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Article Excerpt
INTRODUCTION
I. THE ECONOMICS OF OLIGOPOLISTIC PRICING A. Monopoly B. Perfect Competition C. Oligopolistic Pricing 1. Single-period games 2. Multi-period games D. Economic Insights II. THE CURRENT LEGAL STANDARD A. The Courts' Treatment of Oligopolistic Pricing B. Donald Turner's Controlling Rationale C. The Advantages Associated with Donald Turner's Approach D. The Shortcomings of Professor Turner's View III. JUDGE POSNER'S SUGGESTED SOLUTION A. The Example of a Simple Duopoly B. The Positive Implications of the Rule 1. Exploring the assumptions of the model C. The Negative Implications of the Rule 1. Expanding the model of simple duopoly 2. The problem of marginal application 3. Relaxing the assumption of zero fixed cost and constant marginal cost 4. An encouraging result IV. THE SUGGESTED SOLUTION V. TESTING THE PROPOSED RULE OF LAW A. A Simple Duopoly B. A More Realistic Model CONCLUSION
INTRODUCTION
This Note seeks to address a systemic and difficult issue in the field of antitrust, namely the problem of proving concerted action for the purpose of price-fixing claims in oligopolistic markets, (l) While antitrust law has been markedly successful in eliminating express cartels, (2) competition policy has been equally noteworthy for its failure to effectively address instances of parallel pricing that may have an economically analogous effect to explicit price-fixing. (3) Though the law has long viewed this shortcoming as an inevitable consequence of market structure, this Note will articulate both a different conclusion and a novel solution.
An oligopoly is a market in which the level of concentration causes firms residing therein to operate strategically. (4) In other words, an oligopolist must factor the expected reaction of its competitors into its first order condition for profit maximization. A firm operating in a monopolized market, or one subject to perfect competition, simply equates marginal revenue with marginal cost in setting price. (5) Doing so in an oligopolized market is not profit-maximizing, however, as the profitability of a given price depends on the price being charged by other firms in the market. This is so because, in selling its goods, a firm will have a unilateral impact on the residual demand facing the other firms in the market. (6)
A major, and very interesting, problem arises in the context of such markets, where it may be possible for oligopolists to reach a self-sustaining, supracompetitive equilibrium. Essentially, it may be feasible for a group of firms to reach a collusive outcome without overt acts of detectable communication. Such tacit collusion results from a "meeting of the minds," whereby competitors recognize that it is in their collective best interests to set price or quantity equal to the collusive level. (7) In such circumstances, application of the antitrust laws becomes challenging. This difficulty emanates from the makeup of the antitrust regime put in place by the Sherman Act.
Section 2 of that Act prohibits firms with monopoly power from improperly maintaining or abusing their dominance. (8) Most firms operating within an oligopoly do so without possessing or exercising such puissance, however. As a result, their unilateral actions cannot be attacked under the Act.
Firms lacking monopoly power can nonetheless be found guilty of violating the Sherman Act under section 1 when they act in concert with their competitors. Accordingly, "contract[s], combination[s,] ... or conspirac[ies] in restraint of trade" may be held illegal, if unreasonable. (9) Hence, at a theoretical level, concerted action by oligopolists can be reached by section 1. The difficulty, which has so far proven to be prohibitive, lies in demonstrating that oligopolists' parallel pricing is a manifestation of concerted, rather than unilateral, behavior.
The problem is acute and may fairly be characterized as one of the most serious in the field of antitrust law, for the economic consequences of a failure to fill the current "gap" are ominous. (10) This is so as instances of firms pricing in parallel at supracompetitive levels are ubiquitous. (11) The fact that such equilibria are readily observable highlights a continuing flaw in the application of competition law. It shall be seen, however, that finding a solution to the problem is far from straightforward and will inevitably be draped in controversy.
This Note will express an opinion on how an antitrust regime should tackle those cases where self-sustaining, output-restricting equilibria can exist absent overt communication of any kind. This question is especially interesting as the law is currently incapable of reaching such market outcomes, though there have been forceful, and highly controversial, arguments that the law ought to be able to do so in appropriate circumstances. (12)
In this regard, Judge Richard Posner has articulated something of a radical view, according to which economic evidence of tacit collusion may in itself lead to a violation of the antitrust laws. (13) It will be shown that such an approach would not be attractive, given that it would perversely cause insolvency in certain markets and lead to inadvertent monopolization in others. Professor Donald Turner, in contrast, has argued that any prohibition of parallel pricing is necessarily improper. (14) Turner's position is characterized by the belief that a ban would require irrational behavior on the part of companies, would effectively compel marginal cost pricing, and would frustrate entry into oligopolistic markets. Yet, it will be demonstrated that these concerns constitute an unsatisfactory foundation for allowing tacit collusion, which is a practice that clearly causes significant societal harm.
This Note seeks to add a new dimension to the Posner-Turner debate, by showing that although Judge Posner's suggestion may be somewhat quixotic, elements of it may nevertheless be successfully employed to achieve a superior outcome. To the extent Professor Turner would believe that prohibition of parallel behavior is inherently inappropriate, it will be shown that he would be mistaken. In short, it will be demonstrated that a suitably moderate version of Judge Posner's approach would carry myriad economic benefits whilst avoiding the concerns advocated by Professor Turner.
The structure of the Note shall be as follows: first, a basic economic framework shall be introduced that will facilitate analysis throughout the remainder of the Note. Second, the current approach taken by the law will be discussed in the context of the rationale supporting the modern rules. Third, Judge Posner's controversial solution will be considered. Last, this Note will attempt to advocate a new approach to the problem of proving tacit collusion.
I. THE ECONOMICS OF OLIGOPOLISTIC PRICING
In order to make the discussion of oligopolistic behavior more concrete, a representative model will be employed throughout the Note. This model will additionally serve as a baseline for the competitive effect of various rules. Accordingly, a numerical example will illustrate the workings of oligopolistic interdependence and the extent to which the ensuing outcome departs from contexts of competition and monopoly. We begin with the simplest form of oligopoly: a duopoly. Assume that two firms, Alpha and Beta, comprise the market. For the sake of simplicity, it shall be assumed that both firms have identical cost and production functions, that there are no fixed costs, and that the industry demand curve is linear. (15) The industry demand curve and market conditions for our model have the following parameters:
P = 200 - Q [MC.sub.A] = [AC.sub.A] = [MC.sub.B] = [AC.sub.B]= 20
where P = price; Q = quantity; MC = marginal cost; and AC = average cost. (16)
Before applying these figures to various game theoretic models of oligopolistic behavior, we will calculate the outcomes under (1) monopoly, and (2) perfect competition. Doing so will illustrate the effect of those oligopolistic Nash equilibria (17) that are currently beyond the reach of the antitrust laws.
A. Monopoly
A monopolist's demand curve is the market demand curve and is, therefore, downward sloping. (18) Consequently, the monopolist can choose between a variety of price levels without having the quantity of its good demanded drop to zero. Like any other firm, the monopolist wishes to maximize its profits. It does so by equating marginal cost (MC) with marginal revenue (MR); that is, it will continue to expand output to the point where the extra cost associated with producing one more unit just equals the incremental revenue brought in by selling that unit. (19) So, the monopolist s profits ([pi]) will increase as the quantity it produces approaches the point where MC = MR, will peak at MC = MR, and [pi] will decline as the quantity it produces begins to exceed the point of output where MC = MR. Thus, the monopoly price for either Alpha or Beta would be 110 and market output would be 90. (20)
B. Perfect Competition
Under perfect competition, every producer is a price taker; that is, each firm faces a horizontal demand curve and therefore cannot influence the price at which its good is sold by unilaterally reducing its output. (21) Accordingly, marginal revenue always equals price. (22) In order to maximize profit, the firm facing perfect competition will produce at the point where marginal cost equals marginal revenue. (23) As a result, a firm under perfect competition maximizes profit by producing at the point where price equals marginal cost. (24) Thus, the market price under perfect competition would be 20 and market output would be 180. (25)
One can readily see by the stark difference in these figures why competition is typically favored over monopoly. Section 1 of the Sherman Act forbids horizontal price-fixing and output-setting agreements so as to avoid the monopoly outcome. Were Alpha and Beta in our example to enter into a collusive profit-maximizing agreement, they would each produce 45 units at a price of 110. By rendering such agreements illegal per se, antitrust rules cause output to be higher and prices lower than they would be absent such laws.
C. Oligopolistic Pricing
Having gained an appreciation for the divergence in market outcomes between competition and monopoly, we now consider how the results of oligopoly may differ. As oligopolists operate and compete on a strategic basis, game theory is a useful economic tool in this context.
A number of competition models exist, (26) but the one employed here to calculate the price and quantity outcomes is based on Cournot economics. The Cournot model predicts that firms will engage in quantity-based competition, each making individual profit-maximizing output decisions based on the assumption of output maintenance by the other firms. (27) Eventually, an equilibrium is reached where the reaction functions of all firms intersect--that is, where the expectations of output maintenance by each firm as to every other holds true. (28)
Continuing the foregoing example of duopoly, the issue arises as to how Alpha and Beta would engage in competition. In addressing this question, a distinction may be drawn between single- and repeated-play games. In the former case, the inference is that we ought not to be overly concerned about the ability of oligopolists to tacitly achieve the monopoly outcome. The more realistic, dynamic model compels a different conclusion.
1. Single-period games
Where Alpha and Beta enter into a single-period game, each firm wishes to maximize its profit at the end of the period and is unconcerned about any future periods. Unlike in the case of monopoly or perfect competition, they will not do so by producing at the point where MC = MR. Rather, each firm will factor its rival's anticipated reaction into its profit-maximizing decision.
The joint-maximization solution for Alpha and Beta is to enter into an illegal (though, we will assume, undetected) agreement to set price at the monopoly level. Crucially, however, there is an enormous incentive to deviate from the agreement. Alpha and Beta agree to produce 45 units each (that is, half what a monopolist would produce) at a price of 110. Each will thereby enjoy a profit of 4050. (29) If Beta commits itself to charge the price of 110, Alpha has an incentive to undercut Beta--to cheat--and thereby to increase its own profit beyond 4050.
The joint profit-maximizing, cartel price is not, therefore, stable. Employing the Cournot-Nash model introduced above, the equilibrium in this situation will involve price equaling 80 and each firm producing 60 units. This can be calculated by the fact that a Cournot-Nash equilibrium in a duopoly, under a linear demand curve, results in each firm producing one-third of the competitive level of output. (30) Thus, both Alpha and Beta will earn a profit of 3600. (31) It is clear, therefore, that both Alpha and Beta are worse off than they would have been had they both stuck by the agreement.
Game theory demonstrates that the mutually agreed price and quantity do not constitute a Nash equilibrium: neither party is doing the best it can in setting a price equal to the collusive price, given the choice of the other party. Each party's dominant strategy is to defect from the agreement: regardless of whether Beta charges 110 or 80, Alpha will be better off charging 80. (32) Beta reasons the same way. As a result, the Nash equilibrium in this game is for both parties to defect from the agreement. The resulting payoff matrix may be considered as follows (the matrix shows Alpha's profit, then Beta's):
Beta [P.sub.B] = 80 [P.sub.B] = 110 Alpha [P.sub.A] = 80 (3600, 3600) (4556.25, 2025 (33)) [P.sub.A] = 110 (2025, (34) 4556.25) (4050, 4050)
The key lesson taught by game theory is that collusive agreements in single-period games are likely to be highly unstable. What is the consequence of this from an antitrust perspective? It would appear to be agnosticism with respect to the existence of tacitly collusive equilibria that are equal to the monopoly level. If oligopolists such as Alpha and Beta are predicted to deviate from an express agreement, their chances of succeeding tacitly must be even less. This suggests we should not be excessively concerned about tacit collusion in oligopolistic markets. Nevertheless, it must be noted that the Cournot-Nash equilibrium identified above involves price being considerably higher than the competitive outcome. An important issue, which will be addressed shortly, is whether this imperfect outcome is nevertheless the best attainable. It will be seen that adoption of Judge Posner's rule would involve the Nash equilibrium coinciding with the competitive result. Interestingly, however, this is not necessarily a desirable outcome.
2. Multi-period games
Although the single-period outcome is not perfect, it does involve a Nash equilibrium below the monopoly level. In games where there is more than one period, however, it may be possible for the players to escape the prisoners' dilemma outlined above. This is made feasible through the possibility of detection and punishment.
Take the case of a game in which there is an infinite number of rounds (35) or a game with a limited number of rounds, but where the end is undetermined. (36) In these circumstances, it may be possible for firms to maintain their collusive agreements as the one-period benefit of deviating from an agreement may be outweighed by the future periods where all parties deviate from the agreement. (37) Depending on a number of factors, including each competitor's discount rate, the likelihood of detection, and the punishment strategies employed by the colluding firms, it may be the case that a Nash equilibrium will occur at the collusive level. That is, no party can unilaterally increase its profits--including its future profits discounted to present value--by deviating from the agreement. Let us employ the example of Alpha and Beta to illustrate this:
Starting in period N and moving to infinity (N[right arrow][infinity]), Alpha and Beta compete in a duopoly under the same conditions outlined above. In making a pricing decision, each firm can decide to abide by the price-fixing agreement and charge 110 or can deviate from the agreement and charge the single-period, unilateral, profit-maximizing price of 80. Under the conditions of this example, there is a 100% probability of detection should either party "cheat." If Alpha deviates from the agreement and charges 80, Beta will find that it is only able to sell 22.5 units at a price of 110, instead of the 45 units it would have otherwise been able to sell. Detection of cheating is, therefore, guaranteed.
In time period N - 1, then, both Alpha and Beta abide by the agreement, whether tacit or collusive. In period N, both parties must make a choice of whether to continue with the agreement or to defect. Much of the choice will be driven by how each rival expects the other to react in future time periods. If both firms employ a trigger price strategy, one defection from the agreement will result in defection forever. (38) In other words, both firms commit themselves to pricing at the collusive level, but if one ever cheats to increase its profits for a single period, the other will deviate from the agreement forever. If that is the case, either firm will defect in period N if, assuming a constant discount rate:
[[pi].sub.N[right arrow][infinity]] (defect) > [[pi].sub.N] (collude) + [[pi].sub.N+1] / [(1 + i).sup.1] + [[pi].sub.N+2] / [(1 + i).sup.2] + [[pi].sub.N+3] / [(1 + i).sup.3] + ... + [[pi].sub.N[right arrow][infinity]] /[(1 + i).sup.N[right arrow][infinity]]
where i represents the discount rate for the relevant firm. As N approaches infinity, we assume that profits will remain constant at 3600, following defection. That is, either firm will defect in N if:
n (defect) > n (collude)
Employing this formula, either firm will defect in N if:
4556 * 25 + 3600/i > 4050/i
Either firm will defect only if its discount rate is greater than 0.1. (39) From this, we can state that colluding constitutes a Nash equilibrium in this market where the discount rate for both Alpha and Beta is less than 0.1. Such a discount rate...
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