues of a particular venue.

ASCAP was a struggling organization until the popularization of radio in the late 1920s. Through the 1930s ASCAP rates and revenues climbed. During this period, rates charged by ASCAP for a blanket license rose from 2% to 7.5% of radio broadcasters' gross revenues [Cirace 1978, 287]. Finally, in 1939, the National Association of Broadcasters, working together with NBC and CBS, created BMI.

ASCAP is a not-for-profit entity owned by its composers, but BMI is a not-for-profit entity owned by broadcasters. In contrast, a third PRO, SESAC, founded in 1930, is a for-profit organization. SESAC specializes in country and Latin music and, until recently, has not been of great importance in the performance rights field. In the early 1990s, however, SESAC's longtime family ownership was replaced with entrepreneurs, who have aggressively marketed the firm. In particular, SESAC has begun paying substantial bonuses (sometimes in the hundreds of thousands of dollars) to induce composers to sign up with it.

Current market shares are extremely difficult to obtain. Krasilowsky and Shemel [1995] estimated ASCAP with around 53% of the market, BMI with 40%, and SESAC about 7%, implying a market Herfindahl index of around 4,458. Together, the three PROs appear to have several millions of songs in their catalogs. Though it is difficult to obtain data, Herfindahl indices for years prior to the growth of SESAC in the 1990s are likely to be higher than current levels.

Competition among PROs is relatively unusual. In other countries, PROs are generally regulated monopolists with fees set by some type of regulatory body. The only exception to this rule (besides the United States) is Brazil, where up to nine PROs compete against each other (see Besen and Kirby [1989]).

PROs, Antitrust, and the CBS Litigation [3]

In 1941 both ASCAP and BMI signed consent decrees with the Justice Department prohibiting them from acquiring exclusive rights to copyrights. Thus, composers could both be a member of one of these PROs and choose to sell performance rights to their works directly to an end user. ASCAP and BMI were precluded from discriminating among users and among contract terms to composers. This latter constraint precludes ASCAP and BMI from offering bonuses to composers, as SESAC is currently doing.

A 1950 Consent Decree between the Justice Department and ASCAP established a "rate court" (the Federal Court in the Southern District of New York) where ASCAP or its users could propose or challenge a rate. BMI, however, signed no such agreement until 1995. This rate court was not used to set an actual ASCAP rate until the late 1980s.

In 1941 ASCAP issued its first licenses to television, albeit ones requiring no licensing fee to aid television during its experimental phase. In 1948 ASCAP canceled these licenses and announced that it would charge a fee for the use of its music on television. BMI soon followed. Until about 1969 the television

networks and the PROs appeared able to reach agreement as to the level of fees and the structure of the contract. In 1969, however, NBC applied for the right to use 2,217 individual ASCAP songs. The rate court, however, refused to order such a license. [4] NBC accepted this decision and proceeded no further.

At the end of 1969, CBS brought suit against both ASCAP and BMI, alleging that the licensing practices used by both PROs constituted illegal price fixing and asking for a remedy that the PROs only offer per-use licenses. [5] The surface logic of CBS's claim is apparent. Particular songwriters clearly compete against each other (though perhaps not against all other songwriters), and PROs bring songs together and "fix" the prices of competing songs. CBS's proposed remedy, that PROs offer only per-use licenses, however, was contrary to the underlying price-fixing claim. Per-use licensing where the PRO sets the per-use fee is just as much "price fixing" (perhaps more so) than blanket licenses. Thus, while CBS contended that its case dealt with price fixing, its real motivation was to eliminate bundling in the market.

The district court found that because the PROs did not require exclusive dealing (as a composer can use both a PRO and individually license his or her own music), their actions did not constitute a restraint of trade (CBS v. ASCAP, 400 F. Supp. 737 [1975]). The appeals court, however, in a confusing decision, ruled that blanket licenses constituted price fixing and therefore were a per se violation of the Sherman Act (CBS v. ASCAP, 562 F.2d 130 [1977]). Part of the confusion stemmed from the appeals court's inability to devise a remedy that did not also constitute price fixing.

In 1979 the Supreme Court ruled that blanket licenses did not constitute a per se offense. [6] It remanded the case to the lower courts, asking for a decision on whether blanket licenses constituted a rule of reason antitrust violation. Upon remand, the appeals court agreed with the original district court opinion that blanket licenses did not constitute a restraint of trade and therefore found against CBS (CBS v. ASCAP, 620 F.2d 930 [1980]). The Supreme Court then refused to grant CBS's petition for certiori (450 U.S. 970 [1981]).

The decision of CBS to sue the PROs generates two important questions. First, why did CBS prefer the per-play license over the blanket license? Stigler [1963] shows that bundling can serve to extract surplus from consumers with negatively correlated demands. This argument could apply to the radio market, where, for example, a country and western station would have significantly different demands from a rock and roll station. But the case concerned television, and the three television networks at that time would seem to have had similar preferences. [7]

Second, why did CBS feel compelled to sue? BMI is governed by a board of directors of network representatives, and CBS, as a part owner of BMI, generally has representation there. It would seem that if blanket license harmed demanders, those demanders, as co-owners of BMI, would have arranged for BMI to change the way it packaged its product.

Sections III and IV generate a model that answers the first question--why the demanders would prefer per-use licenses. Section V presents an explanation for why CBS may have felt it necessary to sue in court to obtain this outcome, rather than act through BMI's board of directors. [8]

III. BLANKET LICENSES

The interaction between producers, composers, and PROs will be modeled in a five-step, one-shot [9] game along the following lines:

1. PROs compete to sign up composers as members. However, when a composer joins a PRO, the PRO does not know where that composer's songs will be located in the product space. This modeling assumption is meant to represent the terms of the 1941 Consent Decrees between ASCAP, BMI, and the Justice Department, which preclude those PROs from discriminating among composers. The decrees effectively require both PROs to take all composers who wish to join them. In this model, each PRO will offer a price to all composers, regardless of their identities, and therefore their expected product location.

2. (Simultaneous with Step 1) PROs sell either blanket or per use licenses to producers of (in this model) television programs. (From here on, producers will be referred to as "demanders.") In the model of section III, PROs set the price of the entire blanket, which provides the demander with unlimited play of the PRO's catalog. Alternatively, if per-use licenses are used, as in section IV, PROs decide what price to charge for the use of one playing of one song.

3. Composers write songs that compete against each other. Songs are differentiated products [10] and so will be modeled using the circle approach of Salop [1979]. At this point songs will be assumed to be distributed evenly across the unit circle. Later in this section, even distribution of songs across the unit circle will be shown to be an equilibrium. [11]

4. Demanders discover their location in the product space. That is, the demanders determine what product characteristic best meets the needs of their particular program. Demanders choose which songs to put on their programs. If a per-use license is used, fees are then paid to the relevant PRO.

5. PROs pay royalties to composers whose songs were used by demanders.

I will assume, consistent with the consent decree provisions that govern behavior by ASCAP and BMI, that PROs cannot choose to concentrate their efforts on particular parts of the product space by signing up composers who specialize in one area. I will also model all PROs as profit-maximizing firms.

Using the Salop [1979] circle model, assume N songs (N an integer) distributed evenly around a unit circle. [12] (Step 3 will show even distribution to be an equilibrium.) Thus, the distance between each song is 1/N. In Figure 1, for example, eight songs are distributed uniformly around a circle, spaced 1/8 units apart. Let i index the number of PROs, = 1,2, ... , r, where r is the total number of PROs, r [less than] N. Let R equal the average payment to risk-neutral competitive composers.

Assume there is one representative producer ("demander") of one television show. The demander desires to use one song on her program. [13] While she knows that she will need one song, her optimal song (or "optimal song position") is distributed randomly and uniformly across the unit circle, until it is revealed to her at the beginning of Step 4. Because it is unlikely that the precise song a producer wants is available, the producer will have to "travel" across the unit circle to "reach" a song. The cost of travel will be assumed to have quadratic form, following Levy and Reitzes [1992], equaling [k.sub.1][d.sup.2], where [k.sub.1] is a positive constant and d is the distance traveled. In this section, PROs will be restricted to offering only blanket licenses. I am now in a position to solve for the equilibrium of this model step by step.

Step 5: Paying the Composer

Average payments to composers are R, and there are N composers. Since, however, only one song is used, the one composer of that song receives payment RN.

Step 4: Selecting the Song to Be Played

With blanket licenses, the demander will pick the song "closest" to her desired product once she realizes what that product is. For example, assume that the demander's position on the unit circle is at a point X in Figure 2. Assume, without loss of generality, that the songs are numbered so that the song to the immediate left of X, "the left-hand song," is at point 0, while the song to the immediate right of X, the "right-hand song," is at point 1/N. Also assume the demander has blanket licenses for both songs.

With no marginal fee for the use of a song, the demander will choose the song closest to X. If X [less than] 1/(2N), the demander is closer to the "left-hand" song and will "travel" a distance X to obtain her song, incurring travel costs of [k.sub.1][X.sup.2]. If X [greater than] 1/(2N), the demander will travel distance (1/N) - X to obtain her song, at a cost of [k.sub.1][[(1/N) - X].sup.2].

Step 3: Even Spacing of Songs around the Circle Is an Equilibrium

Assume a composer who writes a song labeled here c. Let [M.sub.c] equal the closest distance song c is to another song on the unit circle. Let each PRO assess a membership fee for composers equal to [[epsilon].sup.*]((1/N) - [M.sup.c])), [epsilon] [greater than] 0. The rationale for this assumption is as follows: With quadratic costs, it can be shown that consumer travel costs rise, and therefore payments to a particular PRO fall, if the songs of that PRO are not evenly spaced, while the songs of the other PROs are. If songs are evenly spaced, the (minimum) distance between songs will equal (1/N). An up-front fee negatively related to the distance between songs will encourage composers to write songs as "different" as possible.

PROPOSITION 1. Even spacing of songs around the unit circle constitutes a Nash equilibrium.

Proof. Consider any three songs in a row, song one (without loss of generality) at position 0, song two at some position P, and song three at position 2/N, 0 [less than] P [less than] 2/N. Song two is used by all demanders who land in the segment ([X.sub.1], [X.sub.2]), where [X.sub.1] represents the indifference point for the demander between songs one and two, and [X.sub.2] represents the indifference point for the demander between songs two and three. Given a circle of unit length, the probability that a demander will use the second song is therefore [X.sub.2] - [X.sub.1]. With quadratic travel costs and zero marginal fees to the relevant PROs, the definitions of [X.sub.1] and [X.sub.2] imply

(1) [k.sub.1][([X.sub.1] - 0).sup.2] = [k.sub.1][(P - [X.sub.1]).sup.2]; [X.sub.1] = .5P,

(2) [k.sub.1][([X.sub.2] - P).sup.2] = [k.sub.1][((2/N) - [X.sub.2]).sup.2];

[X.sub.2] = (l/N) + .5P, [X.sub.2] - [X.sub.1] = 1/N.

Thus, the composer of song two always has his song played 1/N of the time wherever the song is located in (0, 2/N). Without loss of generality, assume that if the composer deviates from the position P = 1/N, he only moves toward position 0. P is now in (0, 1/N), and P = [M.sub.c]. The expected payoff [[pi].sub.c] to the composer is now [[pi].sub.c] = (RN)(1/N) - [[epsilon].sup.*]((1/N) - P), which is maximized with respect to P at P = 1/N. [14] Q.E.D.

Step 2: Calculating the Charge for the Blanket License

Let the PRO make a "take it or leave it" offer, consistent with Stigler [1963], of a blanket license to the demander. The charge for the blanket license will therefore be the expected travel costs to the demander without a license from a particular PRO minus the expected travel costs to the demander with that license. To calculate expected travel costs in a particular circumstance for the demander, it is first necessary to calculate expected travel costs for the demander if she lands in a segment on the unit circle of any given length, as addressed by Proposition 2.

PROPOSITION 2. Assume N songs evenly distributed on the unit circle where the cost of traveling a distance d is [k.sub.1][d.sup.2], [k.sub.1] [greater than] 0. Assume the demander finds herself in a segment of length A/N, A [less than or equal to] N, A and N are positive integers. Assume that the demander's location on the segment is uniformly distributed. Expected travel costs for the demander, ETC(A, N), will be [k.sub.1][A.sup.2]/(12[N.sup.2]).

Proof. Consider any segment on the circle running from 0 to A/N. Assume the demander lands at spot X on that segment. With quadratic costs, travel costs, TC, for the demander will therefore be TC = [k.sub.1][{min(X, (A/N) - X)}.sup.2]. Using symmetry, consider only those values of X [less than or equal to] A/(2N). Total travel cost will now equal TC = [k.sub.1][X.sup.2]. Expected travel costs ETC(A, N) are therefore

(3) ETC(A, N) = [[[integral].sup.A/2N].sub.0] [k.sub.1][X.sup.2]pdf(X)dX,

where pdf(X) represents the probability distribution function of X. Because the demander is restricted to the line segment [0, A/(2N)] and X is uniformly distributed, pdf(X) = 2N/A, and therefore equation (3) implies ETC(A,N) = [k.sub.1][A.sup.2]/(12[N.sup.2]). Q.E.D.

Given Proposition 2, I can now calculate the expected travel costs to the demander given that she has obtained licenses from all PROs. Let [T.sub.i] be the blanket license fee charged by PRO i. If a demander chooses to obtain blanket licenses from all r PROs, she will always find herself in a segment of length A = 1, and therefore, by Proposition 2, has expected costs of using one song equal to

(4) EC = [[[sigma].sup.r].sub.i=1] [T.sub.i] + ([k.sub.1]/(12[N.sup.2])).

We can also now calculate the expected cost to the demander of not having one PRO and, therefore, the price that PRO can command for its blanket license. Assume now that all but one of the PROs has sold the demander a blanket license. The demander would be willing to pay the reduction in travel costs resulting from acquiring the last blanket license. The PRO will offer the blanket license at that value, and in equilibrium the demander will have licenses with all the PROs.

PROPOSITION 3. Let F, be the fraction of songs belonging to a PRO i and [F.sub.-i] = 1 - [F.sub.i] equal the fraction of songs not belonging to that PRO. The expected travel cost to the demander if she has licenses to all PROs except [PRO.sub.i], [ETC.sub.-i], is [k.sub.1](1 + 4[F.sub.i] + [[F.sup.2].sub.i])/(12[N.sup.2][[F.sup.2].sub.-i]).

Proof. Let us assume that the demander has landed in a segment of length A. Proposition 1 implies the expected travel cost for the demander will be ETC(A) = [k.sub.1][A.sup.2]/(12N). To calculate expected travel costs thus requires summing the probabilities over all possible A's of being in a segment of length A times the expected travel cost of being in such a segment.

Now consider the possibility that the demander is in a segment of length A such that the song A "spots" to her right does not belong to PRO i, the next A - 1 songs do belong to PRO i, and the song immediately to her left does not belong to PRO i. The first event occurs with probability [F.sub.-i], the next A - 1 events with probability [F.sub.i] apiece, and the final event with probability [F.sub.-i]. Thus, the probability that the demander finds herself in such a segment is [[F.sup.2].sub.-i][[F.sup.A-1].sub.i].

Now note that there are A opportunities for the demander to find herself in a segment of length A. Such a segment can also begin at the song A - 1 songs to the right of the demander, A - 2 songs to the right of the demander, all the way down to the first song to the right of the demander. The probability of each such segment occurring is equal to the probability of the above segment occurring. Thus, the probability that the demander finds herself in a segment of length A is [[AF.sup.2].sub.-i][[F.sup.A-1].sub.i]

Multiplying the probabilities times the expected costs of being in such a segment yields the expected travel costs to the demander of not having the ith PRO, [15]

(5) [ETC.sub.-i] = [[[sigma].sup.[infinity]].sub.A=1] [[AF.sup.2].sub.-i][[F.sup.A-1].sub.i]([k.sub.1][A.sup.2]/12[N.sup.2]

= [k.sub.1][[F.sup.2].sub.-i]/12[N.sup.2][F.sub.i] [[[sigma].sup.[infinity]].sub.A=1] [A.sup.3][[F.sup.A].sub.i]

= [k.sub.1][[F.sup.2].sub.-i]/12[N.sup.2][F.sub.i] ([F.sub.i](1 + 4[F.sub.i] + [[F.sup.2].sub.i])/[[F.sup.4].sub.-i])

= [k.sub.i](1 + 4[F.sub.i] + [[F.sup.2].sub.i])/12[N.sup.2][[F.sup.2].sub.-i]

Q.E.D. [16]

The value to the demander of the ith PRO is the reduction in expected travel costs generated by signing up with that PRO. Let [N.sub.i] equal the number of songs belonging to the ith PRO [N.sub.-i] equal the number of songs not belonging to the ith PRO, with [N.sub.i]+[N.sub.-i] = N Since the PRO can make a "take it or leave it" offer to the demander the payment from the demander will equal [T.sub.i],

(6) [T.sub.i] = [ETC.sub.-i] - ETC

= [[k.sub.1](1 + 4[F.sub.i] + [[F.sup.2].sub.i])/(12[N.sup.2][[F.sup.2].sub.-i])] - [[k.sub.1]/(12[N.sup.2])]

= [k.sub.1][F.sub.i]/(2[N.sup.2][[F.sup.2].sub.-i]) = [k.sub.1][N.sub.i]/(2[[N.sup.2].sub.-i]N).

The intuition behind [T.sub.i] is clear. The higher [k.sub.1], the higher the relevant travel costs and the more valuable a blanket license will be. The larger N, the smaller space between songs and the less valuable the blanket will be. The larger [N.sub.i] and [F.sub.i] (and therefore the smaller [N.sub.-i] and [F.sub.-i]), the more important the ith PRO is in the market and therefore the more valuable.

Step 1: PROs Sign up Composers as Members

Let the supply curve of songs be R = [k.sub.2]N, [k.sub.2] [greater than] 0, where R is the average revenue paid per song and N is the number of songs written by composers. Assume that the PROs have Cournot-Nash assumptions when "signing up" songs. The ith PRO's profits are therefore

(7) [[pi].sub.i]([N.sub.i], N) = [T.sub.i]([N.sub.i], N) - R(N)[N.sub.i]

= [k.sub.1][N.sub.i]/(2[[N.sup.2].sub.-i]N) - [k.sub.2]N[N.sub.i].

Maximizing profit by taking derivatives with respect to [N.sub.i] using Nash assumptions yields

(8) d[[pi].sub.i]/d[N.sub.i] = [k.sub.1]/(2[N.sub.-i][N.sup.2]) - [k.sub.2](N + [N.sub.i]) =0.

Note that this equation implicitly assumes that the PROs cannot discriminate among composers based on expected location in the product space.

Now assume r identical PROs. Then [N.sub.i]r = N, as well as [N.sub.-i]r/(r - 1) = N, and

(9) d[[pi].sub.i]/d[N.sub.i] = [[rk.sub.1]/(2(r - 1)[N.sup.3])] - [k.sub.2]N(r+1)/r = 0.

We can now solve equations (6), (7), and (9) for equilibrium in N, T, and PRO i profits, yielding

(10) N = [[[k.sub.1][r.sup.2]/2[k.sub.2]([r.sup.2] - l)].sup.1/4],

(11) T = [[[k.sub.1][k.sub.2]([r.sub.2] - 1)/2].sup.1/2][(r - 1).sup.-2], and

(12) [[pi].sub.i] = [[2[k.sub.1][k.sub.2]/([r.sup.2] - l)].sup.1/2][(r - 1).sup.-1].

Thus, total expected costs to the demander as a function of r are

(13) [EC.sup.B](r) = r[T.sub.i] + [k.sub.1]/(12[N.sup.2])

= [[[k.sub.1][k.sub.2]([r.sup.2] - 1)/2].sup.1/2]r[(r - 1).sup.-2],

with dEC/dr, dT/dR [less than] 0. As r goes to infinity, EC(r) goes to 7[([k.sub.1][k.sub.2]/2).sup.1/2]/6.

IV. PER-USE LICENSES

This section will derive the equilibrium for firms using per-use licenses using the same five-step game. Let [t.sub.i] equal the per-use rate by PRO i, t the per-use rate by the other PROs.

Step 5

The one composer whose song is played receives RN.

Step 4

The demander chooses which song to play facing possibly two per-use rates. Consider any segment on the unit circle. Without loss of generality, set the position of the two ends of that segment at [0, 1/N], and assume that the "left-hand" song at position 0 belongs to PRO i while the "right-hand" song at position 1/N does not. Let [X.sub.i] = X([t.sub.i], t) be the spot on the segment where the demander is indifferent between the two songs. With quadratic costs, [X.sub.i] is determined as

(14) [t.sub.i] + [k.sub.1][[X.sup.2].sub.i] = t + [k.sub.1][[(1/N) - [X.sub.i]].sup.2], [X.sub.i] = [(t - [t.sub.i])N/2[k.sub.1]] + 1/(2N).

If the demander has location X [less than] [X.sub.i] she will choose the PRO i song, and she will choose the non-PRO i song if X [greater than] [X.sub.i].

Step 3

Equal spacing of songs is an equilibrium, as derived in section III.

Step 2

To discover what per-use fee will be charged, it will be necessary to determine PRO i's demand curve. Given its demand, the PRO can set its per-use rate to maximize profits.

Total revenue for PRO i is [R.sub.i]([t.sub.i], t) = [t.sub.i][D.sub.i]([t.sub.i], t). Maximizing PRO i's revenue (profits) using Nash assumptions with respect to [t.sub.i] yields

(15) d[R.sub.i]([t.sub.i], t)/d[t.sub.i] = d[[pi].sub.i]/d[t.sub.i]

= ([N.sub.i]/N) + ([N.sub.i][N.sub.-i]t/[k.sub.1]) - (2[N.sub.i][N.sub.-i][t.sub.i]/[k.sub.1]) = 0.

Step 1

Assume again that the supply curve for songs is R = [k.sub.2]N. Total costs will be [C.sub.i]([N.sub.i], N) = [N.sub.i]R = [N.sub.i][k.sub.2]N. Maximizing profit with respect to [N.sub.i],

(16) d[[pi].sub.i]/d[N.sub.i] = d[R.sub.i]([t.sub.i], t)/d[N.sub.i] - d[C.sub.i]([N.sub.i], N)/d[N.sub.i]

= [t.sub.i][([N.sub.-i]/[N.sup.2]) + [N.sub.i](t - [t.sub.i])/[k.sub.1]] - [k.sub.2]([N.sub.i] + N) = 0.

As before, with identical firms set [t.sub.i] = t, r[N.sub.i] = N = [r/(r-1)][N.sub.-i], and equations (15) and (16) thus imply

(17) N = [[([rk.sub.1])/(r + 1)[k.sub.2])].sup.1/4],

(18) t = [[r(r + 1)[k.sub.1][k.sub.2]].sup.1/2]/(r - 1),

(19) [[pi].sub.i] = [[[k.sub.1][k.sub.2]/(r(r + 1))].sup.1/2] (2/(r - 1)).

Using Proposition 2, expected costs for the demander are therefore

(20) [EC.sup.P](r) = t + ([k.sub.1]/(12[N.sup.2]))

= [[(r+1)[k.sub.1][k.sub.2]].sup.1/2][([r.sup.1/2]/(r-1)) + (1/(12[r.sup.1/2]))].

Expected costs go to 13[[k.sup.1/2].sub.1][[k.sup.1/2].sub.2]/12 as r goes to infinity, greater than the equivalent value for blanket licenses. Thus, as r grows large, demanders prefer bundling. However, for small values of r (less than approximately 2.24991) demanders prefer per use licenses. For PROs, equation (12) and (19) imply that PROs prefer blanket licenses if r [less than] 2 and per-use licenses if r [greater than] 2.

Of course, it does not make sense to have a noninteger number of identical firms. One may, however, read the Herfindahl index (H) as a competitive measure of the number of equivalent-sized firms in the market, with r = 10,000/H; H = 10,000/r. (See Martin [1994, 124-26] for a derivation of this result.) Using this assumption allows the model to imply three possible regimes. First, if H [greater than] 5,000 (r [less than] 2), demanders will prefer per-use licenses and PROs will prefer blanket licenses. This is a result consistent with the positions of the parties in the BMI-CBS case. Second, if H [less than] 4,445 (r [greater than] 2.24991, and close to the estimated market H of 4,458 calculated in Section II), demanders will prefer blanket licenses and PROs will prefer per-use licenses, which is inconsistent with both the positions of the parties in BMI. Finally, if 4,445 [less than] H [less than] 5,000 (2 [less than] r [less than] 2.24991), both sets of parties will prefer per-use licenses. Section V, howeve r, will suggest that it is by no means inevitable that such licenses will be generated in equilibrium, even if both sets of parties prefer them.

Intuitively, the fee a blanket license can command is the "hold-up" value of the license--the chance that a demander will have to incur large travel costs without that license. In equilibrium, the probability that a demander without a particular blanket will not have access to either her "left-hand" or "right-hand" song equals 1/[r.sup.2], where r is the number of firms (a 1/r chance of not having the left-hand song times a hr chance of not having the right-hand song). This probability falls dramatically as the number of firms increases. [17]

V. COMPETITION BETWEEN BLANKET AND PER-USE LICENSES

Given that two types of licenses are possible, which set of licenses will arise in equilibrium? Put another way, why did CBS, a member of BMI, not try to get BMI to offer per-use licenses and instead chose an antitrust action? This section will discuss that question, using the example of two firms in the industry, one using blanket licenses and the other using per use licenses.

Let [N.sub.B] be the number of songs owned by the blanket license PRO and [N.sub.p] be the number of songs owned by the per-use PRO. (Therefore, N = [N.sub.B] + [N.sub.P]) Accordingly, [F.sub.B] = [N.sub.B]/N, [F.sub.P] = [N.sub.P]/N = 1 - [F.sub.B]. Let T equal the blanket fee charged by the blanket PRO and t the per-use fee charged by the per-use PRO.

Steps 3, 4, and 5

These results will be similar to those of sections III and IV.

Step 2 Blanket PRO

PROPOSITION 4. Again, assume that the per-use PRO does not set its song price so high that a demander would wish to "travel over" one of its songs, implying [t.sub.i] - t [less than] [k.sub.1]/[N.sup.2]. Then the blanket fee charged by the blanket PRO will be T = [k.sub.1][N.sub.B]/(2[[N.sup.2].sub.P]N) + [N.sub.b]t/N + [N.sub.B][N.sub.P][t.sup.2]/(2[k.sub.1]).

Proof. See Kleit [1997].

Step 1, Blanket License PRO

Given T derived in Proposition 4 and the supply curve for composers used in Sections III and IV, the blanket PRO maximizes profits with respect to [N.sub.B], yielding

(21) d[[pi].sub.B]/d[N.sub.B] = ([k.sub.1]/(2[N.sub.P][N.sup.2])) + (t[N.sub.P]/[N.sup.2]) +([N.sub.P][t.sup.2]/(2[k.sub.1])) - [k.sub.2](N + [N.sub.B]) = 0.

Steps 1 and 2, Per-Use PRO

The optimization conditions for the per-program PRO can be derived directly from equations (15) and (16), setting the per-use license fee of the "other" firm to zero. Maximizing profits with respect to t and [N.sub.P] yields

(22) d[[pi].sub.P]/dt = ([N.sub.P]/N) - 2[N.sub.P][N.sub.B]t/[k.sub.1] = 0,

(23) d[[pi].sub.P]/d[N.sub.P] = t[([N.sub.B]/[N.sup.2]) - (t[N.sub.P]/[k.sub.1])] - [k.sub.2](N + [N.sub.P]) = 0.

Any equilibrium that exists in [N.sub.B], [N.sub.P], T, and t can be generated by solving for T and equations (21), (22), and (23). Solving for this equilibrium, however, yields 12 solutions, each of which contain imaginary roots. This implies that no equilibrium exists in real numbers with both firms in the market.

Such a result can be illustrated by showing how the blanket PRO can block entry into the market by the per-use PRO, while the per-use PRO cannot block entry by the blanket PRO. First, for the blanket PRO, let [[N.sup.B].sub.B] be the number of songs that the blanket PRO could obtain that would deter the per-use PRO from entering the market. Thus, I am seeking a [[N.sup.B].sub.B] such that d[[pi].sub.p]/d[N.sub.p] [less than or equal to] 0 when [N.sub.p] = 0. Since [N.sub.p] = 0, this implies N = [N.sub.B] = [[N.sup.B].sub.B]. Equation (23) implies that the limit of t as [N.sub.P] [right arrow] 0 = [k.sub.1]/2[([[N.sup.B].sub.B]).sup.2]. Substituting in for t in equation (23), where the per-use firm maximizes over [N.sub.p], with [N.sub.p] =0, setting d[pi]/d[N.sub.p] = 0, and solving for [[N.sup.B].sub.B] yields [[N.sup.B].sub.B] = [([k.sub.1]/2[k.sub.2]).sup.1/4]. Thus, the blanket PRO can block entry by the per-use PRO by acquiring [[N.sup.B].sub.B] = [([k.sub.1]/2[k.sub.2]).sup.1/4] songs. [18]

In contrast, there is no [N.sub.p] that blocks entry by the blanket PRO. To see this, consider if the per-use PRO can acquire songs and setting a per use fee ([[N.sup.B].sub.p], [t.sup.B]) such that the blanket PRO does not enter. This PRO is constrained, however, to non-negative profits. [19] Since [N.sub.B] = 0, [[N.sup.B].sub.p] = [N.sub.p] = N. Non-negative profits imply [[[pi].sup.B].sub.p] = [t.sup.B] - [[RN.sup.B].sub.p] = [t.sup.B] - [k.sub.2]([[N.sup.B].sub.p] [greater than or equal to] 0. Setting profits equal to zero and inserting [[N.sup.B].sub.p] into equation (21) yields d[[pi].sub.B]/d[N.sub.B] = [k.sub.1]/2[([[N.sup.B].sub.p]).sup.3] + [[k.sup.2].sub.2][([[N.sup.B].sub.p]).sup.5]/2[k.sub.1], which is always positive. Thus, a per-use PRO cannot block entry by a blanket PRO.

Intuitively, at the margin, the blanket PRO has an advantage on any contested segment. A demander who wishes to use the per-use PRO's song will have to pay a marginal fee for usage, unlike using the blanket PRO's song. This gives the blanket PRO the ability to drive the per-use PRO out of the market.

This result may help explain CBS's choice to sue both ASCAP and BMI, rather than seek change through BMI's board of directors. If BMI changed licenses practices, it would put it at a substantial competitive disadvantage to ASCAP and likely increase the ability of ASCAP to charge higher rates from CBS.

This result also explains the reluctance of ASCAP to issue attractive per-program licenses when BMI is not required to do so. As one court explained, "ASCAP contends that any requirement that it offer a per program license to a network already holding a BMI blanket license will result in discrimination by that network against ASCAP... In addition, there can be no disputing the intuitive accuracy of ASCAP's observation that a network which holds a blanket license from one organization and a per program license from the other has an economic incentive to favor use in its program of music covered by the blanket license." [20]

One can apply this result to recent competition between Microsoft and Netscape for Internet browsers. Given that one firm chose to sell its product at zero marginal cost, the other firm, barring significant product differentiation, also had to chose this form of competition. In that case, however, it is unclear what the market equilibrium number of firms is, although it seems that such an equilibrium may be driven by the question of how valuable product differentiation is in that market (see Liebowitz and Margolis [1995]).

VI. CONCLUSION

Only in a narrow set of circumstances do blanket licenses generate losses for customers and gains for PROs. Those circumstances, however, may well be those that apply to the BMI-CBS case. In addition, it appears that in an unregulated market the equilibrium between competing PROs will involve blanket licenses. The use of per-program or per-use licenses gives broadcasters incentives not to use the product of those firms issuing such licenses. This in turn explains both why CBS chose to sue BMI and why ASCAP has been reluctant to issue per-program licenses at a regulated price when BMI was under no such obligation.

More generally, this paper represents a significant departure from the previous economic literature on bundling. It presents a model where the number of firms is allowed to vary and the number of products in the market is a function of the number of firms. This model finds that bundling has the potential to generate anticompetitive results, but only if the number of firms is small. On the other hand, this model may imply that modern-day bundling in computer sectors that have fewer firms may well be driven by the opportunity to capture more surplus than simple unit pricing would.

Extensions of the model to PRO competition are also possible. It may be fruitful to determine the results of competition between three different firms with three different structures, not-for-profit owned by composers (ASCAP), not-for-profit owned by broadcasters (BMI), and for-profit (SESAC). It would also be interesting to model competition among such firms, assuming they can aggressively market one part of the product space, in contrast to the current antitrust restraints on ASCAP and BMI.

(*.) I would like to thank John Bigelow, David Butz, Carter Hill, Tom Lyon, Kaz Miyagiwa, Geoff Turnbull, and two anonymous referees for their assistance with this paper.

Kleit: Associate Professor, Department of Energy, Environmental, and Mineral Economics, 2217 Earth Engineering Sciences, The Pennsylvania State University, University Park, Penn. 16802. Phone 1-814-865-0711, Fax 1-814-863-7453, E-mail ankl@psu.edu

(1.) Technically, composers can simultaneously market their own licenses for their compositions and charge the rates they determine best.

(2.) If a composer switches PROs mid-career, the right to catalog a particular song belongs to the PRO with whom the song was originally registered.

(3.) This section presents a very concise summary of the many antitrust challenges PROs have faced.

(4.) U.S. v. ASCAP (application of National Broadcasting, Inc.), CCH 73,491 (S.D.N.Y., 1970).

(5.) PROs also sometimes issue "per-program" licenses (sometimes called a "mini-blanket"), where a broadcaster pays a blanket fee for using any and all compositions on a particular performance. Both ASCAP and BMI are required to offer per-program licenses under the Consent Decrees, though only ASCAP's fee has been regulated by the rate court. Though per-program licenses were not directly at issue in the BMI litigation, they have also had their share of controversy. In particular, ASCAP has fought efforts to make its per-program licenses attractive to its customers. Historically, per-program license fees, measured on a per-program basis, have been approximately four times that of blanket fees. Thus, if the ASCAP blanket license fee was 2% of a broadcaster's revenue, the per-program fee would be 8% of the revenue of the performance where that license was used. Recently, however, the rate court determined that for local television stations the per program fee should only be 40% higher than the blanket license f ee, measured on a per-program basis. (See U.S. v. ASCAP, Civ. 13-95 [February 26, 1993] [Dolinger, Magistrate, S.D.N.Y.].)

(6.) In particular, the Court noted that if blanket licenses constituted illegal price fixing, CBS's proposed remedy, per-sue fees set by ASCAP and BMI, would also constitute price fixing.

(7.) There are, of course, other models of bundling. Adams and Yellen [1976] show how a firm with a monopoly in two products can increase profits by offering its products both separately and together. Schmalensee [1982] extends this model into a situation where a firm has a monopoly in one product and competes in another. In Carbajo et al. [1990], bundling serves to "soften" competition in a two-market oligopoly model. Whinston [1990] shows that if a monopoly can precommit to bundling it can deter entry in a second market. Seidmann [1991] presents a model with two firms, each of which has a monopolized product and whom compete against each other in a third product. None of the market structures in these models appear to fit the circumstances of the BMI case.

(8.) I abstract from any efficiency effects of bundling, as in Kenney and Klein [1983]. Reviewers also suggest that blanket licenses were used to reduce monitoring costs for the PROs. It is unclear, however, why blanket licenses would significantly reduce monitoring costs for the PROs in television. Unlike radio, there are a limited number of television stations to be monitored. Furthermore, much of the programming on television is recorded, allowing a PRO to determine what was played on television after the relevant program was over. Finally, even with blanket licenses a PRO still must monitor at least some programming to determine how its composers should be reimbursed. In any event, monitoring was not an issue in the case as tried.

(9.) Of course, the true game in this market is dynamic, rather than occurring at one time.

(10.) One could think of songs as being differentiated by harmony or melody or, of course, along a number of other dimensions. Implications of the assumption of only one product dimension are discussed infra note 17.

(11.) In the actual market composers are often aided in their search for product space by either their recording companies or their PROs.

(12.) Without loss of generality, the length of the circle could be set equal to some number I [greater than] 0, and the variable [k.sub.1] described below, set equal to 1.

(13.) Perhaps the best way to think about this is to consider the production problem embodied in the opening scene of the popular television show Murphy Brown. For the opening of each episode, a particular song was played for a few seconds as background music in order to convey a certain theme for that episode.

(14.) Note that if [epsilon] = 0 (that is, there is no up-front fee related to distance between songs) equal spacing of songs can be shown to be a weak Nash equilibrium. The up-front fee is required to make equal spacing a unique equilibrium.

(15.) This calculation takes advantage of the fact that the sum of [k.sup.3][x.sup.k] from k = 1 to infinity equals x(1 + 4x + [x.sup.2])/[(1 - x).sup.4]. See Hansen [1975, 66].

(16.) The reader will no doubt be relieved to learn that this is the simplest of three methods devised to prove this lemma. Note that this analysis is done using sampling with replacement. Thus, the probability of being in a sample of a particular length does not depend on the length of previous segments. This seems a reasonable approximation, as at the time of the BMI decision ASCAP and BMI had between them around 4 million songs (See 620 F.2d 933 [1980]). A Monte Carlo experiment along the lines of Davidson and MacKinnon [1993, 731-68] was run assuming two equally sized PROs and 1 million songs between them. One hundred trials were run. The mean difference between the expected search costs estimated in these trials and the theoretical result derived above in Proposition 3 above was 0.00631%. The hypothesis that this difference was not statistically greater than zero could not be rejected, as the relevant t-statistic was 0.773.

(17.) The hold-up problem is thus driven by the possibility the demander will find herself a "long way" from the nearest available song, and that probability rises as the market share of a PRO rises. It therefore does not appear to be qualitatively a function of the assumption of only one product dimension.

(18.) Equation (10) implies that the blanket PRO would have to increase its number of songs by approximately 86% over the "same license" equilibrium result to block entry by the per-use PRO.

(19.) Without per-use PRO, a blanket PRO can set T to infinity in this model. More realistically, the monopoly blanket PRO would set T equal to the finite reservation price of the demander.

(20.) U.S. v. ASCAP, 586 F. Supp. 729, 730 (1984).

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