Collusive monopsony in theory and practice: the NCAA.
"Monopsony" is the inelegant label attached to the structural condition in which there is a single buyer of a good or service.(1) In the United States, this market structure is no more common than structural monopoly, which is rare indeed. But collusive monopsony is not so rare. Examples can be found throughout the economy. For example, buyer cartels have been found among antique dealers,(2) sugar refiners,(3) and bidders on timber rights,(4) real estate,(5) and used commercial equipment.(6) There are examples in the sports industry as well. For instance, the owners of major league baseball teams were found guilty of collusion in the free agent market.(7) In the sports arena, our focus is on the National Collegiate Athletic Association (NCAA) as a collusive monopsony.(8)
The NCAA's members collude on two key inputs in the production of athletic competition: the athletes themselves and their coaches. With respect to athletes, the agreement restricts quantities by placing a ceiling on the number of scholarships. In addition, in the name of amateurism,(9) the compensation of these athletes is limited to room, board, tuition, books, and incidentals. Bonuses for winning conference championships are limited to relatively inexpensive rings or watches. With respect to coaches, the number employed in each sport is limited by NCAA Bylaw. In this connection, we examine the Hennessey v. NCAA litigation.(10) The compensation of coaches is typically unconstrained, although there have been attempts to restrict the earnings of some coaches. In this connection, we examine the Law v. NCAA litigation,(11) which led the NCAA to rescind its rule restricting the earnings of some assistant coaches.
In this article, we present a positive theory of collusive monopsony. In doing so, we examine the problems inherent in organizing a cartel, coordinating the efforts of the members, and enforcing the terms of agreement. We also explore the implications of collusive monopsony for price and quantity as well as the returns to the colluders. In this regard, we show the effect of collusive monopsony on average and marginal cost as well as on profit. We extend the standard analysis to the case involving quality variation in the purchased input. Finally, we examine the welfare consequences and the implications for antitrust policy.
II. The incentive to collude
When buyers behave independently the forces of supply and demand will typically lead to a price and quantity that maximizes social welfare.(12) Figure 1 shows the market for good or service L, which will be an input to production in our application. The independent decisions of buyers and sellers of L will lead to a price of [w.sub.1] and a quantity of [L.sub.1]. Now, consumer surplus is the difference between the most that buyers are willing to pay for the good or service and what the market requires them to pay.(13) Analogously, producer (or supplier) surplus represents the difference between the lowest price that suppliers are willing to accept and the actual market price.(14) Social welfare is the sum of supplier surplus (area [w.sub.1]BC) and consumer surplus (area AB[w.sub.1]), which is represented by area ABC in figure 1. Absent market failure, unfettered competition leads to the maximization of social welfare, which provides the economic foundation for our antitrust policy.(15) The buyers, of course, enjoy consumer surplus, or buyer profits, equal to area AB[w.sub.1]. Through collusion, they may be able to exercise collective buying power and increase their profits at the expense of the suppliers and to the detriment of society.(16)
[FIGURE 1 GRAPH OMITTED]
If the formerly independent buyers pool their demands and coordinate their purchases, they can exploit the potential buying power that exists. We assume that L and K are inputs in the production of good or service Q, the aggregate output described by a standard production function Q = Q(L,K).(17) The profit ([Pi]) of the buying cartel can be written as
[Pi] = PQ - w(L)L - rK
where P is the invariant price of Q, r is the invariant price of input K, and w(L) is the price of L. We assume that the supply of L has a positive slope and, therefore, increased purchases of L require paying a higher price, i.e., dw(l)/dL [is greater than].(18) Our assumptions on input prices imply monopsony opportunities in hiring L but not K for simplicity, although opportunities could exist in both input markets.(19) To simplify further the presentation, we fix employment of K to a value [K.sub.0], i.e., we pursue a short-run analysis.(20)
With respect to the hiring decision on L, profit maximization will lead to the quantity of L where
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The first term is the value of the marginal product, which corresponds to the demand for L (see figure 1). The term in brackets is the marginal factor cost (MFC). Note that the MFC must exceed w since dw/dL [is greater than] 0. As we can see in figure 1, in order to maximize the benefits of their buying power, the colluders will restrict their collective purchases to [L.sub.2], which is the quantity at which the marginal factor cost equals the value of the marginal product. The collusive monopsony will then pay only [w.sub.2], which is the price on the supply curve that corresponds to quantity [L.sub.2]. This hiring restriction is generally supported by agreement on hiring quotas among the members; the sum of the quotas is equal to [L.sub.2]. The lower input price is, of course, the motive for collusion. In comparison to the competitive outcome, buyer surplus increases by the excess of area [w.sub.1]EF[w.sub.2] over area DBE. The latter difference in areas must be positive since we have found the profit-maximizing solution for the buyer coalition.(21) As is apparent from figure 1, the cartel converts supplier surplus of area [w.sub.1]EF[w.sub.2] into profit for the cartel members. Thus, the gains come solely at the expense of the suppliers of L. Hence, social welfare falls, by area DBF, which is the deadweight social welfare loss of monopsony. This is the economic foundation for an antitrust policy that proscribes collusive monopsony.
Effect of collusive monopsony on costs
When members of the NCAA agree among themselves to restrict demand for and thereby pay less to athletes and coaches than unfettered competition would dictate, one might suppose that this will reduce their costs and benefit consumers. Sadly, however, this is not correct. A complete understanding of this result is important for an informed antitrust policy.
When a buying cartel exercises monopsony power, it pays a lower price for the input in question. This might seem to reduce the cartel's costs, which in turn should lead to greater output and lower prices for consumers. In fact, the opposite occurs -- the exercise of monopsony power leads to a reduction in output. This can be derived from the effect of monopsony power on the cartel's cost curves.(22) Since final output declines, there is no consumer welfare rationale for encouraging monopsony.(23)
MARGINAL COST The formation of a collusive monopsony will cause the industry marginal cost curve of Q to shift upward. To see this, observe first that the cartel correctly understands that the marginal factor cost equals the marginal cost of expanding the variable input L. Specifically, the marginal factor cost measures the increase in the total expenditure on L that is necessary to increase employment by one unit. The added employment necessary to produce one more unit of output equals the inverse of the marginal product of L (denoted [MP.sub.L]) Thus, if we multiply the marginal factor cost of L by the inverse of the marginal product of L, we will have the incremental cost of expanding output by one unit. That is, cartel marginal cost is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Before the exercise of monopsony power, the perceived marginal cost was
MC = w/[MP.sub.L],
since a competitive buyer's individual employment choice negligibly impacts w, thus eliminating the Ldw/dL term from the numerator. Since MFC = w + Ldw/L [is greater than] w, the marginal cost curve shifts up from MC to MC' due to monopsony as shown in figure 2.
[FIGURE 2 GRAPH OMITTED]
AVERAGE COST The profit incentive for behaving as a collusive monopsony derives from the effect on average cost. While the marginal cost rises, the average cost falls at output levels below the competitive one. This, of course, is why profit rises.
The perceived average cost of a competitive firm is given by
AC = F + [w.sub.1]L(Q)/Q,
where [w.sub.1] is the wage in competitive equilibrium (see figure 1), F is the fixed capital cost, and L(Q) the labor input necessary to produce output Q.(24) The average cost of the cartel is given by
AC' = F + w(L)L(O)/Q,
where w(L) is again the (inverse) labor supply. Since w(L) [is less than] ([is greater than]) [w.sub.1] as L is less (greater) than the competitive labor input, AC' [is less than] ([is greater than]) AC as output is less (greater) than the competitive output. The effect of monopsony on the average cost curve is shown in figure 2. The clear implication is that a lower than competitive output permits the cartel greater profits as further discussed below.
WELFARE EFFECTS OF MONOPSONY The welfare effect of monopsony is shown in figures 2 and 3. Prior to the exploitation of monopsony power, the average and marginal cost curves were AC and MC, respectively.(25) The exploitation of monopsony power causes the average cost curve to shift to AC' while the marginal cost shifts to MC' as discussed above. Thus, a monopsonist with no power in the output market would optimally reduce its output from [Q.sub.1] to [Q.sub.2]. The monopsony profits equal (P - AC'([Q.sub.2]))[Q.sub.2]. The reduction in social welfare associated with the exploitation of monopsony power is given by the striped area, which measures the difference between the consumer valuation and the social cost of producing the incremental output [Q.sub.1] - [Q.sub.2]. This social welfare loss can be expressed as
[integral of] [Q.sub.1] [Q.sub.2] (P - MC(Q))dQ. (1)
An alternative representation of the social welfare loss is given by the striped area in figure 3.
[FIGURE 3 GRAPH OMITTED]
Prior to the exploitation of monopsony power, the supply of labor was perceived as being the perfectly elastic line at [w.sub.1]. With the advent of monopsony, however, the supply of labor is seen as the positively sloped line S. The marginal factor cost associated with S is shown as MFC. As we saw above, profit maximization leads to reduced employment from [L.sub.1] to [L.sub.2]. The resulting social welfare loss is the striped area, which is given by
[integral of][L.sub.1][L.sub.2](P [multiplied by][MP.sub.L](L) - (L))dL. (2)
Clearly, the two measures of welfare loss must be the same since they are alternative ways of measuring the same thing. Differentiating the production function Q = Q(L,[K.sub.0]):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Moreover, social marginal cost can be written as
MC = w(L)/[MP.sub.L](L] (4)
Substituting (3) and (4) into (2), and accordingly adjusting the limits of integration, yields expression (1). Thus, the two measures of welfare loss are indeed equal.
III. Quality variation and monopsony
Because student-athletes differ widely in their capabilities of playing a sport, it is important for our application of monopsony to analyze variation in input "quality." Does the above analysis of monopsony apply when quality variation is present? Can a buyer cartel be assured of attracting the players with the most potential? Here we develop a model of the NCAA buyer cartel that extends the theory of monopsony in the presence of quality variation. We show that the standard analysis largely carries over with some reinterpretations. One notable difference is that quality variation intensifies competition, increasing both the incentive to collude and the resulting losses to suppliers of the input.
A. A model of quality variation
Each potential student-athlete has an observable (expected) quality denoted q, with [q.sub.x]. the maximum quality in the population. Let n(q) denote the number of athletes in the population of quality q.(26) There are N teams. The quality of team i is increasing in the number and quality of its players. Specifically, team i's index of quality is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [n.sub.i](q) is the number of quality q players on team i.(27)
The gross revenues of a team depend on the team's quality. Specifically, the revenues of team i equal:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The assumption that r'([I.sub.i]) [is less than] 0 indicates diminishing returns to quality. This is a simple, albeit nonrigorous, way to capture the idea that teams benefit from competitive balance.(28) If r' were to exceed zero, then one team should have all the talent whether social welfare or profits are maximized! Additionally, there are reasons to believe that such diminishing returns exist in sports. For one thing, the probability of winning is bounded above by one so that there is diminishing room for improvement as the probability rises. Second, a few good players may be enough to attract an audience, with then less gain from adding more quality players. Last, positive externalities within a team -- high quality players inducing better performance from less talented ones -- ultimately cause diminishing returns to adding talent.
Any potential player bears costs and receives benefits from playing at (and attending) a school. The costs are comprised of out-of-pocket costs such as tuition and housing, and opportunity costs such as the forgone income from not working. For simplicity, we presume that these costs do not vary with the player's quality (or anything else), and denote them by c. This presumption says that quality is largely unique to the sport in question; i.e., higher quality does not imply higher opportunity cost from forgoing alternative pursuits. If the best alternative is playing the sport elsewhere, either at a semiprofessional or professional level, then it is likely that the forgone benefits would rise with quality. This possibility is accounted for in the benefit function discussed next.
An NCAA player receives benefits, independent of any direct payments, from playing the sport in the school. For those who are likely to go on to play the sport professionally, these benefits consist of the value of training and exposure. We assume that these benefits rise with quality. When the individual would alternatively play the sport elsewhere, these should be understood to be the net benefits from playing in the NCAA school. If the outside market for players reduces wages for the value of training, then any benefits from playing outside the NCAA disappear.(29) Further, NCAA schools probably provide the best player development in most sports.(30) It is also reasonable to presume that benefits rise with quality for those who are certain not to play professionally, e.g., in sports where professional leagues do not exist. Higher quality players have better chances of being coaches and are likely to get more utility from playing.
Hence, let b(q) denote the benefit function from playing at the NCAA school, with b'(q) [is greater than] 0. The minimum wage necessary to attract a player of quality q into the NCAA school and sport is then given by:
w(q) = c - b(q); (7)
with w'(q) = -b'(q) [is less than] 0.(31) Note that w(q) [is less than] 0 is possible, meaning the individual would be willing to pay to play the sport at the NCAA school. This, of course, is an empirical reality: there are many "walk ons" who do not receive grant-in-aid benefits.
B. The socially efficient allocation
To evaluate market outcomes, we consider first the socially efficient allocation. We go on to show that a competitive market induces the efficient allocation, while a buyer cartel does not.
Given N schools, the socially efficient allocation maximizes net surplus, the difference between gross revenues and costs. Mathematically, the problem is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The constraints on the problem are that the number of players of each quality assigned to a team is nonnegative, and the total number of each quality assigned to all teams does not exceed the number in the population.
Solving problem (8) one obtains the following properties of the efficient allocation:(32)
All players above a threshold minimum quality
[q.sub.m] are assigned to a team (and none below). (9.1)
Teams are of equal quality: their index of
quality is equal to 1/N [integral of][q.sub.x][q.sub.m] qn(q)dq. (9.2)
The efficient minimum quality assigned, denoted [q.sub.m.sup.e],
satifies: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Efficiency condition (9.1) confirms one's intuition that only (and all) relatively high quality players should play. Condition (9.2), which indicates that teams should be of equal quality, results from the diminishing returns to quality. Note that the efficient outcome can be attained by equally dividing each quality of those who play among the N teams.(33) Condition (9.3) is the marginal condition that describes the minimum efficient quality of those who play. The left-hand side of the equation is the value of the marginal product of type [q.sub.m.sup.e] (not counting the benefits, b(.), to the player), and the right-hand side is the social cost of his (or her) playing (adjusted for b(.)).
A simple graphical interpretation of the efficient and market outcomes can be given if we assume n(q) does not vary with q. We make this assumption but emphasize that it is purely for expositional convenience and that all our results carry over qualitatively when n(q) varies.(34) With this simplification, it is also convenient and innocuous to adopt the normalization that n(q) = 1 for all q. To provide the graphical interpretation, let [R.sub.e]([q.sub.m]) [equivalent] [Sigma.sup.N.sub.i = 1] R (1/N [integral of] [q.sub.x][q.sub.m] qdq) denote the revenues from efficiently employing all athletes of quality [q.sub.m] or higher, i.e., given that efficiency conditions (9. 1) and (9.2) are satisfied. Using n(q) = 1 for all q, observe that the quantity of athletes employed for given [q.sub.m] is given simply by: Q = [integral of][q.sub.x][q.sub.m] dq = [q.sub.x] - [q.sub.m]. Hence, efficiently increasing the number of athletes employed corresponds to decreasing [q.sub.m]. Now let [r.sub.e]([q.sub.m]) denote the value of the marginal product (i.e., the marginal revenue) from increasing employment of athletes when minimum quality is [q.sub.m]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Figure 4 depicts the efficient outcome (ignore W([q.sub.m]) for now). The horizontal axis has two scales. As usual, the quantity of athletes increases as one moves to the right, shown by the dashed scale. Along with a quantity increase, the minimum quality employed decreases as we move to the right, shown by the solid scale. The figure also shows the wage function of the minimum quality employed, w([q.sub.m]). As quality decreases, the necessary wage payment rises as discussed above. The case depicted in figure 4 presumes w([q.sub.m]) is negative at high minimum qualities. The figure also contains the value of the marginal product at each minimum quality employed. As the minimum quality employed declines moving to the right, the value of the marginal product declines since lower quality is added and due to diminishing returns.(35) We see that the social surplus at the efficient minimum quality employed equals area ABC. How this surplus is shared depends on how the efficient outcome is engendered, e.g., as in a competitive market discussed next.
[FIGURE 4 GRAPH OMITTED]
C. Competitive equilibrium
We must generalize the notion of perfect competition to the case where athletes vary in observable quality. We presume a team will bid for a player of quality q up to the point where the wage bid equals the value of the player's marginal product to the team. Players choose the team that makes the highest offer if it is at least as high as w(q), since this maximizes the player's net benefit. Of course, absent quality differences in players, this definition of a competitive market yields the standard competitive equilibrium.
The competitive equilibrium with N schools satisfies the efficiency conditions (9.1)-(9.3) and pays players the quality dependent wage:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [I.sub.e], is the quality index of teams at the efficient allocation. To see these results, first observe that school qualities must be equalized (i.e., the first part of (9.2) must be satisfied).(36) If school i were of higher quality than school j, then the value of the marginal product of any quality player would be higher at school j than i due to diminishing returns. Then school j would out-bid i for any player, a contradiction.
Condition (9.1) is satisfied by the following argument. Given that any player is employed at a school, all higher quality players have higher values of their marginal products at that school. Since the higher quality players require lower wages to matriculate, they would be made acceptable offers.
Now, whatever minimum quality, [q.sub.m], is employed, each school must have quality index: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to have equalized qualities.
Property (9.3) and the second part of (9.2) are established if [q.sub.m] = [q.sub.m.sup.e]. If [q.sub.m] [is greater than] [q.sub.m.sup.e], then the value of the marginal product of player of quality epsilon lower than q. exceeds the wage necessary to attract the player. Teams would have quality indices lower than [I.sub.e], implying higher values of marginal products than when the quality index equals I,, hence values for marginal players that exceed w(.). Teams would find it profitable to make wage offers to players of quality lower than [q.sub.m], offers that the players would accept. A similar argument establishes that [q.sub.m] [is less than] [q.sub.m.sup.e] would imply teams take losses on players employed of quality near [q.sub.m]. Hence, the minimum quality employed in competitive equilibrium equals [q.sub.m.sup.e], and properties (9.1) - (9.3) have been established.
Teams would continue to bid higher wages for a player with q [greater than or equal to] [q.sub.m.sup.e] as long as the wage is below the value of the player's marginal product, qr([I.sub.e]). Hence, the competitive wage is bid up to each employed type's equilibrium value of the marginal product as stated in (11).
Figure 4 shows W([q.sub.m])), and thus the competitive equilibrium. The competitive wage exceeds the wage necessary to attract the player (w([q.sub.m.sup.e])) and rises with quality. These follow since qr([I.sub.e]) increases with q, and we know type [q.sub.m.sup.e] is paid exactly w([q.sub.m.sup.e]). Hence, higher quality commands a higher wage.
What may be slightly less intuitive is that W([q.sub.m]) [is less than] [r.sub.e]([q.sub.m]) for all [q.sub.m] [is greater than] [q.sub.m.sup.e], implying schools obtain some surplus in competitive equilibrium.(37) Mathematically, the result follows because
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
since r' [is less than] 0. The corresponding intuition is that the diminishing returns to team quality cause the value of any inframarginal player's marginal product to be below the same if the player were the marginal player. This is the analogue in the standard model without quality variation to an input's marginal product being below its average product when there are diminishing returns.
We see in figure 4 that competitive equilibrium shares the efficient surplus, with area ABD accruing to the schools, and area DBC going to the players. The vertical distance between W([q.sub.m]) and w([q.sub.m]) equals the surplus accruing to player of quality [q.sub.m].(38)
D. Cartel equilibrium
The ideal cartel would price discriminate over quality, paying each student-athlete just w(q). Higher quality athletes would receive lower wages, perhaps negative wages, reflecting the additional benefits they receive from playing at the NCAA school. We believe such discrimination fails to occur mainly because it would attract attention, likely working to the detriment of the cartel.(39) Hence, we consider the buyer cartel that pays all qualities employed the same wage, denoted [w.sub.c].
It is clear that the cartel will set [w.sub.c] equal to w([q.sub.m]) of the lowest quality employed, and employ all higher qualities. The latter is because all those of higher quality than the minimum employed generate more revenues and are willing to matriculate at this wage. It is also easy to show that each school will be of equal quality to maximize profits, again deriving from diminishing returns. Hence, efficiency conditions (9.1) and (9.2) will be satisfied. The issue facing the cartel is determining the minimum quality and wage (and associated quantity of athletes) that is optimal.
This problem can be written:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
The first-order condition describing the cartel's choice of [q.sub.m] is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [q.sub.m.sup.c] denotes the cartel's optimal minimum quality. The righthand side of equation (14) is the marginal factor cost (MFC) of increasing the minimum quality. One must be careful in interpreting the MFC here since [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the wage change from increasing [q.sub.m], i.e., from decreasing the quantity employed. The implication is that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is negative, and the MFC exceeds w(q.sub.m]) at all [q.sub.m].
The cartel's optimum is depicted in figure 5. The cartel increases the minimum quality relative to the competitive/efficient minimum quality to pay the lower wage [w.sub.c]. Of course, it is accordingly restricting the number of athletes employed. A nearly analogous welfare analysis to the standard case applies. The cartel increases its profits by the excess of area DFG[w.sub.c] over area EBF. The cartel gains come solely at the expense of the athletes, who collectively lose area [w.sub.c]DBG in surplus. The net social welfare loss is area EBG.(40)
[FIGURE 5 ILLUSTRATION OMITTED]
The difference from the standard analysis is one of magnitude. Corresponding to the fact that W([q.sub.m]) is downward sloping, the transfer away from athletes rises relative to the case having all athletes paid the value of the marginal product of the marginal athlete in competitive equilibrium. Not only does the cartel permit a lower wage to the marginal player, but it also limits the competition for quality by fixing a single wage. Consequently, higher quality players lose the most from the formation of the buyer cartel. The flip side of this is an added incentive for formation of the cartel.
IV. A positive theory of collusive monopsony
In the preceding sections, we assumed that the colluders encountered neither difficulty nor cost in forming and implementing the cartel. But a stable buying cartel must perform three vital functions, which are neither simple nor free:
2. coordination, and
3. compliance.(41) If a cartel fails to provide for all three of these, the prospects for success are dim.
Concurrence is necessary because the members of the buying cartel must agree on the optimal price to pay. This will not be a trivial exercise because of differences across cartel members. Absent side payments among members of the buying cartel, there will be disagreement about the best price. Side payments are unlikely both because they invite antitrust scrutiny and an incentive to renege can be anticipated. Moreover, the cartel must agree on various nonprice parameters that can serve as substitutes for monetary compensation. Athletes might be compensated with posh housing and coaches with extraordinary fringe benefits for example. Hence, concurrence is a complicated, multidimensional problem.
Coordination is essential to assure that the outcome is as intended. Buyers must avoid inadvertently obtaining mom than their quota of the input and otherwise inducing supply to exit the market. A member team might unintentionally generate excessive interest among the scarce supply of quality athletes to the point that some prefer to matriculate as walk-ons (nonscholarship athletes), with unintended and adverse consequences for the cartel. Or, consider the two-sport star who chooses to play basketball rather than football because an acceptable school fails to offer him a football scholarship in a timely fashion. Likewise, a quality coach interested in a subset of college coaching jobs may be of interest to some of these teams, but may opt for a job in the professional ranks due to a coordination failure among college teams.
Compliance is the most celebrated of cartel problems.(42) The temptation to cheat will be hard to resist. At the cartel solution, the value of the marginal product will exceed the wage being paid. Consequently, the return to exceeding one's quota is an immediate increase in profits. There is no inexpensive way of disciplining cheaters.(43) But if cheating cannot be prevented, the buying cartel will fail because the members will behave competitively. Nonprice, instruments exacerbate the problem. If the cartel members are free to use nonprice measures to allocate the reduced quantity (and quality) among themselves, they will tend to dissipate the monopsony profits through fringe benefits, deferred compensation, and the like.(44) In effect, the value of the nonprice components will increase until the monetary value of the sum of the price and nonprice components equals the noncollusive price, and the conspirators will have gained nothing.
Thus, a successful buying cartel must carve out an agreement among its members, it must work out a plan to implement the agreement, and it must police that agreement. All of this may be feasible, but none of it is free. Even when collusion is legal, its high costs of success frequently precludes it.(45) When the costs are small relative to the gains, however, then we should expect collusion to flourish in the absence of legal prohibitions.
V. NCAA as a collusive monopsony
The NCAA behaves like a collusive monopsony in acquiring two crucial inputs: student-athletes and coaches.(46) As a result, it faces the usual problems confronted by all cartels: deciding on payments, input quotas, and nonprice parameters, sharing the resulting profits, coordinating activities, and deterring cheating.(47) The structure of the NCAA is designed to deal with these problems. The NCAA's durability, resilience, and enormous success is testament to its ability to evolve in ways that are necessary to cope with the changing needs of its member institutions.
Before intercollegiate athletics became big business, there was a need for uniform rules regarding the games being played. As a result, a precursor to the NCAA was formed in 1905. Between then and now, the NCAA has evolved in size, scope, and power.(48)
The NCAA members -- some 1000 educational institutions -- meet annually to vote on a variety of matters. If necessary, special sessions can be called between the annual meetings. There are various committees that advise the NCAA members at large on specific issues of interest. Once agreement is reached, the policies of the NCAA are set out in bylaws that are binding on the members. Among these bylaws are those that deal with student-athletes and with coaches. There are rules governing the compensation of student-athletes. Generally, athletes may not receive more than a "full grant-in-aid," which is defined as "financial aid that consists of tuition and fees, room and board and required course-related books."(49) In addition to the limits on compensation, the NCAA limits the number of grants-in-aid that can be awarded in each sport.(50) These limitations are summarized in table 1. As one might expect, there are detailed rules regarding how one counts the student-athletes in the various sports and how to deal with those that participate in two sports. There are also detailed rules regarding recruiting. All of this is fully consistent with cartel theory. If restrictions on prices and quantities are to be fully effective, indirect means of skirting the restrictions must be foreclosed.
Table 1 Maximum Number of Grants-In-Aid 1996-1997 Men's sports No. Women's sports No. Baseball 11.7 Archery 5 Basketball 13.0 Badminton 6 Cross country/track 12.6 Basketball 15 Fencing 4.5 Bowling 5 Football 85.0 Crew 20 Golf 4.5 Cross country/track 18 Gymnastics 6.3 Fencing 5 Ice hockey 18.0 Field hockey 12 Lacrosse 12.6 Golf 6 Rifle 3.6 Ice hockey 18 Skiing 6.3 Lacrosse 12 Soccer 9.9 Skiing 7 Swimming 9.9 Soccer 12 Tennis 4.5 Softball 12 Volleyball 4.5 Squash 5 Water polo 4.5 Swimming 14 Wrestling 9.9 Synchronized swimming 5 Team handball 10 Water polo 8
SOURCE: 1996-97 NCAA DIVISION I OPERATING MANUAL, articles 15.5.3-15.5.5.
As one might suspect, the limitations on the number of coaches by sport are fairly detailed for football, but are less so for the other sports. A "countable" coach is anyone who "participates (in any manner) in the coaching of the intercollegiate team in practice, games or organized activities directly related to that sport...."(51) For Division I-A football, there is a limit of one head coach, nine assistant coaches, and two graduate assistant coaches. In addition, an institution may employ a strength and conditioning coach who does not count against the number of football coaches. The limitation on the number of coaches for the other sports are summarized in table 2. The designation of "restricted earnings coaches" has been abandoned due to litigation that will be examined in the next section.
Table 2 Maximum Number of Coaches 1996-1997 Men's sports No. Women's sports No. Baseball 2/1 Archery 2/0 Basketball 3/1 Badminton 2/0 Cross country/track 2/1 Basketball 3/1 Fencing 1/1 Bowling 2/0 Football(*) 10/0 Crew 3/0 Golf 1/1 Cross country/track 2/1 Gymnastics 2/1 Fencing 1/1 Ice hockey 2/1 Field hockey 2/1 Lacrosse 2/1 Golf 1/1 Rifle 1/1 Gymnastics 2/1 Skiing 1/1 Ice hockey 2/0 Soccer 2/1 Lacrosse 2/0 Swimming 1/1 Rifle 1/1 Tennis 1/1 Skiing 1/1 Volleyball 2/1 Soccer 2/1 Water polo 1/1 Softball 2/1 Wrestling 2/1 Squash 2/0 Swimming 2/1 Synchronized swimming 2/0 Team handball 2/0 Tennis 1/1 Water polo 2/0
(*) In football, two graduate assistant coaches are also permitted.
SOURCE: 1996-97 NCAA Division I Operating ManuaL, article 11.7.4. Each entry shows the number of head or assistant coaches and the number of restricted earnings coaches. For example, in women's basketball, the NCAA permitted three head or assistant coaches and one restricted earnings coach.
A. Revenue sharing
In simple, textbook cartel models, there is no real need to worry about revenue sharing When al the cartel members are symmetric, the restrictions can usually be spread proportionately. As a result, each member just keeps the excess profit that its own operation generates and equal profit sharing results.(52) In the real world, of course, firms are not apt to be symmetric and this may pose problems in sharing the cartel's spoils. This is particularly true of sports franchises. To retain cartel stability, revenue sharing may be necessary. In professional football, for example, revenue sharing is extremely important. Much the same is true in intercollegiate athletics. Gate receipts are shared with opposing teams, bowl revenues are shared, television revenues are shared, and the NCAA basketball tournament revenues are shared. Now, revenue sharing is not complete. For example, individual institutions keep private donations, licensing receipts, concession revenues, and gate receipts (net of payments to opposing teams), which means that some cartel members are going to be much better off financially than others. The revenue sharing algorithm has evolved over time, however, to prevent the defection of a coalition of the most powerful athletic programs.
The NCAA has developed sanctions to deal with cheating by member institutions. This gives the NCAA an enormous advantage over most cartels that have limited enforcement options. Consider, for example, the cartel in the Trans-Missouri case.(53) There, competing railroads agreed to change freight rates at monthly meetings. Any rate deviation that violated this agreement resulted in a $100 fine. In contrast, when the NCAA found the University of Washington guilty of recruiting violations, it imposed substantial sanctions: (1) a 2-year ban on bowl participation, (2) a 1-year ban on receiving television revenue, (3) a reduction in football scholarships for 2 years, (4) a reduction in the number of permissible football recruiting visits for 2 years, and (5) a 2-year probation.(54) Even on an inflation adjusted basis, this is considerably more than a $100 fine.
In the 1946-1953 period, the major conferences met and decided on rules for recruiting and limitations on financial aid. Earlier efforts had been largely unsuccessful, but this time they also created an enforcement mechanism. Committees were established to investigate cheating and to enact punishment. Unfortunately, the only available punishment was expulsion, which is a rather blunt instrument. Eventually, however, the NCAA refined the sanctions to include the elimination of revenue sharing and reductions in the number of grants-in-aid, television appearances, bowl appearances, and eligibility for championships. In extreme cases, the NCAA may issue the "death penalty" by suspending a program for a period of several years.
VI. Two examples of the NCANS collusive monopsony
There are two cases that demonstrate the NCAA's behavior as a collusive monopsonist. These cases also illustrate the judiciary's difficulty in understanding some fundamental economic concepts. In the first case, economic misconceptions mattered, but not in the second.
A. Hennessey v. NCAA(55)
In Hennessey, there were numerous allegations, but we will focus on the antitrust issues.(56) At a special session in 1975, the NCAA members agreed to limit the maximum number of assistant football and basketball coaches. This restriction applied only to Division I schools. As a result of the restriction, Hennessey was demoted to part-time status after being an assistant coach for 16 years. His compensation was reduced by 90% from $20,000 to $2 100.(57)
The court found that the NCAA Bylaw limiting the number of coaches resulted from an agreement among the member institutions that obviously restrained trade. But the question was whether the agreement constituted an unreasonable restraint of trade. Before analyzing the reasonableness of the restraint, the court found that Hennessey had antitrust standing to assert his claims against the NCAA.(58) Hennesey argued that the bylaw amounted to a group boycott and, therefore, was illegal per se. This would not seem to be an apt characterization. NCAA members were free to deal with Hennessey. There was neither an individual nor a group of individuals who were specifically excluded.
The restraint was not on those with whom NCAA members could deal. Rather, the restraint was simply on the number of coaches that could be hired by any single institution.(59)
The court refused to grant the NCAA and its member institutions a blanket antitrust exemption, but it did decide that it was appropriate to evaluate the restraint under the rule of reason. In this connection, the court noted an absence of specific intent to injure the named plaintiffs or other assistant coaches, either individually or as a group. This observation, however, reveals a lack of understanding of supply. If the supply function of assistant coaches has a positive slope, an agreement to reduce the number of assistant coaches hired has two effects. First, some coaches will lose their jobs entirely or be demoted as Hennessey was. Second, there is movement along the supply curve to a lower wage. As a consequence, the record may be devoid of any articulation that this is the unabashed intent, but it nonetheless is true that the restraint will have an adverse effect on the community of assistant coaches.(60) The fact that the NCAA members apparently were concerned about the welfare of those whom they knew would be hurt seems to have influenced the Court.(61) To see how silly this is, one need only ponder whether similar expressions of concern would get price fixers in the output market off the hook.
The court clearly understood the nature and purpose of the NCAA's endeavor: Bylaw 12-1 was ... intended to be an `economy measure.' In this sense, it was both in design and effect one having commercial impact."(62) What then were the redeeming virtues of the restraint?
Apparently, some member institutions were having financial difficulty. Those colleges with athletically and economically more successful programs were seen as taking (unfair) advantage of their success by expanding their programs.(63) This sounds very much like more output or higher quality output is bad. The acknowledged concern was that the less successful programs were having a hard time catching up to and keeping up with the more successful programs. Success had to be harnessed so all could enjoy being mediocre. This is not to say that competitive balance is undesirable, but the goal should be to raise quality to a common level. It should not be to reduce the quality of superior programs.
The NCAA has had a measure of success in peddling the line that it is concerned with preserving amateurism. This, of course, is a sham. Everything about Division I football and basketball is big business. The only amateurs (arguably) are the players. As for Hennessey and his brethren, restricting their number was deemed necessary to preserve "the competitive, and the amateur nature of the programs." Incredibly, the court found that "the fundamental objective [of the bylaw] was to preserve and foster competition in intercollegiate athletics by curtailing ... potentially monopolistic practices by the more powerful and to reorient the programs into their traditional role as amateur sports operating as part of the educational process."(64) But there was no proof that this restraint would save intercollegiate athletics. And the court did not demand any. One would think that the NCAA should have had to shoulder the burden of proving that a plainly anticompetitive restraint will have redeeming features. It should not have been allowed to point to some vague ideal of preserving amateurism. But this court was "of the view admittedly bordering on speculation that the Bylaw will be of value in achieving the ends sought...."(65)
Finally, the court fashioned a "ruinous competition" defense for the NCAA members. The restraint, according to the court, may have beneficial effects for the assistant coaches by preserving employment opportunities.(66) Absent the restraint -- and the consequent cost saving -- financially marginal athletic programs may shut down. Thus, the restraint will have the long-run effect of increasing the number of potential employers above the free market level. This, of course, is analogous to telling consumers that price fixing in the presence of ruinous competition really benefits them because there will be more sellers (and, therefore, more choice) than without the price fixing. It is hard to take such a suggestion seriously.
B. Law v. NCAA
In spite of a few methodological slips along the way, Judge Vratil got to the correct result in Law v. National Collegiate Athletic Association.(67) This case involved a collusive effort on the part of the NCAA and its members to reduce the salaries paid to certain assistant coaches. The explicit purpose of the resultant NCAA bylaw 11.02.3 was to stabilize and depress the compensation the coaches designated as restricted earnings coaches. At least since Socony-Vacuum,(68) such interference with the price mechanism has been illegal per se. In this case, however, the court engaged in a rule of reason analysis.
Apparently, a large number of NCAA members were still experiencing financial difficulties of one sort or another in the late 1980S.(69) In 1989, the NCAA formed a Cost Reduction Committee to explore alternative ways of reducing the costs of the intercollegiate athletic programs. The goal was to reduce cost without sacrificing competitive balance or curtailing access to higher education by student-athletes. At the same time that some schools were eliminating certain nonrevenue sports, there were pressures to spend even larger sums to recruit the most talented athletes and coaches. To do otherwise would have meant becoming less competitive on the field.
The NCAA decided that a collaborative effort to reduce costs was necessary. Of course, each school could have acted unilaterally to reduce its costs in any number of ways -- reducing the number of sports offered, the number of scholarships, the value of a scholarship, the number of coaches, the salaries of the coaches, travel budgets, equipment budgets, and the like. But a unilateral cost reduction, if unmatched by rival schools, would create an uneven playing field. The cost cutter would become less competitive than its rivals that did not reduce costs and competitive balance would be lost. As a school begins to lose on the field, spectator interest wanes and revenues fall thereby worsening the school's financial position. The net result may not be improved financial viability if revenues fall by more than the cost savings.
The NCAA's Cost Reduction Committee felt that cost savings could be achieved by reducing the number of coaches in all Division I sports. In addition, in every sport other than football, one coach would be designated a restricted earnings coach. A restricted earnings coach's compensation could not exceed $12,000 during the academic year and $4000 during the summer.(70) Some of the coaches that were affected had been earnings $60,000-70,000 annually. For them, this was draconian.
The court began by noting that an agreement fixing the maximum salaries that will be paid to one class of employees attracts antitrust attention. In fact, in most circumstances, one would expect such an agreement to be a per se violation of section I of the Sherman Act.(71) But the NCAA enjoys rule of reason treatment because the NCAA and its members sell competition: athletic contests between rival schools. Consequently, some horizontal restraints on competition in the market are deemed necessary to make the output possible.(72) The court conceded that the NCAA plays a vital role in making intercollegiate athletic events available to the public and, therefore, its restraints should be examined for their reasonableness. At the same time, however, the court expressed its belief "that the Supreme Court [did not intend] to give the NCAA carte blanche in imposing restraints of trade on its member institutions or other parties because of its role in the marketplace. There can be no doubt that the NCAA is subject to the antitrust laws...."(73)
The usual rule of reason formula is to examine a business practice and identify its procompetitive and anticompetitive effects. These effects must be weighed and legality under the Sherman Act thereby determined. This, of course, is no mean feat.(74) But one may think of this exercise in terms of the ancillary restraints doctrine, which can be traced to Judge Taft's reasoning in Addyston Pipe & Steel.(75) There, Judge Taft found that restraints of trade that were ancillary to a lawful main purpose, were essential to its success, and were no more restrictive than necessary to accomplish the desired end did not violate section 1 of the Sherman Act. Applying the ancillary restraints doctrine to the NCAA's bylaw 11.02.3 reveals that the agreement to restrain competition in hiring basketball coaches is not an ancillary restraint. The main purpose of the restraint was to reduce compensation.
It is clear on its face that the restricted earnings coach rule has an adverse anticompetitive effect in the market. Some of the restricted earnings coaches had earned salaries of $60,000 to $70,000 prior to the rule,76 which reduced their maximum compensation to $12,000 to $16,000. Presumably, the higher salaries resulted from market forces that were blunted by the agreement. Thus, the adverse anticompetitive impact of the rule was apparent to the court:
Because the Restricted Earnings Coach Rule specifically prohibits the
free operation of a market responsive to demand and is thus
inconsistent with the Sherman Act's mandates, it is not necessary for the
Court to undertake an extensive market analysis to determine that the rule
has had an anticompetitive effect on the market for coaching services.(77)
But the NCAA argued that the cost savings flowing from the restraint were necessary to assure the NCAA's survival, which would mean that the product of college basketball would continue to be provided. As a consequence, there would continue to be a market for college basketball coaches, which might not exist otherwise. In essence, the NCAA argued that its restraint was really procompetitive in this sense.
In this regard, the court pointed out that a procompetitive justification for a restraint must apply to the same market in which the restraint is imposed. In other words, the NCAA cannot argue that a restraint in the input market for coaching services can be offset by an expansion (or preservation) of output in the output market for intercollegiate athletic contests. The court's concern is legally justified by the cases that it cites,(78) but the court's economic justification is incorrect:
If price-fixing buyers were allowed to justify their actions by claiming
procompetitive benefits in the product market, they would almost
always be able to do so by arguing that the restraint was designed to
reduce their costs and thereby make them collectively more
competitive sellers. To permit such a justification would be to give
businesses a blanket exemption from the antitrust laws and a practically
limitless license to engage in horizontal price-fixing aimed at
As we have shown above, the court's concern rests on a misunderstanding of the economic effects of monopsony. While it is true that average cost falls and the price-fixing buyers will become more profitable, it is also true that marginal cost will rise and thereby reduce the profit-maximizing output.
The NCAA responded by arguing that the rule was necessary to maintain "a level playing field in the sports arena, retaining and fostering the spirit of amateurism ..., and protecting NCAA member institutions from self-imposed, ruinous cost increases."(80) In part, the NCAA pointed to its success in Hennessey, which we may recall challenged an NCAA bylaw restricting the number of football and basketball coaches that member institutions could employ. There, the court found that the plaintiffs failed to prove that the intent was to hurt them. The court found that the NCAA's motivation was more noble: "to preserve and foster competition in intercollegiate athletics ... and to reorient the programs into their traditional role as amateur sports operating as part of the educational process."(81) But it is the athlete -- not the coach -- who is supposed to be an amateur. It is not apparent that the rule at issue in Law will level any playing field or contribute to competitive balance. It will, of course, tend to weed out competent, experienced coaches and tend to weaken the quality of the coaching staff. This would tend to reduce the quality of the athletic performance.(82)
The NCAA's concern with its members' "self-imposed, ruinous cost increases" is reminiscent of long-abandoned claims that price fixing in the output market was necessary to avoid the ravages of "ruinous competition." This defense was offered to and rejected by the Supreme Court in United States v. Trans-Missouri Freight Association(83) some 100 years ago. Over 50 years ago, Justice Douglas pointed out that ruinous competition is no defense to a price-fixing charge.(84) It would not seem sensible to resurrect this defense for the NCAA. Apparently, the court agreed.
In Law, the court found that the restricted earnings coach rule may be intended to further some legitimate goals of the NCAA, but the NCAA failed to do more than assert that the rule would, in fact, further these goals. No evidence was presented to support the NCAA's claims. Given this finding, the court did not have to consider whether the rule was the least restrictive way of achieving the stated goals. Accordingly, the court found in favor of the plaintiffs.
VII. Concluding remarks
Gary Becker has objected to the cartel activities of the NCAA.(85) In the name of "amateurism," the member institutions agree among themselves on the permissible compensation of athletes. As we have seen, the NCAA also restrains competition in the market for coaches. To some extent, the NCAA's behavior goes unchallenged because the NCAA hides behind a "smokescreen of good intentions." But the harmful economic effects should not be ignored. There are social welfare losses associated with the NCAA's collusive behavior toward athletes and coaches. Relative to a competitive marketplace, athletes and some coaches clearly suffer. The restrictions on prices and quantities have no clearly demonstrated redeeming virtues. If such restrictions are the least cost means of correcting competitive externalities among sports teams, then it behooves the NCAA to demonstrate this clearly. While such externalities were not part of our model, it seems clear that these could be controlled by revenue-sharing agreements -- since the externality is on teams' revenues. Revenue-sharing agreements that correct such an externality will preserve the distribution of the surplus that would result in a competitive market not subject to the externality. In principle, revenue sharing in extreme forms could provide a means of restricting payments to players and coaches, but this is unlikely to be enforceable and, in any case, clear in intent.(86) We believe that the NCAA's direct restrictions on compensation and quantities is indicative of their purpose of enhanced profitability at the expense of athletes and some coaches. We also believe that the NCAA should be fair game for antitrust prosecution by the Department of Justice and by private litigants.
(1) For a thorough treatment of the antitrust law and economics of monopsony, see Roger D. Blair & Jeffrey L. Harrison, Monopsony (1993).
(2) Meg Cox, At Many Auctions, Illegal Bidding Thrives as a Long Time Practice Among Dealers, Wall St. J., Feb. 19, 1988, at 23, col. 1.
(3) Mandeville Island Farms v. American Crystal Sugar Company, 334 U.S. 835 (1947).
(4) United States v. Portac, Inc., 869 F. 2d 1288 (9th Cir. 1989).
(5) Cox, supra note 2.
(6) United States v. Perfection Machine Sales, Inc., Criminal No. 88-00281 (E.D.Pa., July 18, 1988).
(7) See Blair & Harrison, supra note 1, at 10-11.
(8) A more extensive and somewhat different treatment is provided by Arthur A. Fleisher, III, Brian Goff & Robert D. Tollison, The National Collegiate Athletic Association: A Study in Cartel Behavior (1992).
(9) "Everyone" knows that the ideal of amateurism is a sham. See, e.g., William C. Rhoden, A Charade Continues in Front of Thousands, N.Y. Times, Aug. 26, 1996, at B5, col. 3.
(10) Hennessey v. National Collegiate Athletic Association, 564 F. 2d 1136 (5th Cir. 1977).
(11) Law v. National Collegiate Athletic Association, 902 F. Supp. 1394 (1995).
(12) Here we presume the market is otherwise competitive and the transacted good or service is associated with no externalities that might lead to market failure. On market failure, see F. M. Bator, The Anatomy of Market Failure, 72 Q. J. Econ. 351 (1958).
(13) See, e.g., Hal Varian, Intermediate Microeconomics 258-60 (1987).
(14) Id. at 262-63.
(15) See Roger D. Blair & David L. Kaserman, Antitrust Economics 3-45 (1985).
(16) Many of the antitrust concerns with monopsony are explored in Roger D. Blair & Jeffrey L. Harrison, Antitrust Policy and Monopsony, 76 Cornell L. Rev. 297 (1991) and Roger D. Blair & Jeffrey L. Harrison, Cooperative Buying, Monopsony Power and Antitrust Policy, 86 Nw. U. L. Rev. 331 (1991).
(17) More formally, Q(L,K)=[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] where N is the number of producers of Q, [q.sub.i](*) is the neoclassical production function of the ith producer, [L.sub.i] and [K.sub.i] are the inputs of the ith producer, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), and inputs are allocated across the producers so that output is maximized (i.e., marginal products are always equalized). This aggregation to a single production function is valid both in a competitive market and under an optimal cartel.
(18) Formally, the supply of L is the inverse function: [w.sup.-1](w).
(19) We have also abstracted from possible monopoly opportunities in the selling of Q by assuming the cartel faces an invariant output price.
(20) The results all carry over when K is variable, but the demonstrations are substantially more complicated.
(21) The intuition as to why a buyer cartel is profitable when w(L) is upward sloping is as follows. The wage savings from decreasing the purchase of L a little below [L.sub.1] is applied to all L purchases, with virtually no loss in buyer surplus since the value of the L forgone (i.e., the value of the marginal product near [L.sub.1]) approximately equals the forgone costs [w.sub.1]). The optimal extent of the purchase restriction depends on the demand and supply elasticities.
(22) An extremely useful reference is provided by C. E. Ferguson, The Neoclassical Theory of Production and Distribution 169-86 (1969).
(23) Because our analysis presumes an invariant price of final output, consumers of Q experience no net loss from the output reduction, since their cost savings equal their loss in benefits. All losses are borne by the suppliers of L. If the buyers also have monopoly power in the Q market, then additional losses would result that would be borne by consumers of Q.
(24) L(Q) is found by inverting the production function given K is fixed.
(25) We treat AC and MC here as the average and marginal cost in the entire competitive industry, i.e., the aggregation of the individual competitive producers' curves. We are also assuming every producer earns only a normal return in the competitive equilibrium, but this simplification is unimportant to the results.
(26) Formally, n(q) is the measure of types q in the population since we treat q as a continuous variable.
(27) Realistically, a team will need to be of minimum size for quality to be positive (i.e., [integral of][q.sub.x] 0 [n.sub.i](q)dq [is greater than] minimum). We ignore this constraint for simplicity, which would rarely be binding in our application to the NCAA.
(28) We have chosen not to model explicitly the possible dependence of one team's revenues on its relative quality. We avoid considerable complication by abstracting from such externalities.
(29) Offsetting this, however, would be the marketable value of play while the player is developing. Our model applies most cleanly when players have little marketable value while developing outside of NCAA schools. We believe this is the more common case, with, perhaps, baseball being a debatable application (because it has a well-developed "farm system").
(30) Baseball may be the exception. See the previous footnote.
(31) One might object that c should be adjusted when the player's alternative is playing professionally. Being explicit about this does not change anything.
(32) Proofs are available on request.
(33) There are degrees of freedom in assigning the players to achieve equal qualities and the efficient outcome. Beginning with the equal division of players among teams, one team could "trade" one higher quality player with another team for more than one lower quality player and maintain all teams' qualities for example. Such reallocations are completely inconsequential in our model.
(34) Realistically, n(q) would decline as quality rises, at least beyond some threshold. We indicate in footnotes the quantitative adjustment to results when n(q) varies.
(35) Mathematically, the slope of [r.sub.e]([q.sub.m]) in figure 4 equals -[r.sub.e]'([q.sub.m]) since minimum quality decreases as we move to the right. We have from (10): -[r.sub.e]'([q.sub.m]) = -r + r'[multiplied by][q.sub.m] [sup.2/N] < 0, the inequality using (6). The first term of -[r.sub.e]' captures the declining quality and the second term diminishing returns to the quality index.
(36) The mathematical counterparts of the verbal explanations we offer here are straightforward.
(37) This "surplus" might be dissipated on other inputs. For example, if other costs to schools consist of only fixed costs, then free entry equilibrium would have this surplus just cover these costs.
(38) If player numbers varied with quality, then this distance would equal the surplus per player of this quality type, and the total surplus of this type would equal n([q.sub.m]) multiplied by the distance. Likewise the surplus to schools would be adjusted at each [q.sub.m]. The graphical analysis would be the same except that the quantity scale would be adjusted to reflect variability in n([q.sub.m]) as [q.sub.m]. Quantity along the horizontal axis would satisfy
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
(39) The discrimination would also exacerbate the concurrence, coordination, and compliance problems discussed below.
(40) These areas would need to be adjusted as in footnote 38 above if n(q) varies. The qualitative results would all be the same.
(41) Kenneth G. Elzinga, New Developments on the Cartel Front, 29 Antitrust Bull. 3, 7 (1984).
(42) See, e.g., Blair & Kaserman, supra note 15, at 141-45.
(43) For an examination of this complex problem, see Daniel Orr & Paul W. MacAvoy, Price Strategies to Promote Cartel Stability, 32 Economica 186 (1965).
(44) See, e.g., George J. Stigler, Price and Nonprice Competition, 72 J. Pol. Econ. 23 (1968).
(45) Andrew R. Dick, When Are Cartels Stable Contracts?, 39 J. L. & Econ. 241 (1996), provides an interesting examination of legal cartels formed under the Webb-Pomerene Export Trade Act. He demonstrated empirically that legal cartels are frequently unstable.
(46) The NCAA has been so successful that "the NCAA is the clear and deserving winner of the first annual prize. for best [monopsony] in America." Robert J. Barro, Let's Play Monopoly, Wall St. J., Aug. 27, 1991, at A12, col. 4. The Antitrust & Trade Reg. Rep., Jan. 30, 1997, at 101, reported that the NCAA "continues in many regards to operate as a cartel...."
(47) For a proposed solution, see D. K. Osborne, Cartel Problems, 66 Am. Econ. Rev. 835 (1976).
(48) For a more detailed historical account, see Fleisher, et al., supra note 7.
(49) 1996-97 NCAA Division I Operating Manual, article 15.02.5.1. The specific definition of each component of a full grant-in-aid is contained in article 15.2.
(50) The limitations for men's and women's basketball are found in id., at article 15.5.4; the limit for football is in article 15.5.5. For the other sports, see article 15.5.3.
(51) Operating Manual, Supra note 24, at article 188.8.131.52.1.
(52) For a classic treatment, see Don Patinkin, Multiple-Plant Firms, Cartels, and Imperfect Competition, 61 Q.J. Econ. 173 (1947).
(53) United States v. Trans-Missouri Freight Association, 166 U.S. 290 (1897).
(54) Hairston v. Pacific-10 Conference, 9th Cir. No. 95-35309, Dec. 3, 1996.
(55) Hennessey v. National Collegiate Athletic Association, 564 F. 2d 1136 (5th Cir. 1977).
(56) Hennessey also alleged tortious interference and civil rights violations. Both of these were rejected by the court.
(57) Hennessey, 564 F. 2d at 1141.
(58) The court was satisfied that the NCAA was not entitled to an educational exemption based on its reading of Goldfarb v. Virginia State Bar, 421 U.S. 773 (1975), and that interstate commerce was affected.
(59) In an appalling effort to "pigeon hole" the restraint, the court considered calling it a "division of markets" or an allocation of market shares." Hennessey, 564 F. 2d at 1151.
(60) Precisely the same is true of price fixing in output markets: some people are hurt because they do not consume at all while others are hurt because they continue to buy but at higher prices.
(61) "There was, to be sure, an awareness by the members of the association that there would be some adversely affected by the Bylaw, but the attitude expressed was one of concern, not indifference." Hennessey, 564 F. 2d at 1153.
(65) Id. Emphasis added.
(66) Id. at 1154.
(67) 902 F. Supp. 1394 (1995). Similar claims were involved in Hall v. NCAA, Case No. 94-2392, September 30, 1994; and Schreiber v. NCAA, Case No. 95-2026, January 13, 1995. The parties in Hall and Schreiber agreed to be bound by the court's ruling in Law.
(68) United States v. Socony-Vacuum Oil Co., 310 U.S. 150 (1940).
(69) We have relied on the court's rendition of the facts in Law.
(70) These figures were roughly equivalent to the cost of graduate assistant coaches as they were about equal to out-of-state tuition of public schools and average tuition at private schools.
(71) In Mandeville Island Farms v. American Crystal Sugar Co., 334 U.S. 219, 235 (1947), the Supreme Court recognized that price fixing by buyers is the sort of restraint condemned by [sections] of the Sherman Act.
(72) NCAA v. Board of Regents of the University of Oklahoma, 468 U.S. 85, 101 (1984). For an analysis, see Ira Horowitz, The Reasonableness of Horizontal Restraints: NCAA in The Antitrust Revolution (J. Kwoka & L. White, eds., 2d ed. 1994). This recognition that some restraints may be needed to make the production of some products viable drove the decision in Broadcast Music, Inc. v. Columbia Broadcasting System, Inc., 441 U.S. 1 (1979).
(73) 902 F. Supp. at 1404.
(74) In most of its formulations, Judge Posner found the rule of reason to be a poor guide to judicial resolution. See Richard A. Posner, The Rule of Reason and the Economic Approach: Reflections on the Sylvania Decision, 45 U. Chi. L. Rev. 1 (1977).
(75) United States v. Addyston Pipe & Steel, 85 F. 172 (6th Cir. 1898), aff'd, 175 U.S. 211 (1899).
(76) 902 F. Supp. at 1405.
(78) Id. at 1406.
(81) Hennessey, 564 F. 2d at 1153.
(82) In National Macaroni Manufacturers Association v. Federal Trade Commission, 345 F. 2d 421 (7th Cir. 1965), rival firms agreed to change the recipe for macaroni due to an increase in the price of durum wheat. This collusive reduction in quality was deemed a per se violation of [section] 5 of the Federal Trade Commission Act.
(83) 166 U.S. 290 (1897). Judge Taft rejected the argument in Addyston Pipe & Steel, note 75 supra.
(84) United States v. Socony-Vacuum Oil Co., 310 U.S. 150 (1940): "Thus for over 40 years this court has consistently and without deviation adhered to the principle that price-fixing agreements are unlawful per se under the Sherman Act and that no showing of so-called competitive abuses or evils which those agreements were designed to eliminate or alleviate may be interposed as a defense."
(85) Gary S. Becker, The NCAA: A Cartel in Sheepskin Clothing, Bus. Wk., Sept. 14, 1987, at 24.
(86) Witness the success of revenue sharing in the NFL, while players earn large surpluses in spite of a salary cap.
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|Title Annotation:||Antitrust in the Sports Industry; National Collegiate Athletic Ass'n|
|Author:||Blair, Roger D.; Romano, Richard E.|
|Date:||Sep 22, 1997|
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