Versioning Goods and Joint Purchase: Substitution and Complementarity Strategies

We analyze the monopolist’s decision about how to design different versions of a good, i.e. whether to make them substitutes or complements, when consumers can buy them simultaneously. In this context, we find that versioning goods as substitutes or complements may be optimal for the monopolist, and the final result depends on the degree of concavity and convexity of the cost function.Versioning Goods, Joint Purchase Option, Substitutes, Complementarity, Price Discrimination, Market Segmentation.

Income Stratification Across Public and Private Education: The Multi-community Case

This paper analyses the question of which households opt out of public education in a multi-community economy with local school finance and housing markets. In particular, the objective is to investigate whether perfect income stratification across public and private educational sectors predicted by single jurisdiction models and by multiple jurisdiction ones without housing markets holds in this setting. Nechyba (1999) has shown that the existence of a fixed stock of heterogeneous houses can prevent perfect income stratification from arising in equilibrium. Here we demonstrate that, even with homogeneous housing, perfect income stratification is not assured. On the contrary, it is possible to find equilibria in which households from intermediate income intervals use private schools, while richer ones prefer to send their youths to a local public school of higher quality. The emergence of very high quality public schools that attract students from the best-off households and survive the competition of private schools is therefore possible. The paper identifies a new way whereby housing markets affect how the market for education works.

The peer group effect and the optimality properties of head and income taxes

This paper studies a Tiebout model with two school districts, housing markets and peer effects to re-evaluate the optimality properties of the allocation of households to districts induced by head and income taxes. The main novel results reveal that head taxes are not superior to income taxes and that the indirect redistribution implied by income taxation is not necessarily at odds with location optimality or associated to welfare losses. Many combinations of head taxes differentiated by household type can sustain the optimal outcome as an equilibrium. While this may not be possible using differentiated income taxes, a combination of non-differentiated ones and differentiated head taxes levied on the residents of the rich district can lead to the optimal outcome and effect significant local redistribution. In turn, non-differentiated head taxes are suboptimal (unless optimality requires one of the districts to be type-homogeneous) and a combination of uniform income taxes and head taxes levied on the rich district's population can do as well as them. Moreover, non-differentiated income taxes may generate smaller welfare losses than their lump-sum counterpart, a result which clashes with the benefit view of head taxes.Tiebout; peer effects; head tax, income tax; optimality

Current-driven skyrmion motion along disordered magnetic tracks

The motion of skyrmions along ferromagnetic strips driven by current pulses is theoretically analyzed by means of micromagnetic simulations. Analytical expressions describing the skyrmion dynamics during and after the current pulse are obtained from an extended rigid skyrmion model, and its predictions are compared with full micromagnetic simulations for perfect samples with a remarkable agreement. The dynamics along realistic samples with random disorder is also studied by both models. Our analysis describes the relevant ingredients behind the current-driven skyrmion dynamics, and it is expected to be useful to understand recent and future experimental.Comment: Micromagnetic simulations and analytical expressions describing the dynamics of skyrmions under current-pulses along realistic strip

Statistical evidence about human influence on the climate system

Working Paper No WP2012-012We use recent methods for the analysis of time series data, in particular related to breaks in trends, to establish that human factors are the main contributors to the secular movements in observed global and hemispheric temperatures series. The most important feature documented is a marked increase in the growth rates of temperatures (purged from the Atlantic Multidecadal Oscillation) and anthropogenic greenhouse gases occurring for all series around 1955, which marks the start of sustained global warming. Also evidence shows that human interventions effectively slowed global warming in two occasions. The Montreal Protocol and the technological change in agricultural production in Asia are major drivers behind the slowdown of the warming since 1994, providing evidence about the effectiveness of reducing emissions of greenhouse gases other than CO2 for mitigating climate change in the shorter term. The largest socioeconomic disruptions, the two World Wars and the Great Crash, are shown to have contributed to the cooling in the mid 20th century. While other radiative factors have modulated their effect, the greenhouse gases defined the secular movement in both the total radiative forcing and the global and hemispheric temperature series. Deviations from this anthropogenic trend are shown to have transitory effects

Modelling hydrological connectivity in burned areas. A case study from South of Spain

Overland flow connectivity depends on the spatio-temporal interactions of hydrological and geomorphic processes as well as on the human footprint on the landscape. This study deals with the modelling of hydrological connectivity in a burned area with different levels of fire severity. Namely, the objectives are to: i) characterize and ii) modelling the pre- (PreF) and post-fire (PostF) scenarios, as well as iii) evaluate the effect of the vegetation changes due to the fire and the initial post-fire management practices (construction of new skid trails and check-dams) on the magnitude and spatial pattern of connectivity. Four post-fire scenarios are simulated: immediately after the fire (PostF1), with new skids and without check-dams (PostF2), with new skids and check-dams and without vegetation recovery (PostF3), and with new skids and check-dams and incipient vegetation cover (PostF4). The study area corresponds to eleven headwater sub-catchments (total area of 329 ha) that cover the entire burned area of the mountain in the West and Southwest facing hillslopes (ca. 200 ha). This site is located in the province of Malaga, South of Spain, and all sub-catchments are disconnected between them. The fire started in 2014, 27 June and lasted two days. The landscape is mainly mountainous, with very steep slopes and marble rocks, Mediterranean climate, and a land use of shrubs and pine forests (pre-fire scenario). Settlements appear at the bottom of the slopes. After the wildfire, land management were carried out in order to remove completely the burned trees and thus new skid trails were built. Then, eleven concrete check-dams and twelve wooded check-dams were built in the main gullies. The different scenarios of linear landscape elements, vegetation cover and modifications on the topography related to the construction of new trails and check-dams were included in the simulations. The IC index of hydrological connectivity was chosen to perform this metric at a spatial resolution of 5 x 5 meters. The analysis of the different spatial patterns and temporal changes was done considering the different levels of fire severity and changes on hydrological connectivity were also analysed at the outlet of each sub-catchment.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On the Whitham Hierarchies: Reductions and Hodograph Solutions

A general scheme for analyzing reductions of Whitham hierarchies is presented. It is based on a method for determining the $S$-function by means of a system of first order partial differential equations. Compatibility systems of differential equations characterizing both reductions and hodograph solutions of Whitham hierarchies are obtained. The method is illustrated by exhibiting solutions of integrable models such as the dispersionless Toda equation (heavenly equation) and the generalized Benney system.Comment: 24 page