A Schumpeterian Growth Model with Heterogenous Firms

A common assumption in the Schumpeterian growth literature is that the innovation size is constant and identical across industries. This is in contrast with the empirical evidence which shows that: (i) the innovation size is far from being identical across industries; and (ii) the size distribution of profit returns from innovation is highly skewed toward the low value side, with a long tail on the high value side. In the present paper, we develop a Schumpeterian growth model that is consistent with this evidence. In particular, we assume that when a firm innovates, the size of its quality improvement is the result of a random draw from a Pareto distribution. This enables us to extend the class of quality-ladder growth models to encompass firm heterogeneity. We study the policy implications of this new set-up numerically and find that it is optimal to heavily subsidize R&D for plausible parameter values. Although it is optimal to tax R&D for some parameter values, this case only occurs when the steady-state rate of economic growth is very low.Schumpeterian Growth, R&D, optimal policy

The Metallicity and Reddening of Stars in the Inner Galactic Bulge

We present a preliminary analysis of K, J-K color magnitude diagrams (CMDs) for 7 different positions on or close to the minor axis of the Milky Way at Galactic latitudes between +0.1^\circ and -2.8^\circ. From the slopes of the (linear) giant branches in these CMDs we derive a dependence of on latitude for b between -0.8^\circ and -2.8^\circ of -0.085 \pm 0.033 dex/degree. When combined with the data from Tiede et al. we find for -0.8^\circ \leq b \leq -10.3^\circ the slope in is -0.064 \pm 0.012 dex/degree. An extrapolation to the Galactic Center predicts [Fe/H] = +0.034 \pm 0.053 dex. We also derive average values for the extinction in the K band (A_K) of between 2.15 and 0.27 for the inner bulge fields corresponding to average values of E(J-K) of between 3.46 and 0.44. There is a well defined linear relation between the average extinction for a field and the star-to-star scatter in the extinction for the stars within each field. This result suggests that the typical apparent angular scale size for an absorbing cloud is small compared with the field size (90\arcsec on a side). Finally, from an examination of the luminosity function of bright giants in each field we conclude that the young component of the stellar population observed near the Galactic center declines in density much more quickly than the overall bulge population and is undetectable beyond 1^\circ from the Galactic center.Comment: accepted for publication in Astron. Jour. Compressed file contains the text, 9 figures, and 6 tables prepared with AAS Latex macros v. 4.

Heavy elements Ba, La, Ce, Nd, and Eu in 56 Galactic bulge red giants

Aims. The aim of this work is the study of abundances of the heavy elements Ba, La, Ce, Nd, and Eu in 56 bulge giants (red giant branch and red clump) with metallicities ranging from -1.3 dex to 0.5 dex. Methods. We obtained high-resolution spectra of our giant stars using the FLAMES-UVES spectrograph on the Very Large Telescope. We inspected four bulge fields along the minor axis. Results. We measure the chemical evolution of heavy elements, as a function of metallicity, in the Galactic bulge. Conclusions. The [Ba, La, Ce, Nd/Fe] vs. [Fe/H] ratios decrease with increasing metallicity, in which aspect they differ from disc stars. In our metal-poor bulge stars, La and Ba are enhanced relative to their thick disc counterpart, while in our metal-rich bulge stars La and Ba are underabundant relative to their disc counterpart. Therefore, this contrast between bulge and discs trends indicates that bulge and (solar neighbourhood) thick disc stars could behave differently. An increase in [La, Nd/Eu] with increasing metallicity, for metal-rich stars with [Fe/H] > 0 dex, may indicate that the s-process from AGB stars starts to operate at a metallicity around solar. Finally, [Eu/Fe] follows the [{\alpha}/Fe] behaviour, as expected, since these elements are produced by SNe type II.Comment: 12 pages, 10 figures, accepted for publication in A&

VLT Spectroscopy of the z=4.11 Radio Galaxy TN J1338-1942

We present optical, infrared and radio data of the z=4.11 radio galaxy TN J1338-1942, including an intermediate resolution spectrum obtained with FORS1on the VLT Antu telescope. TN J1338-1942 was the first z>4 radio galaxy to be discovered in the southern hemisphere and is one of the most luminous Ly-alpha objects in its class. The Ly-alpha and rest-frame optical emission appear co-spatial with the brightest radio hotspot of this very asymmetric radio source, suggesting extremely strong interaction with dense ambient clouds. The VLT observations are sufficiently sensitive to detect the continuum flux both blue-ward and red-ward of the Ly-alpha emission, allowing us to measure the Ly-alpha forest continuum break (Ly-alpha 'discontinuity', D_A) and the Lyman limit. We measure a D_A=0.37+-0.1, which is ~0.2 lower than the values found for quasars at this redshift. We interpret this difference as possibly due to a bias towards large D_A introduced in high--redshift quasar samples that are selected on the basis of specific optical colors. If such a bias would exist in optically selected quasars, - and even in samples of Lyman break galaxies -, then the space density of both classes of object will be underestimated. Furthermore, the average HI column density along cosmological lines of sight as determined using quasar absorption lines would be overestimated. Because of their radio-based selection, we argue that z>4 radio galaxies are excellent objects for investigating D_A statistics. [abridged]Comment: 6 Pages, including 4 PostScript figures. Accepted for publication in the Astronomy & Astrophysics Letter

Faint blue objects on the Hubble Deep Field North & South as possible nearby old halo white dwarfs

Using data derived from the deepest and finest angular resolution images of the universe yet acquired by astronomers at optical wavelengths using the Hubble Space Telescope (HST) in two postage-stamp sections of the sky (Williams et al. 1996a,b), plus simple geometrical and scaling arguments, we demonstrate that the faint blue population of point-source objects detected on those two fields (M\'endez et al. 1996) could actually be ancient halo white dwarfs at distances closer than about 2 kpc from the Sun. This finding has profound implications, as the mass density of the detected objects would account for about half of the missing dark matter in the Milky-Way (Bahcall and Soneira 1980), thus solving one of the most controversial issues of modern astrophysics (Trimble 1987, Ashman 1992). The existence of these faint blue objects points to a very large mass locked into ancient halo white dwarfs. Our estimate indicates that they could account for as much as half of the dark matter in our Galaxy, confirming the suggestions of the MACHO microlensing experiment (Alcock et al. 1997). Because of the importance of this discovery, deep follow-up observations with HST within the next two years would be needed to determine more accurately the kinematics (tangential motions) for these faint blue old white dwarfs.Comment: Accepted for publication on The Astrophysical Journal, Part 1. 8 pages (AAS Latex macros V4.0), 1 B&W postscript figure, 2 color postscript figure

Carbon star survey in the Local Group. VII. NGC 3109 a galaxy without a stellar halo

We present a CFH12K wide field survey of the carbon star population in and around NGC 3109. Carbon stars, the brightest members of the intermediate-age population, were found nearly exclusively in and near the disk of NGC 3109, ruling out the existence of an extensive intermediate-age halo like the one found in NGC 6822. Over 400 carbon stars identified have = -4.71, confirming the nearly universality of mean magnitude of C star populations in Local Group galaxies. Star counts over the field reveal that NGC 3109 is a truncated disk shaped galaxy without an extensive stellar halo. The minor axis star counts reach the foreground density between 4' and 5', a distance that can be explained by an inclined disk rather than a spheroidal halo. We calculate a global C/M ratio of 1.75 +/- 0.20, a value expected for such a metal poor galaxy.Comment: Accepted in Astronomy and Astrophysic

Li-rich RGB stars in the Galactic Bulge

We present Lithium abundance determination for a sample of K giant stars in the galactic bulge. The stars presented here are the only 13 stars with detectable Lithium line (6767.18 A) among ~400 stars for which we have spectra in this wavelength range, half of them in Baade's Window (b=-4) and half in a field at b=-6. The stars were observed with the GIRAFFE spectrograph of FLAMES@VLT, with a spectral resolution of R~20,000. Abundances were derived via spectral synthesis and the results are compared with those for stars with similar parameters, but no detectable Li line. We find 13 stars with a detectable Li line, among which 2 have abundances A(Li)>2.7. No clear correlations were found between the Li abundance and those of other elements. With the exception of the two most Li rich stars, the others follow a fairly tight A(Li)-T_eff correlation. It would seems that there must be a Li production phase during the red giant branch (RGB), acting either on a very short timescale, or selectively only in some stars. The proposed Li production phase associated with the RGB bump cannot be excluded, although our targets are significantly brighter than the predicted RGB bump magnitude for a population at 8 kpcComment: 8 pages, 9 figures, accepted for publication in A&