The fraction of BL Lac objects in groups of galaxies

Context: BL Lac objects are a rare class of active galactic nuclei that typically show featureless optical spectra that make it difficult to estimate the redshift. A novel method for estimating the redshift of BL Lac objects has recently been proposed which assumes that these objects typically reside in groups of galaxies. Aims: The aim of this work is to estimate the fraction of BL Lac objects that reside in groups of galaxies. Methods: We use a sample of groups (M12 catalogue) selected by applying a friends-of-friends algorithm in the SDSS DR12. Galaxies in the M12 sample were cross-correlated with the sample of blazars in the BZCAT. Results: We found that 121 galaxies in the M12 catalogue are blazars in the BZCAT sample, all but one are BL Lac objects, and a large fraction are classified as BL Lac-galaxy dominated. Analysing the fraction of galaxies in groups as a function of redshift we have estimated a correction factor that takes into account the typical incompleteness of the catalogues based on the friends-of-friends algorithm. Once this factor was applied to the sample of BL Lac objects with a counterpart in the M12 catalogue, we found that the percentage of BL Lac objects in groups is $\gtrsim 67 \pm 8\%$. Conclusions: The high rate of BL Lac objects in groups found in this work strongly supports a recent method that has successfully estimated the redshift of BL Lac objects with featureless spectra.Comment: Accepted for publication in Astronomy and Astrophysics (Letter

A generalized index of market power

This paper analyses two approaches to measuring market power-the commonly used Lerner index and a range of exploitation measures-. Itis argued that the Lerner index is designed to quantify market power fromthe supply side and the exploitation measures are designed to quantify marketpower from the demand side, and that the two approaches do not always behavein a symmetric way, since they do not always have the same bounds. To sortout these potentially undesirable properties, this paper proposes a new generalindex to measure market power, which is symmetrical in the sense that it isbounded between zero and one, regardless of whether the market power comesfrom the supply or the demand side. The index proposed allows for the presenceof more than one firm and for the existence of conjectural variations.*******************************************************************************************************************Este documento analiza dos enfoques para medir poder de mercado-el frecuentemente utilizado índice de Lerner y un conjunto de medidas de explotación-. Se argumenta que el índice de Lerner está diseñado para cuantificarel poder de mercado por el lado de la oferta y que las medidas de explotaciónestán diseñadas para cuantificar el poder de mercado por el lado de la demanda,y que esos dos enfoques no siempre tienen los mismos límites. Paracorregir estas propiedades potencialmente no deseables, este documento proponeun nuevo índice general para medir poder de mercado, que es simétrico-estando restringido a valores entre cero y uno-, independientemente de si elpoder de mercado proviene del lado de la oferta o de la demanda. El índice propuestopermite la presencia de más de una firma y la existencia de variacionesconjeturales.market power, mark up, mark down, Lerner index, exploitation measures, industrial organization, conjectural variations

A FORMAL PROOF OF THE FACTOR PRICE EQUALIZATION THEOREM

This paper provides a formal proof of the Factor Price Equalization Theorem within the Heckscher Ohlin model derived by Ronald W. Jones in The Structure of Simple General Equilibrium Models" (1965), where formal proof is provided for the Heckscher Ohlin, Stolper Samuelson and Rybczynski Theorems."International Trade