Remedies for Price Overcharges: The Deadweight Loss of Coupons and Discounts

This article evaluates two different remedies for consumers who have been injured by a price overcharge on the sale of a good. Under a coupon remedy, injured consumers are awarded coupons that can be used for a limited period of time to purchase the good at a price below that which prevails after the overcharge has been eliminated, that is, below the competitive price. Under a discount remedy, any consumer, without proof of injury, may purchase the good for a limited period of time at a price that is set below the competitive price. Both remedies generally cause consumers to buy an excessive amount of the good during the remedy period. Under the coupon remedy only a subset of consumers are affected in this way (those holding a relatively high number of coupons), while under the discount remedy all consumers are affected. We show nonetheless that the resulting deadweight loss could be lower under the discount remedy. We also consider how the deadweight loss changes when the length of the remedy period is increased by extending the expiration date for the use of coupons or by employing a lower discount for a longer period of time. The deadweight loss may or may not decline under the coupon remedy, though it does decline under the discount remedy. In neither case, however, does it go to zero in the limit.

The Welfare Implications of Costly Litigation in the Theory of Liability

One of the principal results in the economic theory of liability is that, assuming litigation is costless, the rule of strict liability with compensatory damages leads the injurer to choose the socially appropriate level of care. This paper reexamines this result when litigation is costly. It is shown that strict liability with compensatory damages generally leads to a socially inappropriate level of care and to excessive litigation costs. Social welfare can be increased by adjusting compensatory damages upward or downward, with the desired direction depending on the effect of changes in the level of liability on the injurer's decision to take care and on the victim's decision to bring suit.

Optimal Awards and Penalties when the Probability of Prevailing Varies Among Plaintiffs

This article derives the optimal award to a winning plaintiff and the optimal penalty on a losing plaintiff when the probability of prevailing varies among plaintiffs. Optimality is defined in terms of achieving a specified degree of deterrence of potential injurers with the lowest litigation cost. Our main result is that the optimal penalty on a losing plaintiff is positive, in contrast to common practice in the United States. By penalizing losing plaintiffs and raising the award to winning plaintiffs (relative to what it would be if losing plaintiffs were not penalized), it is possible to discourage relatively low-probability-of-prevailing plaintiffs from suing without discouraging relatively high-probability plaintiffs, and thereby to achieve the desired degee of deterrence with lower litigation costs. This result is developed first in a model in which all suits are assumed to go to trial and then in a model in which settlements are possible.

Remedies for Price Overcharges: The Deadweight Loss of Coupons and Discounts

This article evaluates two different remedies for consumers who have been injured by a price overcharge on the sale of a good. Under a coupon remedy, injured consumers are awarded coupons that can be used for a limited period of time to purchase the good at a price below that which prevails after the overcharge has been eliminated, that is, below the competitive price. Under a discount remedy, any consumer, without proof of injury, may purchase the good for a limited period of time at a price that is set below the competitive price. Both remedies generally cause consumers to buy an excessive amount of the good during the remedy period. Under the coupon remedy only a subset of consumers are affected in this way (those holding a relatively high number of coupons), while under the discount remedy all consumers are affected. We show nonetheless that the resulting deadweight loss could be lower under the discount remedy. We also consider how the deadweight loss changes when the length of the remedy period is increased.

A Damage-Revelation Rationale for Coupon Remedies

This article studies optimal remedies in a setting in which damages vary among plaintiffs and are difficult to determine. We show that giving plaintiffs a choice between cash and coupons to purchase units of the defendant's product at a discount -- a "coupon-cash remedy" -- is superior to cash alone. The optimal coupon-cash remedy offers a cash amount that is less than the value of the coupons to plaintiffs who suffer relatively high harm. Such a remedy induces these plaintiffs to choose coupons, and plaintiffs who suffer relatively low harm to choose cash. Sorting plaintiffs in this way leads to better deterrence because the costs borne by defendants (the cash payments and the cost of providing coupons) more closely approximate the harms that they have caused.

Fractal templates in the escape dynamics of trapped ultracold atoms

We consider the dynamic escape of a small packet of ultracold atoms launched from within an optical dipole trap. Based on a theoretical analysis of the underlying nonlinear dynamics, we predict that fractal behavior can be seen in the escape data. This data would be collected by measuring the time-dependent escape rate for packets launched over a range of angles. This fractal pattern is particularly well resolved below the Bose-Einstein transition temperature--a direct result of the extreme phase space localization of the condensate. We predict that several self-similar layers of this novel fractal should be measurable and we explain how this fractal pattern can be predicted and analyzed with recently developed techniques in symbolic dynamics.Comment: 11 pages with 5 figure

Paths reunited: initiation of the classical and lectin pathways of complement activation

Understanding the structural organisation and mode of action of the initiating complex of the classical pathway of complement activation (C1) has been a central goal in complement biology since its isolation almost 50 years ago. Nevertheless, knowledge is still incomplete, especially with regard to the interactions between its subcomponents C1q, C1r and C1s that trigger activation upon binding to a microbial target. Recent studies have provided new insights into these interactions, and have revealed unexpected parallels with initiating complexes of the lectin pathway of complement: MBL–MASP and ficolin–MASP. Here, we develop and expand these concepts and delineate their implications towards the key aspects of complement activation via the classical and lectin pathways

Direction-Dependent Polarised Primary Beams in Wide-Field Synthesis Imaging

The process of wide-field synthesis imaging is explored, with the aim of understanding the implications of variable, polarised primary beams for forthcoming Epoch of Reionisation experiments. These experiments seek to detect weak signatures from redshifted 21cm emission in deep residual datasets, after suppression and subtraction of foreground emission. Many subtraction algorithms benefit from low side-lobes and polarisation leakage at the outset, and both of these are intimately linked to how the polarised primary beams are handled. Building on previous contributions from a number of authors, in which direction-dependent corrections are incorporated into visibility gridding kernels, we consider the special characteristics of arrays of fixed dipole antennas operating around 100-200 MHz, looking towards instruments such as the Square Kilometre Array (SKA) and the Hydrogen Epoch of Reionization Arrays (HERA). We show that integrating snapshots in the image domain can help to produce compact gridding kernels, and also reduce the need to make complicated polarised leakage corrections during gridding. We also investigate an alternative form for the gridding kernel that can suppress variations in the direction-dependent weighting of gridded visibilities by 10s of dB, while maintaining compact support.Comment: 15 pages, 4 figures. Accepted for publication in JA

Using the Man9(GlcNAc)2 – DC-SIGN pairing to probe specificity in photochemical immobilization

We demonstrate the expected preference of an immobilised oligosaccharide Man(9)(GlcNAc)(2) upon a 96-well photochemical array, for its known receptor, the cell-surface lectin Dendritic Cell-Specific ICAM3 Grabbing Nonintegrin (DC-SIGN) when compared to immobilised competing monosaccharides