Collusive Vertical Relations

We investigate the possibility for two vertically related firms to at least partially collude on the wholesale price over an infinite horizon to mitigate or eliminate the effects of double marginalisation, thereby avoiding contracts which might not be enforceable. We characterise alternative scenarios envisaging different deviations by the upstream firm and different punishments. This allows us to show that the most efficient case is that in which the upstream firm deviates along its best reply function and the punishment prescribes the disruption of the vertical relation for good after a deviation from the collusive path

The Molecular Gas Density in Galaxy Centers and How It Connects to Bulges

In this paper we present gas density, star formation rate, stellar masses, and bulge disk decompositions for a sample of 60 galaxies. Our sample is the combined sample of BIMA SONG, CARMA STING, and PdBI NUGA surveys. We study the effect of using CO-to-H_2 conversion factors that depend on the CO surface brightness, and also that of correcting star formation rates for diffuse emission from old stellar populations. We estimate that star formation rates in bulges are typically lower by 20% when correcting for diffuse emission. We find that over half of the galaxies in our sample have molecular gas surface density >100 M_sun pc^-2. We find a trend between gas density of bulges and bulge Sersic index; bulges with lower Sersic index have higher gas density. Those bulges with low Sersic index (pseudobulges) have gas fractions that are similar to that of disks. We also find that there is a strong correlation between bulges with the highest gas surface density and the galaxy being barred. However, we also find that classical bulges with low gas surface density can be barred as well. Our results suggest that understanding the connection between the central surface density of gas in disk galaxies and the presence of bars should also take into account the total gas content of the galaxy and/or bulge Sersic index. Indeed, we find that high bulge Sersic index is the best predictor of low gas density inside the bulge (not barredness of the disk). Finally, we show that when using the corrected star formation rates and gas densities, the correlation between star formation rate surface density and gas surface density of bulges is similar to that of disks.Comment: Accepted for publication in Ap