We investigate a linear state differential game describing an asymmetric Cournot duopoly with\ud capacity accumulation a la Ramsey and a negative environmental externality (pollution), in\ud which one of the firms has adopted corporate social responsibility (CSR) in its statute, and\ud therefore includes consumer surplus and the environmental effects of production in its\ud objective function. If the market is sufficiently large, the CSR firm sells more, accumulates\ud more capital, and earns higher profits than its profit-seeking rival

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The physical properties of the so-called Ostriker isothermal, non-rotating filament have been classically used as benchmark to interpret the stability of the filaments observed in nearby clouds. However, such static picture seems to contrast with the more dynamical state observed in different filaments. In order to explore the physical conditions of filaments under realistic conditions, in this work we theoretically investigate how the equilibrium structure of a filament changes in a rotating configuration. To do so, we solve the hydrostatic equilibrium equation assuming both uniform and differential rotations independently. We obtain a new set of equilibrium solutions for rotating and pressure truncated filaments. These new equilibrium solutions are found to present both radial and projected column density profiles shallower than their Ostriker-like counterparts. Moreover, and for rotational periods similar to those found in the observations, the centrifugal forces present in these filaments are also able to sustain large amounts of mass (larger than the mass attained by the Ostriker filament) without being necessary unstable. Our results indicate that further analysis on the physical state of star-forming filaments should take into account rotational effects as stabilizing agents against gravity

Context. The physical properties of the so-called Ostriker isothermal filament have been classically used as a benchmark to interpret the stability of the filaments observed in nearby clouds. However, recent continuum studies have shown that the internal structure of the filaments depart from the isothermality, typically exhibiting radially increasing temperature gradients. Aims. The presence of internal temperature gradients within filaments suggests that the equilibrium configuration of these objects should be therefore revisited. The main goal of this work is to theoretically explore how the equilibrium structure of a filament changes in a nonisothermal configuration. Methods. We solve the hydrostatic equilibrium equation by assuming temperature gradients similar to those derived from observations. Results. We obtain a new set of equilibrium solutions for nonisothermal filaments with both linear and asymptotically constant temperature gradients. For sufficiently large internal temperature gradients, our results show that a nonisothermal filament could present significantly larger masses per unit length and shallower density profiles than the isothermal filament without collapsing by its own gravity. Conclusions. We conclude that filaments can reach an equilibrium configuration under nonisothermal conditions. Detailed studies of both the internal mass distribution and temperature gradients within filaments are then needed to judge the physical state of filaments.

The increasing attention of prot maximising corporations to corporate social responsibility (CSR) is a new stylized fact of the contemporary economic environment. In our theoretical analysis we model CSR adoption as the optimal response of a prot maximising rm to the competition of a not for prot corporate pioneer in presence of a continuum of consumers with heterogeneous preferences toward the social and environmental features of the nal good. CSR adoption implies a trade-o since, on the one side, it raises production costs but, on the other side, it leads to the accumulation of ethical capital. We investigate conditions under which the prot maximising rm switches from price to price and CSR competition by comparing monopoly and duopoly equilibria and their consequences on aggregate social responsibility and consumers welfare. Our ndings provide a theoretical background for competition between prot maximising incumbents and not for prot entrants in markets such as fair trade, organic food, ethical banking and ethical nance.