How to get the Blanchard-Kahn form from a general linear rational expectations model

In this paper, we prove that every linear model with rational expectations can be transformed by the means of an one-to-one mapping into another model which has one of the following properties: i) it is degenerated, ii) it is backward, ii) it has the Blanchard-Kahn form. In addition to sorne simple illustrations, we provide two applications on two nonlinear forward-looking economic models in order to show how to use our theoretical analysis for local stability assessment

Growth, Environment and Uncertain Future Preferences

The attitude of future generations towards environmental assets may well be different from ours, and it is necessary to take into account this possibility explicitly in the current debate about environmental policy. The question we are addressing here is: should uncertainty about future preferences lead to a more conservative attitude towards environment? Previous literature shows that it is the case when society expects that on average future preferences will be more in favor of environment than ours, but this result relies heavily on the assumption of a separability between consumption and environmental quality in the utility function. We show that things are less simple when preferences are non-separable: the attitude of the society now depends not only on the expectation of the change in preferences but also on the characteristics of the economy (impatience, intertemporal flexibility, natural capacities of regeneration of the environment, relative preference for the environment), on its history (initial level of the environmental quality) and on the date at which preferences are expected to change (near or far future).Growth ; Environment ; Preferences ; Uncertainty c ° 2002 Kluwer Academic Publishers. Printed in the Netherlands.

How to get the Blanchard-Kahn form from a general linear rational expectations model.

In this paper, we prove that every linear model with rational expectations can be transformed by the means of an one-to-one mapping into another model which has one of the following properties: i) it is degenerated, ii) it is backward, ii) it has the Blanchard-Kahn form. In addition to sorne simple illustrations, we provide two applications on two nonlinear forward-looking economic models in order to show how to use our theoretical analysis for local stability assessment.Rational Expectations; Blanchard-Kahn Form; Reduction Algorithms;

With exhaustible resources, can a developing country escape from the poverty trap ?

This paper studies the optimal growth of a developing non-renewable natural resource producer, which extracts the resource from its soil and produces a single consumption good with man-made capital. Moreover, it can sell the extracted resource abroad and use the revenues to buy an imported good, which is a perfect substitute of the domestic consumption good. The domestic technology is convex-concave, so that the economy may be locked into a poverty trap. We study the optimal extraction and depletion of the exhaustible resource and the optimal paths of accumulation of capital and of domestic consumption. We show that the extent to which the country will optimally escape from the poverty trap and the exhaustible resource will be a blessing depends on the characteristics of its technology and of the revenues from the resource function, on its impatience, on the level of its initial stock of capital and on the abundance of the natural resource. If the marginal productivity of capital at the origin is greater than the sum of the social discount rate and the depreciation rate, the country will accumulate capital along the entire growth path and will escape from the poverty trap, whatever its initial stocks of capital and resource, and provided that the marginal revenue obtained from the exportation of the resource is finite at the origin. On the contrary, if the marginal productivity of capital is lower than the depreciation rate whatever the level of capital and if moreover the initial stock of capital is small, then the country will never accumulate ; it will consume the revenues obtained from selling abroad the extracted resource, until there is no resource left and the economy collapses. We also show that any optimal path may be decentralized in a competitive equilibrium by using a tax/subsidy scheme for firms.Optimal growth, exhaustible resource, convex-concave technology, poverty trap, competitive equilibrium with tax/subsidy.

With Exhaustible Resources, Can A Developing Country Escape From The Poverty Trap?

This paper studies the optimal growth of a developing non-renewable natural resource producer. It extracts the resource from its soil, and produces a single consumption good with man-made capital. More- over, it can sell the extracted resource abroad and use the revenues to buy an imported good, which is a perfect substitute of the domes- tic consumption good. The domestic technology is convex-concave, so that the economy may be locked into a poverty trap. We show that the extent to which the country will escape from the poverty trap depends, besides the interactions between its technology and its impatience, on the characteristics of the resource revenue function, on the level of its initial stock of capital, and on the abundance of the natural resource.optimal growth;non-renewable resource;convex-concave technology;poverty trap;resource curse

A non-dictatorial criterion for optimal growth models

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/CESFramDP2008.htmDocuments de travail du Centre d'Economie de la Sorbonne 2008.30 - ISSN : 1955-611XThere are two main approaches for defining social welfare relations for an economy with infinite horizon. The first one is to consider the set of intertemporal utility streams generated by a general set of bounded consumptions and define a preference relation between them. This relation is ideally required to satisfy two main axioms, the Pareto axiom, which guarantees efficiency and the Anonymity axiom, which guarantees equity. Basu and Mitra (2003) show that it is impossible to represent by a function a preference relation embodying both requirements, and Basu and Mitra (2007) propose and characterize a new welfare criterion called utilitarian social welfare relation. In the same framework, Chichilnisky (1996) proposes two axioms that capture the idea of sustainable growth : non-dictatorship of the present and non-dictatorship of the future, and exhibits a mixed criterion, adding a discounted utilitarian part, which gives a dictatorial role to the present, and a long term part, which gives a dictatorial role to the future. The drawback of Chichilnisky's approach is that it often does not allow to explicity characterize optimal growth paths with optimal control techniques. Our aim is less general than Chichilnisky's and Basu and Mitra's : we want to have a non-dictatorial criterion for optimal growth models. We restrict ourselves to the set of utilities of consumptions which are generated by a specific technology. We show that the undiscounted utilitarian criterion pioneered by Ramsey (1928) is not only convenient if one wants to solve an optimal growth problem but also sustainable, efficient and equitable.Il existe deux approches principales pour définir des relations de bien-être social dans une économie à horizon infini. La première consiste à considérer l'ensemble des flux d'utilité engendrés par un ensemble très général de consommations bornées et à définir une relation de préférence entre eux. Cette relation doit idéalement satisfaire deux axiomes principaux : l'axiome de Pareto, qui garantit l'efficacité et l'axiome d'anonymité qui garantit l'équité. Basu et Mitra (2003) montrent qu'il est impossible de représenter par une fonction une relation de préférence satisfaisant de ces deux axiomes. Dans le même cadre, Chichilnisky (1996) propose deux axiomes qui capturent l'idée de croissance durable : non dictature du présent et non dictature du futur et propose un critère mixte satisfaisant ces axiomes, ajoutant une partie utilitariste escomptée qui donne un rôle dictatorial au présent et une partie de long terme qui donne un rôle dictatorial au futur. L'inconvénient de l'approche de Chichilnisky est qu'elle ne permet en général pas de caractériser explicitement les sentiers de croissance optimale à l'aide des techniques de contrôle optimal. Notre objectif est plus modeste que ceux de Chichilnisky et Basu et Mitra : nous désirons disposer d'un critère non dictatorial pour les modèles de croissance optimale. Nous nous intéressons ainsi aux ensembles d'utilités issues de consommations engendrées par une technologie spécifique. Nous montrons alors que le critère utilitariste non escompté de Ramsey (1928) est efficace, non dictatorial et équitable

A note on the consequences of an endogenous discounting depending on the environmental quality

International audienceOur intention is to study, in the framework of a very simple optimal growth model, the consequences on the optimal paths followed by consumption and the environmental quality of an endogenous discounting. Consumption directly comes from the use of environmental services and so is a direct cause of environmental degradation. The environment is valued both as a source of consumption and as an amenity. For a sustainability concern, we introduce an endogenous discount rate growing with the environmental quality, and compare the optimal growth paths with the ones obtained in the usual case of exogenous and constant discounting. We show that the convergence of the environmental quality towards a steady state occurs only for a very special configuration of the parameters in the exogenous discounting case, while it occurs generically in the endogenous discounting one. This happens for a utility discount rate becoming suficiently high when the environmental quality is high and suficiently low when the environmental quality is poor. In this case then, endogenous discounting with a positive marginal discount rate allows us to avoid the depletion of the environment

Ressources renouvelables et incertitude sur lespréférences des générations futures

Rien ne nous permet d'être certains que les générations futures auront les mêmes préférences que nous concernant les biens environnementaux. En outre, même si nous sommes tentés, en raison de la dégradation de la qualité de l'environnement, de croire que leur sensibilité à l'environnement sera plus grande que la notre, rien ne nous permet de l'affirmer avec certitude. Cet article étudie alors, dans un cadre très simple, les conséquences en termes de trajectoires optimales de consommation d'une incertitude sur les préférences des générations futures en matière de consommation d'une ressource environnementale renouvelable. Une telle incertitude va-t-elle induire un comportement optimal plus "conservateur" vis-à-vis de la ressource ? Nous montrons que tel est le cas uniquement si nous anticipons aujourd'hui que les générations futures seront en moyenne plus sensibles que nous ne le sommes à la consommation permise par l'utilisation de la ressource environnementale. Nous montrons en outre que la prise en compte de cette incertitude conduit à une profonde modification de la trajectoire optimale de consommation, qui non seulement devient non-continue mais en outre peut devenir non-monotone.ressources renouvelables, croissance, préférences, incertitude

Phase-locking of two self-seeded tapered amplifier lasers

We report on the phase-locking of two diode lasers based on self-seeded tapered amplifiers. In these lasers, a reduction of linewidth is achieved using narrow-band high-transmission interference filters for frequency selection. The lasers combine a compact design with a Lorentzian linewidth below 200 kHz at an output power of 300 mW. We characterize the phase noise of the phase-locked laser system and study its potential for coherent beam-splitting in atom interferometers.Comment: 7 pages, 4 figure

System efficiency of laser-based white light

For many lighting applications, light-emitting diodes (LEDs) are replacing traditional light sources providing the possibility for smart and efficient systems as well as a reduction in the product weight. A next step in this development is the integration of laser-based light sources to increase luminance and to further scale down the optics possibly leading to a reduction of necessary resources. This article reviews the possibilities and challenges arising from the use of laser diodes especially compared to current high-power LED systems in terms of efficiency, color-rendering properties, and thermal management. © 2014 Thoss Media and De Gruyter