Hartwick's rule and maximin paths when the exhaustible resource has an amenity value

This paper studies the maximin paths of the canonical Dasgupta-Heal-Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. Hartwick's rule then appears as an efficient tool to characterize solutions in a variety of settings. We start with the case without technical progress. We obtain an explicit solution of the mmaximin problem in the case where production and utility are Cobb-Douglas. When the utility function is CES with a low elasticity of substitution between consumption and natural capital, we show taht it is optimal to preserve forever a critical level of natural capital, determined endogeneously. We then study how technical progress affects the optimal maximin paths, in the Cobb-Douglas utility case. On the long run path of the economy capital, production and consumption grow at a common constant rate, while the resource stock decreases at a constant rate and is therefore completely depleted in the very long run. A higher amenity value of the resource stock leads to faster economic growth, but to a lower long run rate of depletion. We then develop a complete analysis of the dynamics of the maximin problem when the sole source of well-being is consumption, and provide a numerical resoultion of the model with resource amenity. The economy consumes, produces and invests less in the short run if the resource has an amenity value than if doesn't whereas it is the contrary in the medium and long runs. However, and without surprise, the resource stock remains for ever higher with resource amenity than without.Exhaustible resources, sustainability, Hartwick's rule.

International Emissions Trading Scheme and European Emissions Trading Scheme : what linkages ?

Simultaneity between commitment periods (2008-2012) of both International and European Emissions Trading schemes may generate distortions in terms of burden distribution among sectors. There will be two levels of trading (a country and an entity level), which both need to be consistent with one another, despite of their different designs. To reach international targets, European governments will adopt an additional policy. It consists in implementing a tax on emissions of non-covered sectors. The tax rates depend on the effort realized within the European market. We propose a modeling of this two-level environmental policy, focusing on the levels of tax rates in each case of linkage. We obtain empirical estimations of the efforts that could be demanded to non-covered sectors and of the price(s) of carbon.Kyoto Protocol, EU-ETS, co-existence of domestic and international emissions trading systems, carbon price, environmental policy.

The optimal carbon sequestration in agricultural soils : does the dynamics of the physical process matter ?

The Kyoto Protocol, which came in force in February 2005, allows countries to resort to «supplementary activities» consisting particularly in carbon sequestration in agricultural soils. Existing papers studying the optimal carbon sequestration recognize the importance of the temporality of sequestration, but overlook the fact that it is a dissymmetric dynamic process. This paper takes explicitely into account the temporality of sequestration. Its first contribution is technical : we solve an optimal control problem with two stages and a dissymmetric dynamic process. The second contribution is empirical : we show that the error made when sequestration is supposed immediate can be very significant, and we exhibit numerically the optimal path of sequestration/de-sequestration for specific benefit, damage and cost functions, and a calibration that mimics roughly the world conditions.Environment, agriculture, carbon sequestration, Kyoto Protocol, optimal control.

Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value

This paper studies the undiscounted utilitarian optimal paths of the canonical Dasgupta-Heal-Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. We use a Keynes-Ramsey rule wich yields a generalization of Hartwick's rule : if society has a zero discount rate but is ready to accept intertemporal substitution, net investment should not be zero as in the maximin case but should be positive, its level depending on the distance between the current and the long run bliss level of utility. We characterize solutions in the Cobb-Douglas utility and production case, and analyse the influence of the intertemporal elasticity of substitution on the time profile of the optimal paths. We show that, in the Cobb-Douglas case, the ratio of the values of the resource and capital stocks remains constant along the optimal path, and is independent of initial conditions.Exhaustible resources ; Hartwick's rule ; intertemporal substitution

Eléments sur l'actualisation et l'environnement

The choice of a discount rate is central in project evaluation, all the more since the project's horizon is distant. The controversy about the appropriate discount rate has been given a new life about environmental projects, characterized by very remote costs and/or benefits, reduced to a trivial level by discounting. This paper is a survey of the recent literature on discounting and the environment. The first proposal in this literature consists in replacing the usual social welfare function, namely the discounted utilitarian one, by another social welfare criterion, based on intergenerational equity issues. The second approach is descriptive rather than prescriptive, and justifies by psychological considerations the use of a time-decreasing pure rate of time preference. The third approach justifies by future uncertainty the use of a time-decreasing consumption social discount rate. We underline that it is very difficult to determine the "good" procedure for choosing a discount rate. The arguments that lead to adopt a time-decreasing social consumption discount rate are nevertheless very convincing, and the paper argues in favour of this approach.Le choix d'un taux d'actualisation est central dans l'évaluation de projets, d'autant plus que l'horizon sur lequel porte le projet est long. La discussion sur le taux d'actualisation approprié a ainsi connu un regain de vigueur à propos de projets à caractère environnemental, caractérisés par un très grand éloignement dans le temps des coûts et/ou des bénéfices, réduits à un niveau insignifiant par l'actualisation. Cet article est une synthèse des apports les plus récents de la littérature sur l'actualisation et l'environnement. La première approche consiste à remplacer le critère de bien-être social utilitariste escompté de l'approche usuelle par un autre critère, en se fondant sur des considérations d'équité intergénérationnelle. La deuxième se place sur un plan positif et non plus normatif, conteste l'idée d'un taux de préférence pure pour le présent constant et justifie par des considérations psychologiques sa décroissance au cours du temps. La troisième approche enfin justifie par l'incertitude sur le futur l'utilisation d'un taux d'escompte de la consommation décroissant au court du temps et faible à long terme. On met en évidence la grande difficulté qu'il existe à déterminer la "bonne" procédure concernant le choix d'un taux d'actualisation. Les arguments qui conduisent à adopter un taux d'escompte de la consommation décroissant au cours du temps sont cependant très convaincants, et l'article plaide pour cette approche. Le Royaume-Uni (dans le "Green Book") et la France (dans le rapport du groupe Lebègue pour le Commissariat Général au Plan) la retiennent d'ailleurs officiellement depuis peu, bien que d'importantes difficultés d'ordre pratique subsistent

The Zero Discounting and Maximin Optimal Paths in a Simple Model of Global Warming

Following Stollery (1998), we extend the Solow-- Dasgupta--Heal model to analyze the effects of global warming The rise of temperature is caused by the use of fossil resources so that the temperature level can be linked to the remaining stock of these resources. The rise of temperature affects both productivity and utility. We characterize optimal solutions for the maximin and zero-discounting cases and present closed form solutions for the case where the production and utility functions are Cobb-Douglas, and the temperature level is an exponential function of the remaining stock of resources. We show that a greater weight of temperature in intratemporal preferences or a larger intertemporal elasticity of substitution both lead to postpone resource use.Global warming;Zero discounting;maximin

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 long can excess pollution persist? The non-cooperative case

International audienceThis paper describes a world composed of two (groups of) countries, which derive their utility from a polluting activity and from the enjoyment of a common environmental quality. The initial situation is both suboptimal and unsustainable: pollution leads to a continuous deterioration of environmental quality. The two countries have heterogeneous preferences for the environment, which are private knowledge. This prevents the adoption of abatement policies negotiated between the two countries, because each one has a strong incentive to announce in every negotiation an arbitrarily low preference for the environment. The two countries then engage in a war of attrition, each of them postponing abatement policies, in the hope that the other will concede ...rst and abate more. We study for how long the adjustment is postponed, according to initial conditions, the greenness of the greenest country, the possible range of preferences and the rates of discount and natural regeneration