Nonlinear pricing, market coverage, and competition

This paper considers a nonlinear pricing framework with both horizontally and vertically differentiated products. By endogenizing the set of consumers served in the market, we are able to study how increased competition affects nonlinear pricing, in particular the market coverage and quality distortions. We characterize the symmetric equilibrium menu of price-quality offers under different market structures. When the market structure moves from monopoly to duopoly, we show that more types of consumers are served and quality distortions decrease. As the market structure becomes more competitive, the effect of increased competition exhibits some non-monotonic features: when the initial competition is not too weak, a further increase in the number of firms leads to more types of consumers being covered and a reduction in quality distortions; when the initial competition is weak, an increase in the number of firms leads to fewer types of consumers being covered, though the effect on quality distortions is not uniform.Nonlinear pricing, product differentiation, market coverage, quality distortions

Electromagnetic equivalent model for phase conjugate mirror based on the utilization of left-handed material

An electromagnetic equivalent model for the phase conjugate mirror (PCM) is proposed in this paper. The model is based on the unique property of the isotropic left-handed material (LHM) - the ability of LHM to reverse the phase factors of propagative waves. We show that a PCM interface can be substituted with a LHM-RHM (right-handed material) interface and associated image sources and objects in the LHM. This equivalent model is fully equivalent in the treatment of propagative wave components. However, we note that the presence of evanescent wave components can lead to undesirably surface resonance at the LHM-RHM interface. This artefact can be kept well bounded by introducing a small refractive index mismatch between the LHM and RHM. We demonstrate the usefulness of this model by modelling several representative scenarios of light patterns interacting with a PCM. The simulations were performed by applying the equivalent model to a commercial finite element method (FEM) software. This equivalent model also points to the intriguing possibility of realizing some unique LHM based systems in the optical domain by substituting a PCM in place of a LHM-RHM interface

Competitive Nonlinear Taxation and Constitutional Choice

In an economy where agents are characterized by different productivities (vertical types) and different abilities to move (horizontal types), we compare a unified nonlinear optimal taxation schedule with the equilibrium taxation schedule that would be chosen by two competing tax authorities if the same economy were divided into two States. The overall level of progressivity and redistribution is unambiguously lower under competitive taxation than under unified taxation; the “rich” are always in favor of competing authorities and local governments, whereas the “poor” are always in favor of unified taxation. The constitutional choice between fiscal regimes depends on the preferences of the middle class, which in turn depend on the initial conditions in terms of the distribution of abilities (incomes), the relative power of the various classes, and mobility costs. In particular, as mobility increases, it becomes increasingly likely that a reform in the direction of unification of fiscal policies in a federation will receive majority support, while a decreased average wealth can have the opposite effect.Competitive nonlinear taxation, Mobility, Integration, Inequality, Type preferencesover institutions.