Critical import supply elasticities and the ‘imports-as-market-discipline’ hypothesis

This paper formally examines the factors underlying how responsive imports must be to domestic prices (the ‘import supply elasticity’) in order to thwart an anticompetitive domestic price increase stemming from a merger––an issue that frequently arises in many antitrust reviews. Domestic firms face a fringe comprised of foreign firms who import their products into the domestic market. In the eyes of domestic consumers, these imports are viewed as imperfect substitutes in demand to the output produced by the domestic firms. The model is solved in terms of the ‘critical’ import supply elasticity that can then be used evaluate the ability of imports to constrain an anticompetitive price increase post-merger. Both general and linear demand specifications are considered. Numerical simulations are conducted to consider the magnitude of perturbations in the model’s exogenous parameters. Potential empirical extensions of the model are also considered.

Competition and cost pass-through in differentiated oligopolies

The impact that competition exerts on the incentives of firms to pass through reductions in their marginal costs is an important consideration in assessing the performance of alternate market structures. This paper examines the role of product differentiation on firm-specific and industry-wide pass-through rates. Relying on Shubik’s (1980) model of differentiated Cournot competition with linear demand, we show that there exists an initial critical range over which the firm-specific cost pass-through rate decreases in the number of firms. Beyond this range the rate continually increases – approaching 50 percent as the number of firms goes to infinity. This contrasts with a model of differentiated Bertrand competition in which cost pass through monotonically decreases in the number of firms. The disparate effects across the Cournot and Bertrand models are shown to stem from the influence of competition and product differentiation on the respective firm reaction functions. Suggestions for future empirical work based upon the models’ predictions and implications for antitrust policy are also discussed.Competitive effects; Oligopoly; Merger; Pass-through; Product differentiation

Critical import supply elasticities and the ‘imports-as-market-discipline’ hypothesis

This paper formally examines the factors underlying how responsive imports must be to domestic prices (the ‘import supply elasticity’) in order to thwart an anticompetitive domestic price increase stemming from a merger––an issue that frequently arises in many antitrust reviews. Domestic firms face a fringe comprised of foreign firms who import their products into the domestic market. In the eyes of domestic consumers, these imports are viewed as imperfect substitutes in demand to the output produced by the domestic firms. The model is solved in terms of the ‘critical’ import supply elasticity that can then be used evaluate the ability of imports to constrain an anticompetitive price increase post-merger. Both general and linear demand specifications are considered. Numerical simulations are conducted to consider the magnitude of perturbations in the model’s exogenous parameters. Potential empirical extensions of the model are also considered.Competitive effects; Critical loss; Market definition; Import supply elasticity

Semiclassical Gravity in the Far Field Limit of Stars, Black Holes, and Wormholes

Semiclassical gravity is investigated in a large class of asymptotically flat, static, spherically symmetric spacetimes including those containing static stars, black holes, and wormholes. Specifically the stress-energy tensors of massless free spin 0 and spin 1/2 fields are computed to leading order in the asymptotic regions of these spacetimes. This is done for spin 0 fields in Schwarzschild spacetime using a WKB approximation. It is done numerically for the spin 1/2 field in Schwarzschild, extreme Reissner-Nordstrom, and various wormhole spacetimes. And it is done by finding analytic solutions to the leading order mode equations in a large class of asymptotically flat static spherically symmetric spacetimes. Agreement is shown between these various computational methods. It is found that for all of the spacetimes considered, the energy density and pressure in the asymptotic region are proportional to 1/r^5 to leading order. Furthermore, for the spin 1/2 field and the conformally coupled scalar field, the stress-energy tensor depends only on the leading order geometry in the far field limit. This is also true for the minimally coupled scalar field for spacetimes containing either a static star or a black hole, but not for spacetimes containing a wormhole.Comment: 43 pages, 2 figures. Reference added, minor changes, PRD versio

Adjustable microchip ring trap for cold atoms and molecules

We describe the design and function of a circular magnetic waveguide produced from wires on a microchip for atom interferometry using deBroglie waves. The guide is a two-dimensional magnetic minimum for trapping weak-field seeking states of atoms or molecules with a magnetic dipole moment. The design consists of seven circular wires sharing a common radius. We describe the design, the time-dependent currents of the wires and show that it is possible to form a circular waveguide with adjustable height and gradient while minimizing perturbation resulting from leads or wire crossings. This maximal area geometry is suited for rotation sensing with atom interferometry via the Sagnac effect using either cold atoms, molecules and Bose-condensed systems

Atom chips on direct bonded copper substrates

We present the use of direct bonded copper (DBC) for the straightforward fabrication of high power atom chips. Atom chips using DBC have several benefits: excellent copper/substrate adhesion, high purity, thick (> 100 microns) copper layers, high substrate thermal conductivity, high aspect ratio wires, the potential for rapid (< 8 hr) fabrication, and three dimensional atom chip structures. Two mask options for DBC atom chip fabrication are presented, as well as two methods for etching wire patterns into the copper layer. The wire aspect ratio that optimizes the magnetic field gradient as a function of power dissipation is determined to be 0.84:1 (height:width). The optimal wire thickness as a function of magnetic trapping height is also determined. A test chip, able to support 100 A of current for 2 s without failing, is used to determine the thermal impedance of the DBC. An assembly using two DBC atom chips to provide magnetic confinement is also shown.Comment: 8 pages, 5 figure

Stress-Energy Tensor for the Massless Spin 1/2 Field in Static Black Hole Spacetimes

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static non-rotating black holes, corresponding to the Schwarzschild, Reissner-Nordstrom and extreme Reissner-Nordstr\"om solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress-energy differs even in sign from the analytic approximation. For the Reissner-Nordstrom and extreme Reissner-Nordstrom solutions, divergences predicted by the analytic approximations are shown not to exist.Comment: 5 pages, 4 figures, additional discussio

Critical import supply elasticities and the ‘imports-as-market-discipline’ hypothesis

This paper formally examines the factors underlying how responsive imports must be to domestic prices (the ‘import supply elasticity’) in order to thwart an anticompetitive domestic price increase stemming from a merger––an issue that frequently arises in many antitrust reviews. Domestic firms face a fringe comprised of foreign firms who import their products into the domestic market. In the eyes of domestic consumers, these imports are viewed as imperfect substitutes in demand to the output produced by the domestic firms. The model is solved in terms of the ‘critical’ import supply elasticity that can then be used evaluate the ability of imports to constrain an anticompetitive price increase post-merger. Both general and linear demand specifications are considered. Numerical simulations are conducted to consider the magnitude of perturbations in the model’s exogenous parameters. Potential empirical extensions of the model are also considered