International audienceThis 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 maximin 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 that 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 resolution 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 it does not, 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

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 which 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 in ‡uence of the intertemporal elasticity of substitution on the time pro…le 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. JEL: D9, Q01, Q3

L’article présente une maquette simple de l’économie française, susceptible d’être utilisée pour des travaux de prévision et d’évaluation des chocs et des politiques macroéconomiques. On se situe dans le cadre d’une petite économie ouverte, en changes fixes, faisant face à un taux d’intérêt réel donné. L’économie comprend un secteur des biens échangeables et un secteur des biens non échangeables. Les comportements sont spécifiés de manière simple et robuste, sans faire intervenir d’anticipations rationnelles et en utilisant systématiquement des représentations à correction d’erreurs. La dynamique des richesses financières est prise en compte, les effets de richesse assurant de manière naturelle la convergence de long terme des niveaux d’actifs et le respect des contraintes de solvabilité des agents. La dynamique de court terme incorpore des éléments keynésiens, liés à la viscosité des prix et salaires. Le long terme de la maquette fait largement appel à la calibration, la dynamique de court terme est estimée

International audienceInternational di¤erences in fuel taxation are huge, and may be justi…ed by different local negative externalities that taxes must correct, as well as by di¤erent preferences for public spending. In this context, should a worldwide uniform carbon tax be added to these local taxes to correct the global warming externality? We address this question in a second best framework à la Ramsey, where public goods have to be …nanced through distortionary taxation and the cost of public funds has to be weighted against the utility of public goods. We show that when lump-sum transfers between countries are allowed for, the second best tax on the polluting good may be decomposed into three parts: one, country-speci…c, dealing with the local negative externality, a second one, country-speci…c, dealing with the cost of levying public funds, and a third one, global, dealing with the global externality and which can be interpreted as the carbon price. Our main contribution is to show that the uniformity of the carbon price should still hold in this second best framework. Nevertheless, if lump-sum transfers between governments are impossible to implement, international di¤erentiation of the carbon price is the only way to take care of equity concerns. keywords: carbon price, second best, Pigovian taxatio

Following Stollery (1998), we extend the Solow-Dasgupta-Heal model to analyze the e¤ects 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 a¤ects 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.

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[fre] Nous nous intéressons à l'imposition du revenu, entendue dans un sens très large puisque nous y incluons l'impôt négatif que constitue le versement de subventions accordées sous conditions de revenu. Dans le barème actuel, les taux marginaux d'imposition ont un profil en U. La progressivité de l'impôt se traduit par des taux élevés au sommet de la distribution des revenus. Mais le caractère d'allocation différentielle du RMI fait aussi apparaître des taux égaux à l'unité au bas de la distribution. Bien entendu, toute action redistributive s'accompagne d'effets désincitatifs dès lors que l'imposition est assise sur le revenu et non sur les caractéristiques personnelles des individus. Le problème est donc de trouver le meilleur compromis entre redistribution et incitation à l'effort. Tel est l'objectif des modèles d'imposition optimale à la Mirrlees. Nous reprenons ici ce type d'analyse en l'appliquant au cas français, sur la base de données fiscales empruntées à B. Salanié. Les agents sont supposés ne différer que par un niveau individuel de capital humain, supposé exogène. Les deux paramètres importants sont alors l'élasticité de l'offre de travail, qui mesure l'ampleur des effets désincitatifs et le paramètre de concernement qui caractérise l'intensité de la redistribution souhaitée. Des simulations numériques permettent de déterminer le barème d'impôt optimal pour une large gamme de valeurs des paramètres. La conclusion générale est que des marges importantes de redistribution existent, dès lors que l'élasticité de l'offre de travail conserve une valeur raisonnable, assez faible. Une deuxième partie de l'article présente en détail les méthodes théoriques employées, une attention particulière étant portée au phénomène de bouchonnement. [eng] We are concerned with income taxation in a broad sense, including elements of negative income tax such as various subsidies conditional to income. The existing tax schedule is characterized by U-shape marginal tax rates. Progressive taxation implies high marginal rates at the top. Minimum income provision also implies a unit marginal tax rate at the bottom. Of course, any redistribution gives rise to disincentive effects as soon as taxation rests on perceived income rather than unobservable personal characteristics. The problem therefore is to find the best compromise between redistribution and incentives. This is the aim of optimal taxation à la Mirrlees. We apply this approach to French fiscal datas, collected by B. Salanié. Agents are supposed to differ only through their individual human capital, which is treated as exogenous. The analysis is dependent on two important parameters : labor supply elasticity, which measures the size of disincentive effects, and the parameter of an Atkinson collective utility function, which describes the concern for redistribution. Numerical simulations determine the optimal tax schedule, for a broad set of parameters. The general conclusion is that important margins for redistribution exist, as soon as labor supply elasticity keeps a...

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