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Collusive monopsony and antitrust damages.

I. INTRODUCTION

Monopolies and cartels are usually the stars of antitrust law and economics. By acting as a single seller, they wield almost absolute power over the supply and therefore over the prices that consumers pay. Because monopolies and cartels cause harm to the consumer, they invite government intervention through antitrust enforcement. In the past, Intel, AT&T, and others have been attacked for their position as monopolies or near monopolies. (1) Monopolies and cartels, however, are not the only superpowers that can be found in violation of the antitrust laws. There are monopsonies, the lone buyers that restrict purchases, depress prices, and enjoy increased profits as a result. When the monopsonist exerts its power, there is a loss in social welfare and antitrust damages result.

A monopsony, however, does not have to be a single buyer; rather it can be a group of buyers who collude to act as one buyer. These collusive monopsonies are held to legal standards even stricter than those that apply to a pure monopsony. Whereas a pure monopsonist may act unilaterally to depress the price that it pays without fear of antitrust prosecution, a buying cartel is highly vulnerable under section 1 of the Sherman Act. A popular example of a collusive monopsony is Major League Baseball (MLB). The MLB teams buy the services of professional baseball players, who have few good alternatives. The MLB monopsony was the focus of past researchers examining the economic implications of collusive monopsonies. Previous research has looked at baseball players' salaries and whether they reflect the players' marginal revenue products. When they do not and a player appears underpaid by the collusive monopsony, the resulting difference between the salary and the marginal revenue product is said to be the rnonopsonistic exploitation of the player.

The purpose of this article is not to estimate the marginal revenue products of baseball players or even the level of exploitation, but instead to further examine the workings of collusive monopsonies and show that the actual damage suffered by the sellers is less than the monopsonistic exploitation and, furthermore, a rather hard number to calculate. These damages along with their estimation problems will be illustrated through a discussion of labor union agreements in professional sports and by reviewing a previous study of the salaries of professional baseball players.

The article is presented as follows: a review of monopsonistic exploitation, followed by a discussion of antitrust damages, an empirical example in Major League Baseball, the problem with damage estimation, and then some concluding remarks.

II. MONOPSONISTIC EXPLOITATION (2)

"Monopsony," first used in print by Joan Robinson, describes a situation in which there is one individual buyer. (3) Almost like an inverted monopolist, a monopsonist has the ability to take advantage of, or exploit, the seller in its position as the lone buyer. A monopsonist maximizes its profits by restricting its purchases, leading to a decrease in price below the competitive level. Suppose a firm is a monopsonist in the labor market but sells its output in a competitive output market. The profit ([pi]) function for this monopsonist is

[pi] = pq([x.sub.1], ..., [x.sub.n]) - [n.summation over (i=1)] [w.sub.i][x.sub.i] (1)

where p is the competitive output price, q([x.sub.1], ..., [x.sub.n]) is the production function, [x.sub.i] are the inputs, [w.sub.i] are the corresponding input prices, and Y denotes summation. Assume that [x.sub.i], the workers, is the only input for which the firm is a monopsonist. In this case, [w.sub.i], the wages, will be a function of the amount of [x.sub.i] purchased by the firm:

[w.sub.1] = [w.sub.1]([xsub.1]) (2)

and

[dw.sub.1]/[dx.sub.1] > 0.

Therefore, equation (1) can be rewritten as

[pi] = pq([x.sub.1], ..., [x.sub.n]) - [w.sub.1] ([x.sub.1])[x.sub.1] - [n.summation over (i=2)] [w.sub.i][x.sub.i]. (3)

The first order conditions of the profit function are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where p(dq/[dx.sub.1]) is the marginal revenue product (MRP), the value generated by employing an additional worker, and [w.sub.1] + ([dw.sub.1]/[dx.sub.1])[x.sub.1] is the marginal factor cost (MFC), the cost of employing one additional worker. The monopsonist will therefore buy until the additional revenue generated from hiring one more worker equals the additional cost of hiring another worker or when

MRP = MFC. (6)

If MRP < MFC, then the monopsonist would be spending more on hiring another worker than the revenue generated from the extra worker. In similar fashion, if MRP > MFC, then hiring one additional worker would generate more revenue than the expenditure.

As mentioned above, a monopsony can occur when there is exactly one buyer or when there is a group of buyers colluding to act as one buyer. These colluders form a buying cartel, or a collusive monopsony, and like the single monopsonist, restrict its purchases. We can see graphically in figure 1 how a profit-maximizing collusive monopsony operates, how this affects the seller, and where exactly the monopsonistic exploitation will occur. Assume that the collusive monopsony has monopsony power in a local labor market, but sells its output in a national, competitively structured output market.

For the collusive monopsony, profit maximization requires hiring where MRP, or demand (D), equals marginal factor cost. (4) Thus the cartel will hire xm units of labor. It pays the workers a wage of w, which is the height of the supply curve at [w.sub.m]. This wage is well below the marginal value of this quantity of labor, MRP. The monopsonistic exploitation, therefore, is equal to MR[P.sub.m] - [w.sub.m]. While there is an evident disparity between the marginal value to the buyer (MRP) and the wage paid, the monopsonistic exploitation is not equal to the actual damages suffered by the worker. The issue of damages will be discussed in section III.

[FIGURE 1 OMITTED]

Both the collusive monopsonist and the worker enjoy surpluses. The collusive monopsonist benefits from the consumer surplus, which is the difference between the wage the monopsonist is willing to pay for the worker and the wage that is actually paid. Hence, the consumer surplus for the monopsonist is [abew.sub.m], the area below the demand curve but above the wage paid. The worker, on the other hand, experiences a producer surplus, which is the difference between the wage that the worker is able command for his service and what he would be willing to work for. The producer surplus for the worker, therefore, is triangle [w.sub.m]ef, the area below what the worker is paid but above the supply curve. These two regions added together are said to be the net economic benefit. It is a measure of social welfare.

Figure 1 also illustrates the results in a competitive market, i.e., one without the collusive monopsony. The competitive quantity ([x.sub.c]) and wage ([w.sub.c]) are found where supply (S) and demand meet and are clearly more than the monopsonist's profit-maximizing quantity and wage. In addition, the surpluses enjoyed by the buyer and seller in the competitive market are completely different from those in the market with the monopsonist. In perfect competition, meaning a quantity of [x.sub.c] and wage of [w.sub.c], the consumer surplus is triangle [acw.sub.c] and the producer surplus is triangle [w.sub.c]fc. Notice that the net economic benefit in this case is larger than in the instance of the collusive monopsony. The difference, triangle bce, is known as the deadweight social welfare loss caused by the monopsony. The deadweight loss, which is often referred to as simply the loss in welfare, is the economic foundation for antitrust concern.

III. DAMAGES IN ANTITRUST CASES (5)

The mere exercise of either monopsony or monopoly power to maximize profit is not illegal. Rather, the collusion of either buyers or sellers to restrain trade is presumed to be illegal. This stems from section I of the Sherman Act, which provides that
   [e]very contract, combination in the form of trust or otherwise,
   or conspiracy, in restraint of trade or commerce among the
   several States, or with foreign nations, is declared to be
   illegal. Every person who shall make any contract or engage in
   any combination or conspiracy hereby declared to be illegal
   shall be deemed guilty of a felony.... (6)


Since a collusive monopsony is essentially a cartel that has agreed to engage in price-fixing behavior that results in a social welfare loss, it is a per se violation of section 1 of the Sherman Act. (7) This violation invokes section 4 of the Clayton Act, successor to the Sherman Act with respect to private damages, which contains the provision that
   any person who shall be injured in his business or property by
   reason of anything forbidden in the antitrust laws may sue
   therefor in any district court of the United States in the
   district in which the defendant resides or is found or has an
   agent, without respect to the amount in controversy, and
   shall recover threefold the damages by him sustained, and the
   cost of suit, including a reasonable attorney's fee. (8)


Thus, in order to invoke section 4 of the Clayton Act, the plaintiff must be able to show that an antitrust violation has occurred and that he has been injured by that violation. It is necessary to prove antitrust injury, that is, injury that flows from the anticompetitive consequences of the antitrust violation. Proving antitrust injury is fundamentally an economic task because the plaintiff must demonstrate that the plaintiff's injury directly relates to the anticompetitive practices of the collusive monopsony. (9) If we refer back to figure 1, we can further understand the economics behind measuring the damage caused by the offending party and see that this is different from the monopsonistic exploitation.

Referring back to the labor market example in section II, we know the monopsonistic exploitation is MR[P.sub.m] - [w.sub.m], the difference in the marginal value to the monopsonist and the actual wage paid. Of course, there is undeniable merit to the monopsonistic exploitation calculation as it highlights the extraordinary consumer surplus the monopsonist is enjoying. On the other hand, it does fail to account for the fact that if not for the conspiracy of the colluding buyers, the worker would not be able to enjoy the high wage of MR[P.sub.m] in the competitive market. Thus, the damages suffered by the worker are different from the monopsonistic exploitation. In the competitive market, the worker would be able to command the wage of [w.sub.c], the wage "but for" the collusion. (10) But, in the collusive monopsony, the buyer is undercharged and is able to hire at the wage of [w.sub.m]. The damage (A), therefore, is the difference between the wage "but for" the collusive agreement and the actual wage paid times the number of workers hired:

[DELTA] = ([w.sub.c] - [w.sub.m]) [x.sub.m]. (7)

This is denoted in figure 1 by the shaded area [w.sub.c][dew.sub.m]. It is obvious that not only do the damages not equal the calculated monopsonistic exploitation, but are, in fact, less. In other words, monopsonistic exploitation overstates the damages.

IV. ANTITRUST DAMAGES AND LABOR UNION AGREEMENTS

The importance of understanding the difference between antitrust damages and monopsonistic exploitation is illustrated in the language of labor union agreements within sports leagues. Every major sports league in the United States has a collective bargaining agreement (CBA) between the league and its players' labor union. Within these agreements is typically some provision that protects against collusion among the clubs within the sports league but requires proof of antitrust injury. MLB, the National Football League (NFL), and the National Basketball Association (NBA) all outline within their CBAs anticollusion provisions as well as remedies for economic injury.

Within the "reserve system" portion of MLB's bargaining agreement is a section that deals with the rights of the baseball player. This section explicitly prohibits clubs from "act[ing] in concert with other [c]lubs," and allows for grievance arbitration by the player should collusion be suspected."

If a player feels that he has been a victim of collusion, he may raise his complaint with an arbitration panel. Once the player proves a violation has occurred, he must then show a loss of baseball income due to the infraction. In other words, the player needs to show a difference between his actual baseball income and his income "but for" the violation. If the player is successful in proving a violation, he is entitled to receive three times his lost baseball income.

The NFL and the NBA have very similar anticollusion provisions and almost identical remedies. Both forbid collusion among teams to restrict contract negotiations and offers made to players. Each CBA places the burden of proof with the player and requires the player to demonstrate a clear violation of the anticollusion provision as well as resulting "economic injury to such player." (12) If the burden of proof is satisfied, the injured player is entitled to remedies that are a function of the number of previous violations committed by the team. If it is the first offense for the team(s), the player is awarded twice the amount of economic damages. If it is the second offense by the team(s), the player is entitled to three times the economic damages, and if it is at least the third offense committed by the team(s), the team(s) must pay an additional $3 million fine.

V. AN EMPIRICAL ILLUSTRATION

As observed in the previous section, antitrust damages are a much more relevant measure of the economic harm caused by collusion than monopsonistic exploitation. Throughout the years, however, there have been many empirical papers written that deal with the marginal revenue product versus the salary of professional athletes in MLB. Most of the studies attempt to measure the monopsonistic exploitation suffered by the players. (13) Each paper has its own method of measuring MRP and consequently finds different levels of exploitation. One of the premier works surrounding this subject is Gerald W. Scully's Pay and Performance in Major League Baseball. (14)

Scully describes a baseball player's MRP as the effect that his performance has on gate receipts. Before he begins his calculations, Scully makes other assumptions: (1) teams essentially obtain revenue from gate receipts (home attendance times average ticket prices) and broadcast rights, (2) fans attend and watch games because of the increase in utility they experience from seeing their team win, and (3) revenues are directly related to the team's winning percentage and area population and indirectly related to player performance. Under these assumptions, Scully measures a player's MRP through a two-equation model that determines the effect that player performance has on his team's winning and the effect of the team's winning on revenue.

The first equation is a production function that identifies a linear relationship between the team's winning percentage (15) (PCTWIN), a proxy for team output, and other team performance inputs. Scully theorizes that PCTWIN is related to team slugging average (TSA), the contribution put forth by hitters, and team strikeout-to-walk ratio (TSW), the contribution of the pitchers. He recognizes that hitting and pitching are not everything, especially in close games, so he includes two other variables, CONT and OUT. These are incorporated to control for the idea that teams that win a greater number of close games (i.e., one-run games) most likely have better quality managers, on and off field decision making, and overall better team morale. In theory, those teams that win close games are most likely division leaders or at least contenders within the division. Thus, CONT is equal to one for teams that are five or fewer games behind divisional leaders and OUT is equal to one for teams that are twenty or more games behind divisional leaders at the end of the season. He also introduces another variable, NL, created to account for the superiority of the National League. Since the National League was so much better than the American League at the time, the National League was expected to yield a lower winning percentage than the American League. Therefore, the model for the first equation is

[PCTWIN.sub.t] = a + [bTSA.sub.t] + [cTSW.sub.t] + fNL + [gCONT.sub.t] + [hOUT.sub.t.] (8)

The second equation is a revenue function that relates revenues (REVENUE) to PCTWIN as well as other pertinent factors regarding the market of the area where the team plays. Within this linear function, Scully controls for the size of monopoly income earned by the club by introducing the Standard Metropolitan Statistical Area (SMSA) variable. Monopoly income occurs because "franchises are granted as exclusive monopoly rights" and franchises in larger areas will have larger incomes. He also adjusts for differing fan interests, independent of SMSA, from team to team with the variable MARGA, an estimate using time-series data of the correlation between the winning percentage of a team and attendance. Scully includes the additional variables NL, to account for higher revenues of the superior National League, STD, equal to one for older stadiums with inadequate parking in poor neighborhoods, and BBPCT, the percentage of black players on the team. (16) These variables yield the second equation:

[REVENUE.sub.t] = j + [kPCTWIN.sub.t] + mSMSA + nMARGA + pNL + [qSTD.sub.t] + [rBBPCT.sub.t] (9)

Scully then estimates the MRP for hitters and pitchers to be

[MRP.sub.hittters] = b(k) (10)

[MRP.sub.pitchers] = c(k) (11)

where b, k, and c each represent their respective coefficients from equations 8 and 9. Using data from 1968 and 1969, Scully is able to estimate both the PCTWIN and REVENUE functions. When estimating PCTWIN, the coefficient on TSA is .92, while the coefficient on TSW is .90. Put into words, this means that a one-point increase in TSA increases PCTWIN by .92 points and a one-hundredth point increase in TSW increases PCTWIN by .90. After estimating the REVENUE function, Scully then obtains a coefficient of $10,330 on PCTWIN, meaning a one point increase in the team's win-loss record raises team revenue by $10,330. With this information, Scully is able to calculate the marginal revenue products using equations 10 and 11. These equations, however, do not give individual MRPs. To obtain an individual MRP Scully assumes that team performance is a simple summation of individual performance. Since most team rosters are comprised of eight regular pitchers and twelve regular players, each pitcher will individually contribute .125 of his strikeout-to-walk ratio to TSW, and each hitter will contribute .08333 of his slugging average to TSA. Scully also recognizes that these equations disregard all inputs except for PCTWIN, TSA and TSW, which could result in overestimating MRP. To adjust, Scully treats these MRPs as gross marginal revenue products. Compensation to other inputs and player development costs are then subtracted to obtain player net marginal revenue products (NMRP).

Scully is then able to calculate the rate of monopsonistic exploitation by subtracting a player's salary from his NMRP and then dividing by NMRP. (17) Scully finds that on average, players are being paid only about 20% of their MRP. These results could indicate that baseball players are the victim of a collusive monopsony on the part of the clubs comprising MLB. As we have discussed, however, for a player to prove that he has suffered an antitrust injury, he must show that he would still be underpaid "but for" the conspiracy. Thus, a player must be able to determine what his salary would have been in a competitive market. Finding the competitive price can be an almost impossible task.

VI. PROBLEMS WITH DAMAGE ESTIMATION

An estimate of antitrust damages requires knowing the "but for" price and the actual price paid. In order to determine the "but for" price, we must have reasonable estimates of the supply and demand. The shape of either curve could dramatically affect the estimate of the damages. Figure 2, a slight alteration of figure 1, illustrates this point more clearly.

In figure 2, we have added a new demand curve ([D.sub.2]) and kept everything else the same. As you can see, [D.sub.2] is much steeper than [D.sub.1].

[FIGURE 2 OMITTED]

Because of the steepness of [D.sub.2], supply and demand meet at a quantity of labor ([x.sub.c2]) and a wage ([w.sub.c2]) that is much lower than [x.sub.c1] and [w.sub.c1], the competitive quantity of labor and wage from figure 1. Since the supply curve, and thus the marginal factor cost curve, has remained the same in this figure, the monopsonist still restricts its purchases to [x.sub.m], and buys at [w.sub.m]. Thus, the damages when [D.sub.2] is the demand curve (area [w.sub.c2][geMRP.sub.m]) are much lower than the damages when [D.sub.1] is the demand curve ([w.sub.c1][dew.sub.m]). In other words

([w.sub.c2] - [w.sub.m])[x.sub.m] < ([w.sub.c1] - [w.sub.m])[x.sub.m].

Comparatively, if [D.sub.2] had been flatter than [D.sub.1] the damages would have been larger (i.e., ([w.sub.c2] - [w.sub.m])[x.sub.m] > ([w.sub.c1] - [w.sub.m])[x.sub.m]). Additionally, notice that since supply did not change, monopsonistic exploitation remained the same. In other words, even a drastic reduction in the amount of the damages has no effect on the level of exploitation by the collusive monopsonist.

Figure 2 illustrates the importance of the supply and demand curve in damage estimation. While we can mathematically extract an estimate of the supply curve, finding the demand curve could be impossible. If we know the actual wage and quantity, we can manipulate some well-known equations to find the slope of the supply curve. Referring back to the mathematical model from section II, we know that for the profit-maximizing collusive monopsonist in a labor market

MRP = MFC = [[w.sub.1] + [dw.sub.1]/[dx.sub.1][x.sub.1] (12)

Rearranging equation (12) yields

MRP - [w.sub.1] = [dw.sub.1]/[dx.sub.1]x

where ([d.sub.w1]/[d.sub.x1]) is the inverse elasticity of supply of [x.sub.1]. Another way of looking at ([dw.sub.1]/[dx.sub.1]) would be as the change in wage over the change in quantity of labor, or the slope of the supply curve. (18) Thus, since we have a point on the supply curve and have now derived the slope, we can obtain a reasonable estimation of the supply curve. Even with these calculations, however, we are still left without the necessary information to estimate the demand curve, namely the slope of the demand curve. Thus, the amount of antitrust damages remains indeterminate.

V. CONCLUDING REMARKS

A buying cartel, or a collusive monopsony, is an illegal combination of otherwise competing buyers whose members agree to act as a pure monopsony. Its goal, of course, is profit, which it maximizes by restricting purchases and thereby depressing the prices that it pays. This behavior leads to a social welfare loss because a suboptimal quantity is purchased. As we have discussed, previous studies focus mostly on the level of monopsonistic exploitation caused by the cartel. While collusive monopsonies undoubtedly exploit the seller, the proof of monopsonistic exploitation is insufficient when establishing the economic harm caused to the seller. As section 4 of the Clayton Act and standard labor union agreements require, the injured seller must be able to show a tangible level of antitrust damages, which equal the difference in the price "but for" the conspiracy and the actual price paid to the seller. The calculation of antitrust damages, however, is nearly impossible as the "but for" price and quantity cannot be determined satisfactorily.

AUTHOR'S NOTE: I would like to thank Roger D. Blair for comments on an earlier draft.

(1) In May of 2009, Intel was fined a record $1.45 billion by the European Union for anticompetitive practices. See James Kanter, Europe Fines Intel $1.45 Billion in Antitrust Case, N.Y. TIMES, May 13, 2009, http://nytimes.com/2009 /05/iu/business/global/iucomplete.html. In a 1982 settlement, AT&T agreed to break up in to seven regional companies after it was deemed to be using monopoly profits for a subsidiary to fund its network. See United States v. AT&T, 552 F. Supp. 131 (D.D.C. 1982). In another popular antitrust case, Addyston Pipe & Steel, six pipe manufacturers were sued for operating a cartel under which they sold their pipes to local municipalities by dividing certain cities among themselves in order to reduce competition. This was found to be a violation of section 1 of the Sherman Act. United States v. Addyston Pipe & Steel Co., 85 F. 271 (6th Cir. 1898). Perhaps the most famous antitrust case in U.S. history is the break-up of John D. Rockefeller's Standard Oil Trust by the Supreme Court in 1911. See Standard Oil Co. of N.J.v. United States, 221 U.S. 1 (1911).

(2) This section relies on Roger D. Blair & Christine Piette Durrance, The Economics of Monopsony, in 1 ISSUES IN COMPETITION LAW & POLICY 393 (ABA Section of Antitrust Law 2008)

(3) JOAN ROBINSON, THE ECONOMICS OF IMPERFECT COMPETITION (1933). "Monopsony" was a replacement for the previously used "monopoly-buyer."

(4) Notice in figure I that the demand curve is equal to the marginal revenue product curve. This is because the monopsonist is always comparing the MRP of the input to its per unit cost and then purchases where the MRP and per unit cost of the input are equal. Hence, the MRP curve is the monopsonist's demand curve for the input.

(5) For a more complete analysis of antitrust damages, see PHILLIP E. AREEDA, HERBERT HOVENKAMP, ROGER D. BLAIR & CHRISTINE PIETTE DURRANCE, IIA ANTITRUST LAW (2007).

(6) 15 U.S.C. [section] 1 (2008).

(7) See Mandeville Island Farms v. Am. Crystal Sugar Co., 334 U.S. 219 (1948).

(8) 15 U.S.C. [section]15 (2009).

(9) See Brunswick Corp. v. Pueblo Bowl-O-Mat, Inc., 429 U.S. 477 (1977), for a more complete ruling on proof of antitrust injury.

(10) The terms "competitive price" and "competitive quantity" are used interchangeably with "but for" price and "but for" quantity, respectively.

(11) MLB 2007-2011 Basic Agreement, Art. XX(E)(2) (Dec. 20, 2006), available at http://mlb.com/pa/pdf/cba_english.pdf.

(12) See NFL Collective Bargaining Agreement 2006-2012, Art. XXVIII(5) (Mar. 8, 2006), available at http://nflplayers.com/user/template.aspx?fmid=181 &lmid=622&pid=0&type=l and NBA Collective Bargaining Agreement, Art. XIV(5) (July 2005), available at http://www.nbpa.org/documents/CBA2005.pdf.

(13) Some examples include Don N. MacDonald and Morgan O. Reynolds, Are Baseball Players Paid their Marginal Products?, 15 MANAGERIAL & DECISION ECON. 443 (1994); Henry J. Raimondo, Free Agents' Impact on the Labor Market for Baseball Players, 4 J. LAB. RES. 183 (1983); and John Vrooman, The Baseball Players' Labor Market Reconsidered, 63 S. ECON. J. 339 (1996).

(14) Gerald W. Scully, Pay and Performance in Major League Baseball, 64 AM. ECON. REV. 915 (1974). During the period when Scully conducted his study all players were subject to the reserve system because free agency did not come about in MLB until 1976. The reserve system granted exclusive rights to the player's current team to renew, sell, or terminate the contract. For a criticism on the Scully method for measuring MRPs, see Anthony C. Krautmann, What's Wrong with Scully-estimates of a Player's Marginal Revenue Product, 37 ECON. INQUIRY 369 (1999).

(15) PCTWIN is expressed as games won divided by total games times 1000.

(16) BBPCT was included because previous studies conducted by Scully showed the existence of racial discrimination by baseball fans.

(17) To calculate a player's salary, Scully conducts an elaborate salary regression for hitters and pitchers where he controls for the effects of superstars (by making the regression logarithmic), the years a player has spent in the majors (M), total innings pitched ([bar.IP]), lifetime strikeout-to-walk ratio ([bar.SW]), lifetime slugging average, ([bar.SA]), a weighted at-bat contribution for hitters ([bar.AB]), a dummy variable that accounts for good hitters with low slugging averages ([D.sub.[bar.BA]]), and SMSA, MARGA, NL. Thus, Scully runs the following regressions:

[LogS.sub.hitters] = [alpha] + [[beta].sub.1]Log[bar.SA] + [[beta].sub.2]LogM + [[beta].sub.3][LogD.sub.[[bar.BA] + [[beta].sub.4]Log[bar.AB] + [[beta].sub.5][LogSMSA.sub.t] + [[beta].sub.6]LogMARGA + [[beta].sub.7]LogNL

[LogS.sub.pitchers] = [gamma] + [[delta].sub.1]Log[bar.SW] + [[delta].sub.2]LogM + [[delta].sub.3]Log[bar.IP] + [[delta].sub.4][LogSMSA.sub.t] - [[delta].sub.5]LogMARGA + [[delta].sub.6]LogNL

(18) Equation 8 is known as the inverse elasticity pricing rule. For more on this rule, see DAVID BESANKO & RONALD R. BRAEUTIGAM, MICROECONOMICS 404-41 (2005).

BY CHRISTINA DEPASQUALE, Ross School of Business, University of Michigan.
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Title Annotation:Symposium: Antitrust in the Sports Industry
Author:DePasquale, Christina
Publication:Antitrust Bulletin
Date:Dec 22, 2009
Words:4894
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