Faculty Bibliography

This article explores subjects in optimal income taxation characterized by recent research interest, practical importance in light of concerns about inequality, potential for misunderstanding, and prospects for advancement. Throughout the analysis, paths for further investigation are highlighted. Areas of focus include multidimensional abilities and endogenous wages; asymmetric information and the income of founders; production and consumption externalities from labor effort; market power and rents; behavioral phenomena relating to perceptions of the income tax schedule, myopic labor supply, and the interactions of savings, savings policies, and labor supply; optimal income transfers; the relationship between optimal income taxation and the use of other instruments; and issues relating to the social welfare function and utility functions, including non-welfarist objectives, welfare weights, heterogeneous preferences, and taxation of the family.

The philanthropic sector is highly consequential, particularly in the United States, and the most important policies directed toward this sector are tax policies. Yet most economic analysis of the optimal tax treatment of charitable giving is ad hoc, treating it as a subject unto itself. This article advances a different approach: integrating the tax treatment of charitable giving into the optimal income tax framework that has been developed over the past half century. The results supplement or overturn conventional wisdom. Notably, the analysis of revenue effects and the purported efficiency of subsidies to charitable giving is recast, focusing on the pertinent externalities rather than the direct revenue costs, which themselves are irrelevant in the basic case. Distributive concerns regarding donors are also misplaced because distributive effects can be offset by tax rate adjustments to the broader income tax and transfer system. These ideas are developed systematically, with an emphasis on intuition rather than technical formalism. The analysis also broadens and deepens the assessment of externalities from charitable giving, which are more numerous and heterogeneous than is generally recognized. Finally, refocusing our understanding of the optimal tax treatment of charitable giving identifies important subjects requiring further research.

Most industrial organization research, including applications to competition policy, undertakes partial equilibrium analysis in a single sector, often with a fixed number of firms. For welfare analysis, this approach is valid only if the rest of the economy is perfectly competitive, an assumption far from reality. This article examines competition policy in a simple, multisector, general equilibrium model with free entry and exit, allowing for differing distortions in each sector. Flows between sectors readily reverse standard prescriptions. But such results may be partially offset or overturned yet again when incorporating free entry and exit. Analysis of efficiencies also changes qualitatively.

This article explores subjects in optimal income taxation characterized by recent research interest, practical importance in light of concerns about inequality, potential for misunderstanding, and prospects for advancement. Throughout, the analysis highlights paths for further investigation. Areas of focus include multidimensional abilities and endogenous wages; asymmetric information and the income of founders; production and consumption externalities from labor effort; market power and rents; behavioral phenomena relating to perceptions of the income tax schedule, myopic labor supply, and the interactions of savings, savings policies, and labor supply; optimal income transfers; the relationship between optimal income taxation and the use of other instruments; and issues relating to the social welfare function and utility functions, including nonwelfarist objectives, welfare weights, heterogeneous preferences, and taxation of the family.

Economic analysis of competition regulation is most developed in the domain of horizontal mergers, and modern agency guidelines reflect a substantial consensus on the appropriate template for merger assessment. Nevertheless, official protocols are understood to rest on a problematic market definition exercise, to use HHIs and HHIs in ways that conflict with standard models, and more broadly to diverge with how economic analysis of proposed mergers should be and often is conducted. These gaps, unfortunately, are more consequential than is generally appreciated. Moreover, additional unrecognized errors and omissions are at least as important: analysis of efficiencies, which are thought to justify a permissive approach, fails to draw on the most relevant fields of economics; entry is often a misanalyzed afterthought; official information collection and decision protocols violate basic tenets of decision analysis; and single-sector, partial equilibrium analysis is employed despite the presence of substantial distortions (many due to imperfect competition) in many sectors of the economy. This article elaborates these deficiencies, offers preliminary analysis of how they can best be addressed, and identifies priorities for further research.

This article analyzes concerns about market power and inequality in a model with multiple sectors, heterogeneous abilities, endogenous labor supply, and nonlinear income taxation. Proportional markups with no profit dissipation have no effect on the economy, and a policy that reduces a nonproportional markup raises (lowers) welfare when it is higher (lower) than a weighted average of other markups. With proportional (partial or full) profit dissipation, proportional markups are equivalent to a downward shift of the distribution of abilities, and the optimal policy rule with nonproportional markups maximizes consumer plus producer surplus despite concerns for distribution and labor supply distortion.

Specialized theoretical and empirical research should in principle be embedded in a unified framework that identifies the relevant interactions among different phenomena, enables an appropriate matching of policy instruments to objectives, and grounds normative analysis in individuals’ utilities and a social welfare function. This article advances an approach that both provides integration across many dimensions and contexts and also identifies which tasks may be undertaken separately and how such analysis should be conducted so as to be consistent with the underlying framework. It employs the distribution-neutral methodology and welfare analysis developed in Kaplow (2008a) and related work, offering applications to income taxation, commodity taxation, tax expenditures, externalities, public goods, capital income and wealth taxation, social security and retirement savings, estate and gift taxation, and transfer programs. It also explores welfare criteria and examines how their consideration enables the normative analysis of the taxation of families, heterogeneous preferences, and tax administration and enforcement.

Prominent theory research on voting uses models in which expected pivotality drives voters' turnout decisions and hence determines voting outcomes. It is recognized, however, that such work is at odds with Downs's paradox: in practice, many individuals turn out for reasons unrelated to pivotality, and their votes overwhelm the forces analyzed in pivotality-based models. Accordingly, we examine a complementary model of large-N elections at the opposite end of the spectrum, where pivotality effects vanish and turnout is driven entirely by individuals' direct costs and benefits from the act of voting itself. Under certain conditions, the level of turnout is irrelevant to representativeness and thus to voting outcomes. Under others, anything is possible"; starting with any given distribution of preferences in the underlying population, there can arise any other distribution of preferences in the turnout set and thus any outcome within the range of the voting mechanism. Particular skews in terms of representativeness are characterized. The introduction of noise in the relationship between underlying preferences and individuals' direct costs and benefits from voting produces, in the limit, fully representative turnout. To illustrate the potential disconnect between the level of turnout (a focus of much empirical literature) and representativeness, we present a simple example in which, as noise increases, the turnout level monotonically falls yet representativeness monotonically rises.

Despite decades of research on mechanism design and on many practical aspects of cost-benefit analysis, one of the most basic and ubiquitous features of regulation as actually implemented throughout the world has received little theoretical attention: exemptions for small firms. These firms may generate a disproportionate share of harm due to their being exempt and because exemption induces additional harmful activity to be channeled their way. This article analyzes optimal regulation with exemptions where firms have different productivities that are unobservable to the regulator, regulated and unregulated output each cause harm although at different levels, and the regulatory regime affects entry as well as the output choices of regulated and unregulated firms. In many settings, optimal schemes involve subtle effects and have counterintuitive features: for example, higher regulatory costs need not favor higher exemptions, and the incentives of firms to drop output to become exempt can be too weak as well as too strong. A final section examines the optimal use of output taxation alongside regulation, which illustrates the contrast with the mechanism design approach that analyzes the optimal use of instruments of a type that are not in widespread use.

This update applies to the Seventh Edition (2013) of Areeda, Kaplow & Edlin, Antitrust Analysis: Problems, Text, and Cases.

Does significant market power or the presence of large rents affect optimal income taxation, calling for greater redistribution due to tainted gains? Or perhaps less because of an additional wedge that distorts labor effort? Do concerns about inequality have implications for antitrust, regulation, trade, and other policies that influence market power, which contributes to inequality? This article addresses these questions in a model with heterogeneous abilities and hence a concern for distribution, markups, multiple sectors, ownership that is a function of income, allowance for any share of profits to be recoveries of investments (including rent-seeking efforts), endogenous labor supply, and a nonlinear income tax. In this model, proportional markups with no profit dissipation have no effect on the economy, and a policy that reduces a nonproportional markup raises (lowers) welfare when it is higher (lower) than a weighted average of other markups. With proportional (partial or full) profit dissipation, proportional markups are equivalent to a downward shift of the distribution of abilities, and the welfare effect of correcting nonproportional markups associated with nonproportional profit dissipation now depends also on the degree of dissipation and how that is affected by the policy. In all cases, optimal policies maximize consumer plus producer surplus, without regard to a policy’s distributive effects on consumers and profits or how markups and income taxation distort labor effort.

Important doctrines in diverse areas of law employ structured decision procedures requiring, in rough terms, that the plaintiff first make some demonstration of harm; if but only if that is done, the defendant must make some showing of benefit; and if but only if that occurs, balancing is performed. This Article compares such protocols to unconstrained balancing and finds them to be inferior with respect to the quality of final decisions: they sometimes fail to impose liability even though the harm is greater than the benefit, and they sometimes impose liability even though the benefit exceeds the harm. The Article also develops the principles of optimal information (evidence) collection and shows how structured decision procedures violate every core lesson and presuppose distinctions that often are incoherent or impractical to implement. The analysis addresses concerns about balancing that may motivate structured protocols, how less restrictive alternatives should be assessed, and the extent to which legal proceedings are conducted in conformity with either approach, as well as how they might be reformed.

Important doctrines in diverse areas of law employ structured decision procedures requiring, in rough terms, that the plaintiff first make some demonstration of harm; if but only if that is done, the defendant must make some showing of benefit; and if but only if that occurs, balancing is performed. In-depth analysis of such protocols reveals them to be inferior to unconstrained balancing with respect to the quality of final decisions and the guidance they provide for the collection of information and, accordingly, the conduct of adjudication. This article applies this analysis to the rule of reason and merger regulation under antitrust law, Title VII disparate impact law, and the practices of strict scrutiny and proportionality analysis in constitutional law. Longstanding controversies are addressed and unappreciated deficiencies are discovered. In all three domains, existing law is cast in a substantially different light, both descriptively and normatively. Legal rules, adjudication, information, balancing, rule of reason, mergers, disparate impact, Title VII, strict scrutiny, proportionality analysis.

The prohibition against price fixing is competition law's most important and least controversial provision. Yet there is far less consensus than meets the eye on what constitutes price fixing, and prevalent understandings cannot be reconciled with principles of oligopoly theory. This article (1) presents a fundamental reconceptualization of our understanding of horizontal agreements, (2) develops a systematic analysis of price-fixing policy that focuses on its deterrence benefits and chilling costs, and (3) compares this direct approach to commentators’ favored formulations that typically involve some sort of formalistic communications-based prohibition. By targeting a subset of means rather than the illicit ends, conventional formulations tend to impose liability in cases with lower deterrence benefits and greater chilling costs than those reached under a direct approach and to incur greater administrative costs as well.

Recoupment inquiries play an increasingly important role in antitrust analysis, yet they raise a number of conundrums: How can a failure of recoupment due to the plausible long-run profit recovery being dwarfed by short-run losses be reconciled with a defense of no predation that presupposes no short- run sacrifice to begin with? How can recoupment inquiries be diagnostic with respect to competing explanations for defendants’ behavior—such as product promotion or “legal” predation—that likewise require recoupment? This article addresses these questions and others by grounding recoupment and predatory pricing analysis more broadly in a decision framework that focuses on classification (distinguishing illegal predation from other explanations for firms’ pricing) and on the magnitudes of the deterrence benefits and chilling costs of imposing liability. Regarding the latter, although concerns for the chilling of procompetitive activity sensibly drive predatory pricing analysis, the great variation in chilling costs across competing explanations for alleged predation is unrecognized. Much of the analysis here is not particular to recoupment; the investigation aims to inform future research, policy, and practice regarding many aspects of predatory pricing as well as other forms of anticompetitive conduct.

Recoupment inquiries play an important role in predatory pricing cases. Nevertheless, their place in antitrust analysis is unclear and potentially problematic in ways that are not fully appreciated. Does a recoupment requirement define, augment, or replace the preexisting monopoly power requirement that involves similar analysis? How can a recoupment test be inserted in sequential assessments of alleged predatory pricing when all of the steps are intertwined with the others, including those deemed to come later? Why is a plaintiff permitted to show either that recoupment was ex ante plausible or that sufficient ex post profit recovery occurred, rather than requiring one in particular, or both? This article addresses these questions by examining the underlying purposes of recoupment assessments and predatory pricing inquiries more broadly. As will become evident, much of the analysis is relevant not just to predatory pricing but to other forms of anticompetitive conduct as well.

This article translates and extends Becker (1968) from public law enforcement to private litigation by examining optimal legal system design in a model with private suits, signals of case strength, court error, and two types of primary behavior: harmful acts that may be deterred and benign acts that may be chilled. The instruments examined are filing fees or subsidies that may be imposed on either party, damage awards and payments by unsuccessful plaintiffs (each of which may be decoupled), and the stringency of the evidence threshold (burden of proof). With no constraints, results arbitrarily close to the first best can be implemented. Prior analyses of optimal damage awards, decoupling, and fee shifting are shown to involve special cases. More important, previous results change qualitatively when implicit assumptions are relaxed. For example, introducing a filing fee can make it optimal to minimize what losing plaintiffs pay winning defendants and to reduce the evidence threshold as much as possible — even though the direct effect of these adjustments is to chill desirable behavior, a key feature absent in prior work.

In many settings, there are preliminary or interim decision points at which legal cases may be terminated: e.g., motions to dismiss and for summary judgment in U.S. civil litigation, grand jury decisions in criminal cases, and agencies’ screening and other exercises of discretion in pursuing investigations. This article analyzes how the decision whether to continue versus terminate should optimally be made when (A) proceeding to the next stage generates further information but at a cost to both the defendant and the government and (B) the prospect of going forward, and ultimately imposing sanctions, deters harmful acts and also chills desirable behavior. This subject involves a mechanism design analogue to the standard value of information problem, one that proves to be qualitatively different and notably more complex. Numerous factors enter into the optimal decision rule – some expected, some subtle, and some counterintuitive. The optimal rule for initial or intermediate stages is also qualitatively different from that for assigning liability at the final stage of adjudication.

Who will vote quadratically in large-N elections under quadratic voting (QV)? First, who will vote? Although the core QV literature assumes that everyone votes, turnout is endogenous. Drawing on other work, we consider the representativeness of endogenously determined turnout under QV. Second, who will vote quadratically? Conditional on turning out, we examine reasons that, in large-N elections, the number of votes that an individual casts may deviate substantially from that under pure, rational QV equilibrium play. Because turnout itself is driven by other factors, the same determinants may influence how voters who do turn out choose the quantity of votes to cast. Independently, the number of votes actually cast may deviate dramatically from pure QV predictions because of the complex and refined nature of equilibrium play. Most plausibly, voting behavior and outcomes would be determined predominately by social and psychological forces, would exhibit few of the features emphasized in the analysis of hyper-rational equilibrium play, and would have consequential properties that require a different research agenda to bring into focus. Some of our analysis also has implications for voting behavior under other procedures, including one person, one vote.

Market power is the most important determinant of liability in competition law cases throughout the world. Yet fundamental questions on the relevance of market power are underanalyzed, if examined at all: When and why should we inquire into market power? How much should we require? Should market power be viewed as one thing, regardless of the practice under scrutiny and independent of the pertinent anticompetitive and procompetitive explanations for its use? Does each component of market power have the same probative force? Or even influence optimal liability determinations in the same direction? This Article’s ground-up investigation of market power finds that the answers often differ from what is generally believed and sometimes are surprising — notably, higher levels of certain market power measures or particular market power components sometimes disfavor liability. This gulf between conventional wisdom and correct understanding suggests the need to redirect research agendas, agency guidance, and competition law doctrine.

A recent wave of literature, partly motivated by presidential campaign tax reform plans, analyzes tax expenditure limitation proposals. These reforms are often advanced not only, or even primarily, because they reduce distortions caused by favoritism for some types of expenditures over others. Largely they are urged for a number of other reasons: on distributive grounds, because the resulting broader base enables lower marginal tax rates and hence less distortion of labor effort and other margins, and to raise revenue without requiring higher marginal tax rates. It is generally recognized that the particular results on these dimensions are heavily dependent on what sorts of rate adjustments are used to return the proceeds to taxpayers. Often, revenue neutrality is assumed. This essay advances a complementary, distribution-neutral perspective on the analysis of tax expenditure limitations. Distribution-neutral implementation provides an illuminating benchmark against which to understand prior analysts’ large number of results and, more importantly, clarifies the analysis, particularly of the distribution-distortion tradeoff. The central lessons contradict the common belief that one can have less distortion of labor supply through lower marginal tax rates while also maintaining or enhancing progressivity.

This law school casebook was developed by a team of professors at Harvard Law School to introduce students with little or no quantitative background to the basic analytical techniques that attorneys need to master to represent their clients effectively. This casebook presents clear explanations of decision analysis, games and information, contracting, accounting, finance, microeconomics, economic analysis of the law, fundamentals of statistics, and multiple regression analysis. References and examples have been thoroughly updated for this 3rd edition, and exposition of a number of key topics has been reworked to reflect insights gained from teaching these topics using the 1st edition to many hundreds of Harvard Law students over the past decade.

Competition law’s vertical agreement requirement is widely regarded to be perplexing and to offer a fairly limited unilateral action defense. These views prove to be understated. The underlying distinction is incoherent on a number of levels and difficult to reconcile with pertinent statutes, precedent, and practice. The requirement has little nexus with competition policy, and its satisfaction may even be associated with less, not more, anticompetitive danger. Furthermore, reflection on the thinness or nonexistence of the vertical agreement requirement renders problematic a central feature of competition law: the aim to subject myriad everyday actions of countless firms to more lenient scrutiny than that applicable to agreements, which on reflection are ever-present.

Market definition and market power are central features of competition law and practice but pose serious challenges. On one hand, market definition suffers decisive logical infirmities that render it infeasible, unnecessary, and counterproductive, and the practice of stating market power requirements as market share threshold tests is incoherent as a matter of empirics and policy. On the other hand, market power is often probative of the desirability of liability, yet the typically assumed functional relationship is unexplored and often implausible. These latter deficiencies are addressed through a ground-up analysis of the channels by which market power can be relevant. It is important to explicitly and simultaneously consider both anti-competitive and pro-competitive explanations for challenged practices and to attend to the magnitudes of the social consequences of correct and mistaken imposition of liability in order to identify the various ways and senses in which market power bears on optimal decision-making.

Adjudication is fundamentally about information, usually concerning individuals' previous or proposed behavior. Legal system design is challenging because information ordinarily is costly and imperfect. This Article analyzes a broad array of system features, asking throughout whether design should aim at the truth or at consequences, how these approaches may differ, and what general lessons may be drawn from the comparison. It will emerge that the differences in approach are often large and their character is sometimes counterintuitive. Accordingly, system engineers concerned with social welfare need to aim explicitly at consequences. This message is not one opposed to truth per se but rather a strong admonition: it is dangerous to be attached to the alluring view that adjudication is primarily about generating results most in accord with the truth of the matter at hand.

A central justification for social insurance and for other policies aimed at retirement savings is that individuals may fail to make adequate provision during their working years. Much research has focused on myopia and other behavioral limitations. Yet little attention has been devoted to how these infirmities, and government policies to rectify them, influence labor supply. This linkage could be extremely important in light of the large pre-existing distortion due to income and consumption taxation and income-based transfer programs. For example, might myopic individuals, as a first approximation, view payroll taxes and other withholding to fund retirement savings as akin to an income tax, while largely ignoring the distant future retirement benefits that they fund? If so, the distortion of labor supply may be many times higher than otherwise, making savings-promotion policies much more costly than appreciated. Or consider what may be the labor supply implications for an individual who is defaulted into higher savings and, as a consequence, sees concomitantly lower take-home pay. This essay offers a preliminary, conceptual exploration of these questions. In most of the cases considered, savings policies do not act purely like a tax despite individuals’ non-optimizing savings behavior, and in some cases labor supply actually is raised, not lowered, in which event policies that boost savings may be significantly more welfare-enhancing than recognized. Accordingly, there is a compelling need for empirical exploration of the interaction between nonoptimal savings behavior and labor supply.

This article analyzes the effect of savings-related policies on labor supply in a model that explicitly incorporates myopic decision-making. Both social security and capital taxation may cause labor supply to rise or fall when individuals are myopic, depending on the curvature of individuals' utility as a function of consumption. Moreover, whatever is the sign of these effects under one assumption about how myopia relates to labor supply decisions, the sign is reversed under the other assumption that is considered. Additionally, some interventions have a first-order effect on labor supply from the outset but others do not, and some labor supply effects rise with the magnitude of the intervention whereas others fall.

Various legal decision-making criteria can be formulated as likelihood ratio tests, wherein liability, prohibition, or other outcomes are associated with evidence strength exceeding a posited threshold. Stating rules in this manner clarifies their nature, facilitates the comparison of conventional and optimal rules as well as the identification of differences between rules across contexts, and provides further illumination in instances in which a decision standard is not truly a likelihood ratio test.

Market definition has long held a central place in competition law. This entry surveys recent analytical work that has called the market definition paradigm into question on a number of fronts: whether the process is feasible, whether market share threshold tests are coherent, whether the hypothetical monopolist test in merger guidelines is counterproductive, and whether and when the frequent focus on cross-elasticities is useful.

Legal proceedings often involve multiple stages: U.S. civil litigation allows motions to dismiss and for summary judgment prior to trial; government agencies as well as prosecutors employ investigative and screening processes before initiating formal adjudication; and many Continental tribunals move forward sequentially. Decisionmaking criteria have proved controversial, as indicated by reactions to the Supreme Court's recent decisions in Twombly and Iqbal and its 1986 summary judgment trilogy, which together implicate the Supreme Court cases most cited by federal courts. Neither jurists nor commentators have articulated coherent, noncircular legal standards, and no attempt has been made to examine systematically how decisions at different procedural stages should ideally be made in light of the legal system's objectives. This Article presents a foundational analysis of the subject. The investigation illuminates central elements of legal system design, recasts existing debates about decision standards, identifies pathways for reform, and provides new perspectives on the nature of facts and evidence and on the relationship between substantive and procedural law.

The Seventh Edition incorporates the latest Supreme Court and Circuit Court cases, legal changes, and developments in the law.

In recent articles, I have advanced a number of criticisms of the market definition/redefinition paradigm, chief among them that market definition is impossible and counterproductive. First, there is no valid way to infer market power from market shares in redefined (non-homogeneous-goods) markets. Second, one cannot choose which market definition is superior without already having in hand one’s best estimate of market power, rendering the exercise pointless. Worse, market power inferences in the chosen market are inferior to the best estimate with which one began. After elaborating these points, this Essay applies them to the three main settings in which the hypothetical monopolist test is employed in various jurisdictions’ merger guidelines, showing this test to be counterproductive in every instance. Finally, it addresses reasons that some are nevertheless reluctant to abandon market definition altogether.

A substantial literature examines how the Pigouvian directive that marginal taxes should equal marginal external harms needs to be modified in light of the preexisting distortion due to labor income taxation. Additional literature considers distributive concerns. It is demonstrated, however, that simple first-best rules unmodified for labor supply distortion or distribution are correct in the model examined. Specifically, setting all commodity taxes equal to marginal harms (and subsidies equal to marginal benefits) can generate a Pareto improvement, as can a marginal reform toward the first-best. Qualifications and explanations for differences from previous work are also presented.

The burden of proof is a central feature of all systems of adjudication, yet one that has been subject to little normative analysis. This Article examines how strong evidence should have to be in order to assign liability when the objective is to maximize social welfare. In basic settings, there is a tradeoff between deterrence benefits and chilling costs, and the optimal proof requirement is determined by factors that are almost entirely distinct from those underlying the preponderance of the evidence rule and other traditional standards. As a consequence, these familiar burden of proof rules have some surprising properties, as do alternative criteria that have been advanced. The Article also considers how setting the proof burden interacts with other features of legal system design: the determination of enforcement effort, the level of sanctions, and the degree of accuracy of adjudication. It compares and contrasts a variety of legal environments and methods of enforcement, explaining how the appropriate proof requirements differ qualitatively across contexts. Most of the questions raised and answers presented differ in kind as well as in result from those in prior literature.

This entry addresses two fundamental characteristics of rules. The first concerns the degree of precision, detail, or complexity they embody: how finely are different sorts of behavior to be distinguished? A second aspect of legal commands concerns when a given level of detail is provided -- at the time of promulgation ("rules") or subsequent to individuals' actions, in the context of an adjudication ("standards"). These aspects of rules are considered from a perspective that focuses upon information costs and dissemination: different sorts of legal commands involve differing costs of formulation and application by private parties (deciding upon their own conduct) and adjudicators, and the character of laws also influences how well parties actually will understand the law and conform their conduct accordingly. The discussion encompasses related questions involving the role of precedent, the evolution of the law over time, legal uncertainly, and accuracy in adjudication. This entry also addresses the separate problem of how changes in legal rules should apply to prior behavior or pre-existing investments -- issues of retroactivity and transition.

In a recent series of articles, I argue that the market definition/market share paradigm should be abandoned entirely. Among my central claims are that: (1) as a matter of economic logic, there exists no valid way to infer market power from the market shares in redefined (non-homogeneous-goods) markets — short of entirely reversing the market redefinition; and (2) choosing a best market requires already having in hand one’s best estimate of market power, rendering the exercise pointless — actually worse, since the market power inference from the chosen market is inferior to the estimate with which one began. Not surprisingly, criticisms advanced in this Symposium and elsewhere do not succeed in repealing the laws of logic, any more than medieval alchemists were able to overturn the laws of nature.

The burden of proof, a central feature of adjudication and other decision-making contexts, constitutes an important but largely unappreciated policy instrument. The optimal strength of the burden of proof, as well as optimal enforcement effort and sanctions, involves trading off deterrence and the chilling of desirable behavior, the latter being absent in previous work. The character of the optimum differs markedly from prior results and from conventional understandings of proof burdens. There are important divergences across models in which enforcement involves monitoring, investigation, and auditing. A number of extensions are analyzed, in one instance nullifying key results in prior work.

Substantial evidence suggests that savings behavior may depart from neoclassical optimization. This article examines the implications of raising the savings rate-whether through social security, retirement plans, or otherwise-for labor supply, where labor supply is determined by behavioral utility functions that reflect the non-neoclassical character of savings behavior. Under one formulation, raising the targeted savings rate increases labor supply regardless of the slope of the labor supply curve; under a second, raising the targeted savings rate has the same effect on labor supply as that of raising the labor income tax rate; and under a third, raising the targeted savings rate has no effect on labor supply. Effects on labor supply are particularly consequential because of the significant preexisting distortion due to labor income taxation.

A notable feature and principal virtue of Tax by Design is its system-wide perspective on different elements of the tax system. This review essay builds on this trait and offers a more explicit foundation for the report's general approach, drawing on a distribution-neutral methodology that is developed in other work. This technique is then employed to illuminate and extend Tax by Design's analysis regarding the VAT, environmental taxation, wealth transfer taxation and income transfers.

The recently issued revision of the US Horizontal Merger Guidelines, like its predecessors and mirrored by similar guidelines throughout the world, devotes substantial attention to the market definition process and the implications of market shares in the market that is selected. Nevertheless, some controversy concerning the revised Guidelines questions their increased openness toward more direct, economically based methods of predicting the competitive effects of mergers. By contrast, this article suggests that, as a matter of economic logic, the Guidelines revision can only be criticized for its timidity. Indeed, economic principles unambiguously favor elimination of the market definition process altogether.

In competition law, market power requirements are often articulated in terms of market shares. The use of market share thresholds, however, conflates two distinct questions: First, how much market power exists in a given situation? Second, how much market power should the law require? As a consequence, neither question is answered, or even directly illuminated. Furthermore, because market shares are not themselves measures of market power but instead merely a factor that bears on its magnitude in a given setting, they are inapt answers to both inquiries. Their use involves a category mistake. The identified problems are illustrated by unpacking Learned Hand's famous pronouncement in Alcoa of the market shares required for the offense of monopolization, but the core defects characterize all market share declarations.