Monopoly Mathematical Analysis
Emmaline Sasportas
Ditkowski, Adi. "Mathematical analysis of the optimizing acquisition and retention over time problem." ESAIM: Mathematical Modelling and Numerical Analysis - Modlisation Mathmatique et Analyse Numrique 43.1 (2009): 119-137. .
TY - JOUR
AU - Ditkowski, Adi
TI - Mathematical analysis of the optimizing acquisition and retention over time problem
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modlisation Mathmatique et Analyse Numrique
PY - 2009
PB - EDP-Sciences
VL - 43
IS - 1
SP - 119
EP - 137
AB - While making informed decisions regarding investments in customer retention and acquisition becomes a pressing managerial issue, formal models and analysis, which may provide insight into this topic, are still scarce. In this study we examine two dynamic models for optimal acquisition and retention models of a monopoly, the total cost and the cost per customer models. These models are analytically analyzed using classical, direct, methods and asymptotic expansions (for the total cost model). In order to numerically simulated the models, an innovative numerical method was developed for solving ODE systems with initial/final value problems.
LA - eng
KW - ODE nonlinear boundary value problems; ODE applications; ODE growth; boundedness; comparison of solutions; ODE asymptotic expansions; optimal control; numerical methods ODE boundary value problems
UR -
ER -
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This article seeks an answer to a question that should be well settled: for purposes of antitrust analysis, what is 'market power' or 'monopoly power'? The question should be well settled because antitrust law now requires proof of actual or likely market power or monopoly power to establish most types of antitrust violations. These legal rules follow prevailing antitrust policy analysis, which suggests that concepts of market power or monopoly power should play a crucial role in defining the reach of most antitrust proscriptions.
Examination of key antitrust law opinions, however, shows that courts define 'market power' and 'monopoly power' in ways that are both vague and inconsistent. We conclude that the present level of confusion is unnecessary and results from two different but related errors: (1) the belief or suspicion that market power and monopoly power are two different concepts, when they are in fact, for antitrust purposes, qualitatively identical, and (2) the failure to recognize that anticompetitive economic power may manifest itself in two distinct ways. We argue that attempting to distinguish between market power and monopoly power creates a false dichotomy. Real differences, with significant legal and policy implications, do exist, however, between anticompetitive economic power that is exercised by restricting one's own output and such power exercised by restricting the output of one's rivals. Identifying this fundamental distinction and discarding the false one can help to clarify other troublesome antitrust issues as well.
The body of this article describes these conclusions, and the bases for them, in some detail. The appendix presents a shorter, more technical description of the principal argument. Readers already familiar with the main body of antitrust law and conversant with antitrust economics may wish to begin by reading the appendix.
Most antitrust rules require the plaintiff to show that the defendant has or is likely to obtain 'market power' or 'monopoly power.' The offense of monopolization requires, of course, proof that the defendant has monopoly power. [FN1] An illegal attempt to monopolize occurs, according to the majority view, only when there is a dangerous probability that the defendant will succeed in obtaining a monopoly. [FN2] The Department of Justice measures the antitrust legality of corporate mergers against a set of guidelines whose 'unifying theme' is said to be 'that mergers should not be permitted to create or enhance 'market power' or to facilitate its exercise.' [FN3] The first step in determining the antitrust legality of joint ventures for research and development or for production is to ask whether the partners, if merged, would achieve market power. [FN4] According to the Supreme Court's latest formulation, a tying arrangement is not illegal unless the seller has 'market power' in the tying product. [FN5] Virtually any summary of the relevant factors in a case to be judged under the 'rule of reason' will include the presence or absence of 'market power' as a key factor. [FN6]
Certain antitrust violations, conventionally described as 'per se' offenses, do not require proof of market or monopoly power. [FN7] Indeed, the label 'per se' seems to point to the irrelevance of market power. An essential characteristic of a 'per se' offense, however, seems to be that it constitutes behavior that, if engaged in by a firm with market power, would be egregiously anticompetitive. [FN8] Market power is treated as irrelevant only because 'per se' offenses involve behavior that courts have determined virtually always lacks plausible efficiency justifications; no harm is done, therefore, by condemning the practice without undergoing the expense of an inquiry into monopoly or market power. [FN9]
Market power or monopoly power, then, is a crucial and central issue in almost any complex antitrust case today. Even for the theoretically simpler cases involving claims of 'per se' violations, the concepts of market and monopoly power lurk in the shadows because these concepts are relevant to the threshold question of whether the type of behavior at issue is properly characterized as 'per se' illegal. [FN10]
The widespread and increasing emphasis on the role of market power in antitrust rules fits well with the current dominant strains of antitrust policy analysis. Indeed, antitrust law's increasing absorption of market power standards is due in some measure to the influence of these analytical theories.
Confusion exists over the theoretical bases of antitrust law, confusion which stems directly from the fact that no one can tell from the plain language of the predominant antitrust statutes [FN11] what interests they are designed to protect. Section one of the Sherman Act forbids 'restraint of trade'; [FN12] section two makes it unlawful to 'monopolize' or 'attempt to monopolize;' [FN13] the Federal Trade Commission Act forbids 'unfair methods of competition;' [FN14] and the Clayton Act condemns tying arrangements, exclusive dealing contracts, and mergers that may 'substantially lessen competition or tend to create a monopoly.' [FN15] None of these phrases has any fixed meaning. Indeed, it is questionable whether a more ambiguous antitrust statute could be devised.
Because the statutes do not explicitly tell judges whose interests to protect, judges feel free to choose their own favorite candidates. Consequently, Supreme Court Justices have expressed the opinions, in various cases, that a corporate merger might be held illegal because it would lead to removing a corporation's headquarters from a small town to a big city; [FN16] because it is part of a trend toward lessening the number of single-store groceries; [FN17] because it may eliminate a potential market entrant to whom no firm in the market pays any attention; [FN18] and because it may eliminate competition among firms that may or may not compete in a relevant market. [FN19] Conversely, certain agreements among competitors to restrict their outputs have been held permissible because they permitted a dying industry to keep up its profits until rigor mortis set in; [FN20] because they enabled firms to shorten their work days; [FN21] and because they assisted firms who wished not to compete to achieve that goal. [FN22]
These opinions cannot all be correct. If antitrust law is required to maximize simultaneously the welfare of small communities, the number of Momand-Pop stores, the absolute freedom of entry, all interfirm competition, the wealth of creditors of firms nearing bankruptcy, workers' leisure time, and the ability of firms to avoid competing with each other, than antitrust law is paralyzed. Most business behavior will advance at least one of these interests while retarding at least one other.
Today, a consensus is emerging that the solution to this dilemma is not to call on antitrust enforcers and judges to balance, in some unstated fashion, every social, political, or economic interest or value affected by a business decision. Rather, antitrust should be viewed as 'a consumer welfare prescription.' [FN23] Under this interpretation, a practice restrains trade, monopolizes, is unfair, or tends to lessen competition if it harms consumers by reducing the value or welfare they would have obtained from the market-place absent the practice. [FN24]
Deciding to interpret the antitrust laws to fashion rules designed to protect consumer welfare, however, does not make antitrust analysis uncomplicated or as readily predictable as the late-season demise of the Boston Red Sox. For example, the precise meaning of 'consumer welfare' is debatable. [FN25] Further, antitrust analysis often requires predicting what may happen in the future as a result of recent or proposed behavior. [FN26] Predicating the effects of behavior on future consumer welfare is no easier than, say, predicting its effects on the number of Mom-and-Pop grocery stores. [FN27]
Whatever the merits of this view, treating consumer welfare as the key interest in antitrust law brings market power to center stage. Consumer welfare is reduced most obviously when market prices exceed competitive levels. When economists use the terms 'market power' or 'monopoly power,' they usually mean the ability to price at a supracompetitive level. [FN28] The view of consumer welfare as the central policy goal of antitrust therefore suggests that the law of antitrust is correct as it increasingly focuses on market power.
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