Project 1: On the Joint Use of Liability and Safety Regulations One of the main issues dominating the economic literature concerning the control of externalities is  the choice between ex-ante regulation of risky behavior and ex-post liability for the consequences of risky behavior (henceforth "regulation" and "liability" respectively). Traditionally, economists have viewed these two policy instruments as substitutes. The common wisdom has been that in a perfect setting bothregulation and liability can induce efficiency, and therefore the choice between them should rest on administration costs. In practice, however, it is common that regulation and liability, mainly in the form of tort liability, are jointly used. For example, manufacturers of food, drugs and other products are heavily regulated, and at the same time they may face tort liability if their products causes harm. As a result, economists have tried to provide explanations to this widespread use of regulation and liability.
     In this study we look for a novel justification for the joint use of liability and regulation. In particular, we analyze the role of regulation as a substitute or complement to liability. We aim at showing that under certain plausible conditions neither liability nor regulation can induce an efficient solution to the control of risky behavior when used as a sole policy instrument. However, the joint use of liability and regulation under the same circumstances can lead to the efficient outcome.
     Specifically we analyze the following situation, which we believe reflects many circumstances in which regulation and liability are jointly used. We assume that an accident or more generally expected harm can be avoided if a potential injurer or a potential victim takes care. We also assume that the injurer is the least cost avoider, which means that her costs of care are lower than the costs of care of the victim, so that efficiency mandates that she and only she will take care. These
assumptions capture common cases, known in the literature as alternative care situations, or situations in which precautions by parties are perfect substitutes (see, for example, Calabresi (1970), Landes and Posner (1987), Garoupa and Dari-Mattiacci (2009)). We further assume that if an accident occurs the injurer can pay damages for the entire harm or at least for a portion of the harm that should arguably be sufficient to induce her to take care, but the victim is not or cannot be fully compensated for the harm suffered. This assumption reflects a common situation when an accident will result in the death or serious injury of the victim. In case of death, for example, the injurer may pay damages to the estate or the heirs of the victim, but the victim of course will not be compensated. We note that these cases as to why the victim is not fully compensated for his losses also characterize many instances in which liability and regulation are jointly used in practice. For example, the drug and food industry are heavily regulated, and the harm to victim may be serious harm or even death.
     We aim at showing that under these assumptions—denoted least cost avoidance with partial or no compensation—harm-based liability does not necessarily lead to the efficient outcome. The reason for that, as we explain more fully in a different paper, is that the injurer may act strategically and not take care, in anticipation that the victim will take care, since otherwise in the event of an accident he will not be compensated for his losses. More specifically, it can be showed that situations of least cost avoidance with partial or no compensation can be analyzed as an asymmetric discoordination game, like the classical hawk-dove game. These situations give rise to two stable pure strategy Nash equilibria: One equilibrium corresponds to the efficient outcome in which the injurer takes care and the victim does not take care, while the other equilibrium corresponds to the inefficient outcome in which the opposite is true. Punitive damages can widen the basin of attraction of the efficient equilibrium under a replicator dynamics, but they cannot eliminate the inefficient equilibrium. Therefore we conclude that liability used as the sole policy instrument cannot uniquely induce the efficient outcome.
     We aim at showing that regulation of the behavior of the injurer irrespective of the occurrence of an accident can solve the multiple equilibria problem and induce the efficient outcome, provided that it is not too costly to implement and that the regulator can commit to an enforcement policy. However, we argue that in many instances regulators cannot commit to an enforcement policy. Hence we depart from previous literature by assuming that the interaction between the regulator, in its role as an enforcer, and the injurer, in her role as a potential violator of the regulation, should be analyzed as a simultaneous-move inspection game rather than a Stackleberg game. In this game, the regulator has an incentive to enforce the regulation, that is, to inspect whether the injurer takes care or not, if and only if he believes that the injurer will not take care. Similarly, the injurer, if exposed only to regulation, has an incentive to comply with the regulation, that is, to take care, if and only if she believes the regulator will enforce. Therefore, this game as a stable mixed strategy Nash equilibrium where the injurer sometimes but not always takes care and the victim, depending on the specific parameters of the game, either takes or does not take care with certainty. Such an equilibrium is obviously inefficient.
     We further intend to show that if regulation is ineffective in inducing a sufficiently high level of compliance, regulation is socially inferior to liability. On the other hand, if regulation is effective in inducing a sufficiently high level of compliance, it may or may not be socially preferable to liability. However, when regulation is effective in inducing a sufficiently high level of compliance, the joint use of regulation and liability uniquely induces the efficient Nash equilibrium in which the injurer takes care, the victim does not take care, and the regulator does not enforce. These conclusions provide a novel rationale for using regulation and liability jointly. Even in cases in which regulation is ineffective in inducing a sufficiently high level of compliance the joint use of regulation and liability may be socially
desirable, and we analyze the conditions under which this is true.

Project 2: Optimal Liability of Multiple Injurers and Volunteers This project analyzes two closely related situations; one concerning optimal liability (i.e., optimal damages awards) in a setting with multiple injurers whose costs of care are perfect substitutes and identical. The leading case being Union Stock Co. v Chicago, B&Q.R. Co., 196 U.S. 217 (1905) (in which a brake on a railroad was defective, causing an injury. Both the terminal and the railroad were negligent having failed to discover the defect, and were treated as joint tortfeasors. The costs of inspection that would have revealed the defect was the same to both companies). The other situation concerning optimal liability rules (including whether or not to impose liability at all) in a setting with multiple potential rescuers or savers, whose costs of rescuing/saving are perfects substitutes and identical. The leading examples being the Kitty Genovese story (in which, according to one version of the story, Catherine (Kitty) Genovese was assaulted by a man who stabbed her to death in three attacks that took thirty-five minutes, and although thirty-eight neighbors either heard or saw from behind their apartment windows Genovese being attacked and screaming for help repeatedly, no one called the police until Genovese lay dying) and Prince Diana story (according to which photographers who witnessed the crash of Princess Diana’s speeding car took pictures of her body instead of assisting her and the others who were trapped in the car). Regarding the first situation (multiple tortfeasors), prominent scholars such as Landes and Posner (1980, 1987) noted that they do not know of any liability rule that may lead to the efficient outcome (the outcome in which one and only one potential injurer will take care) but they did not analyze rules leading to second best optimality. Regarding the second situation, there is a substantial difference between the legal rules in U.S. states versus Western Europe countries. In particular, in most U.S. states there is no legal duty to rescue persons in danger, while in most Western Europe countries such as France there is a duty to aid a person in danger. In this project we analyze optimal liability rules (i.e. optimal damages awards) in such settings. Multiple injurers/savers whose costs of care are perfect substitutes and identical can be analyzed as a volunteers’ dilemma situations. We therefore apply a solution concept of mixed strategy Nash equilibrium. Optimality (in the sense of minimizing the expected costs of accidents including expected costs of care) requires that each and every injurer/saver would face the entire harm, regardless of the number of injurers/savers. This rule does not lead to the first best outcome in which only one injurer/save takes care, but rather to a second best outcome (In this regard, it is completely different from standard results in the economic literature of tort according to which if each injurer face the entire harm first best efficiency is attained). We further examine refinements of this result; in particular, where liability/damages are socially costly to impose, where injurers/savers incur costs in case of an accident; and when the victim can take care to avoid the accident (although these costs are greater than the costs of injurers/savers). Finally, we analyze how second-best optimality can be implemented with balanced budget by using both liability for harm and rewards if care is taken.

Project 3: Graduated Income Tax and Risk Taking The public finance literature examined the effects of a proportional tax on risk taking. It shows that a pure proportional income tax, i.e. an income tax with full loss offset (or refundability), under certain conditions, cannot tax risky returns, but only the risk-free rate of return. Similarly, this literature shows that a proportional income tax with full loss offset increases the "social" or "before" tax risk, risk-averse taxpayers take. The literature has not examined analytically or formally the effects of graduated tax rates on risk taking (see, for example, Weisbach 2005). The common view suggests that graduated tax rates discourage risk taking. The reason is that graduation is thought to imply that gains are taxed at a higher rate than losses can be deductible. (see, for example, Weisbach 2005, Zelenak 2004). This project challenges this view and examines the effects of progressive taxation on risk taking. The project first distinguishes between progressive linear tax systems and progressive graduated tax rates. The former - a tax system of the form T= B + tZ (where T is total tax liability, B is a demogrant, t is a constant (linear) tax rate and Z is taxable income) – carries similar results as a proportional income tax.

  The latter, however, is quite different. A crucial point is related to the definition of full loss offsets (or refundability) under graduated tax rates. We adopt two alternative definitions to full loss offset: one based on a suggestion by Campinso and Romano (1981), which we call "progressive refundablity" according to which losses should be refundable by applying the same tax rates that are applicable to gains; the other is based on the regular provisions of loss offset in tax codes.  The project demonstrates that with full loss offset (either progressive refundability or under current tax provisions) a graduated tax system can actually increase risk taking. Moreover, it shows that such a tax system incentivizes taxpayers to engage in inefficient risk taking, indeed in risky activities associated with before-tax negative expected returns.  To illustrate consider a tax system with the following tax rates: 20% which applies to income up to 1000 and 40% which applies to income above 1000. Suppose also that in case of a loss the same tax rates apply (“progressive refundability”). Consider now a business that gains 1000 with probability 2/3 and loses 2000 with probability 1/3. Before tax, the expected gains are zero, while after tax the expected gains are positive. In addition, the project compares refundability and current full loss offset provisions and shows that they are different, but neither is superior or inferior to the other in terms of their effects on risk taking. The project also discusses whether the efficiency costs of progression (which were not identified thus far to our my knowledge) explain some of the restrictions on refundability and loss offsets provisions and whether they justify restricting progressivity. Lastly, the project compares the effects of progression on risk taking when losses are possible to cases where losses are impossible (i.e., when income is positive but uncertain).