Competitive E?ects of Vertical Integration with Downstream Oligopsony and Oligopoly

We analyze the competitive e?ects of backward vertical integration by a partially vertically integrated ?rm that competes with non-integrated ?rms both upstream and downstream. We show that vertical integration is procompetitive under fairly general conditions. It can be anticompetitive only if the ex ante degree of integration is relatively large. Interestingly, vertical integration is more likely to be anticompetitive if the industry is less concentrated. These results are in line with recent empirical evidence. In addition, we show that even when vertical integration is procompetitive, it is not necessarily welfare enhancing

Commuting matrices and Atiyah's Real K-theory

We describe the $C_2$-equivariant homotopy type of the space of commuting n-tuples in the stable unitary group in terms of Real K-theory. The result is used to give a complete calculation of the homotopy groups of the space of commuting n-tuples in the stable orthogonal group, as well as of the coefficient ring for commutative orthogonal K-theory.Comment: Minor changes. To appear in Journal of Topolog

Role of coherence in resistance quantization

The quantization of resistances in the quantum Hall effect and ballistic transport through quantum point contacts is compared with the quantization of the charge relaxation resistance of a coherent mesoscopic capacitor. While the former two require the existence of a perfectly transmitting channel, the charge relaxation resistance remains quantized for arbitrary backscattering. The quantum Hall effect and the quantum point contact require only local phase coherence. In contrast quantization of the charge relaxation resistance requires global phase coherence.Comment: 9 pages, 5 figure

Competitive E?ects of Vertical Integration with Downstream Oligopsony and Oligopoly

We analyze the competitive e?ects of backward vertical integration by a partially vertically integrated ?rm that competes with non-integrated ?rms both upstream and downstream. We show that vertical integration is procompetitive under fairly general conditions. It can be anticompetitive only if the ex ante degree of integration is relatively large. Interestingly, vertical integration is more likely to be anticompetitive if the industry is less concentrated. These results are in line with recent empirical evidence. In addition, we show that even when vertical integration is procompetitive, it is not necessarily welfare enhancing.Vertical Integration; Downstream Oligopsony; Downstream Oligopoly; Competition Policy; Capacity Choice

Market Structure and the Competitive Effects of Vertical Integration

We analyze the competitive effects of backward vertical integration in a model with oligopolistic firms that exert market power upstream and downstream. In contrast to previous literature, we show that a small degree of vertical integration is always procompetitive because efficiency effects dominate foreclosure effects. Moreover, vertical integration even to monopoly can be procompetitive. With regard to market structure, we find, somewhat surprisingly, that vertical integration is more likely to be procompetitive if the industry is more concentrated. Our model thus suggests that antitrust authorities should be particularly wary of vertical integration in relatively competitive industries. We demonstrate that the quantitative welfare effects can be substantial there.Vertical Integration; Market Structure; Downstream Oligopsony; Competitive Policy

Mesoscopic Charge Relaxation

We consider charge relaxation in the mesoscopic equivalent of an RC circuit. For a single-channel, spin-polarized contact, self-consistent scattering theory predicts a universal charge relaxation resistance equal to half a resistance quantum independent of the transmission properties of the contact. This prediction is in good agreement with recent experimental results. We use a tunneling Hamiltonian formalism and show in Hartree-Fock approximation, that at zero temperature the charge relaxation resistance is universal even in the presence of Coulomb blockade effects. We explore departures from universality as a function of temperature and magnetic field.Comment: 4 pages, 3 figure

Interaction induced edge channel equilibration

The electronic distribution functions of two Coulomb coupled chiral edge states forming a quasi-1D system with broken translation invariance are found using the equation of motion approach. We find that relaxation and thereby energy exchange between the two edge states is determined by the shot noise of the edge states generated at a quantum point contact (QPC). In close vicinity to the QPC, we derive analytic expressions for the distribution functions. We further give an iterative procedure with which we can compute numerically the distribution functions arbitrarily far away from the QPC. Our results are compared with recent experiments of Le Sueur et al..Comment: 10 pages, 7 figures, includes 5 pages of supplementary informatio