Article

Self-regenerating environmental absorption efficiency and the $$\varvec{ soylent~green~scenario}$$ s o y l e n t g r e e n s c e n a r i o

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

We consider a stock pollution problem where the biosphere can transform from a sink to a source of pollution in the presence of self-regenerating environmental absorption efficiency. We examine the problem of controlling pollution and the capacity of the biosphere to absorb pollution: the regulator can mitigate emissions and can invest to build-up the absorption capacity of pollution sinks. We examine conditions under which both measures, mitigation and absorption capacity investments, are substitute (complement) to each other, and the relative extent to which environmental self-regenerating capabilities affect these conditions. We also exhibit the possibility of an oscillatory approach to the steady state. Particular attention is paid to the situation where the social planner is impatient.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... Each assumption has non-trivial consequences on the resulting optimal paths as we will show later. Indeed, if the restoration results are assumed to be state-independent, as they have been until now in the literature (El Ouardighi et al. 2014, 2016, 2018a, it dissociates the actual restoration achieved by a given effort and the current state of the absorption efficiency, thus ignoring the ecological conditions in play in the restoration process. It implies in particular that if the natural carbon sinks have turned to sources, they can be restored back to sinks, which is a rather optimistic take on carbon potential recuperation. ...
... Our model is an extended version of the model developed in El Ouardighi et al. (2014Ouardighi et al. ( , 2016. In a dynamic continuous framework, the social planner seeks to maximize intertemporal social welfare by weighing benefits from polluting economic activities, the costs of restoration efforts and environmental damages caused by stock pollution accumulation subject to endogenous variations of the environmental absorption efficiency. ...
Article
Full-text available
An important yet largely unexamined issue is how the interaction between deforestation and pollution affects economic and environmental sustainability. This article seeks to bridge the gap by introducing a dynamic model of pollution accumulation where polluting emissions can be mitigated and the absorption efficiency of pollution sinks can be restored. We assume that emissions are due to a production activity, and we include deforestation both as an additional source of emissions and as a cause of the exhaustion of environmental absorption efficiency. To account for the fact that the switching of natural sinks to a pollution source can be either possible, and in such a case even reversible, or impossible, we consider that restoration efforts can be either independent from or dependent on environmental absorption efficiency, i.e., state-independent versus state-dependent restoration efforts. We determine (i) whether production or deforestation is the most detrimental from environmental and social welfare perspectives, and (ii) how state-dependent restoration process affects pollution accumulation and deforestation policies and the related environmental and social welfare consequences.
... 4 The instantaneous social cost incurred by each player due to the pollution stock is a quadratic function, c i P(t) 2 2, where c i > 0 is a pollution cost coefficient, i 1, 2 (Rubio and Casino 2002;Wirl 2007;Boucekkine et al. 2013). Finally, each player incurs an instantaneous increasing convex cost of effort to restore environmental absorption efficiency, f i w i (t) 2 2, where f i > 0 is a restoration cost coefficient, i 1, 2 (El Ouardighi et al. 2014;El Ouardighi et al. 2015a). ...
... That is, the saddle-path can either converge monotonically or oscillate toward the steady state. This result is consistent with previous findings where a clockwise spiraling path can go through the Soylent Green area, with negative environmental absorption efficiency during a finite time interval (El Ouardighi et al. 2014;El Ouardighi et al. 2015a). ...
Article
Full-text available
In this paper, we suggest a two-player differential game model of transboundary pollution that accounts for time-dependent environmental absorption efficiency, which allows the biosphere to switch from a carbon sink to a source. We investigate the impact of negative externalities resulting from a transboundary pollution non-cooperative game wherein countries are dynamically involved. Based on a linear-quadratic specification for the instantaneous revenue function, we assess differences related to both transient path and steady state between cooperative solution, open-loop and Markov perfect Nash equilibria (MPNE). Regarding the methodological contribution of the paper, we suggest a particular structure of the conjectured value function to solve MPNE problems with multiplicative interaction between state variables in one state equation, so that third-order terms that arise in the Hamilton–Jacobi–Bellman equation are made negligible. Using a collocation procedure, we confirm the validity of the particular structure of the conjectured value function. The results suggest unexpected contrasts in terms of pollution control and environmental absorption efficiency management: (i) in the long run, an open-loop Nash equilibrium (OLNE) allows equivalent emissions to the social optimum but requires greater restoration efforts; (ii) although an MPNE is likely to end up with lower emissions and greater restoration efforts than an OLNE, it has a much greater chance of falling in the emergency area; (iii) the absence of cooperation and or precommitment becomes more costly as the initial absorption efficiency decreases; (iv) more heavily discounted MPNE strategies are less robust than OLNE to prevent irreversible switching of the biosphere from a carbon sink to a source.
Article
Full-text available
In a circular economy, the use of recycled resources in production is a key performance indicator for management. Yet, academic studies are still unable to inform managers on appropriate recycling and pricing policies. We develop an optimal control model integrating a firm’s recycling rate, which can use both virgin and recycled resources in the production process. Our model accounts for recycling influence both at the supply- and demand-sides. The positive effect of a firm’s use of recycled resources diminishes over time but may increase through investments. Using general formulations for demand and cost, we analytically examine joint dynamic pricing and recycling investment policies in order to determine their optimal interplay over time. We provide numerical experiments to assess the existence of a steady-state and to calculate sensitivity analyses with respect to various model parameters. The analysis shows how to dynamically adapt jointly optimized controls to reach sustainability in the production process. Our results pave the way to sounder sustainable practices for firms operating within a circular economy.
Article
Full-text available
It is known that an eco-efficiency strategy, which saves resources in the production process, may be offset by a rebound effect; it may even backfire. Less known are the exact conditions under which eco-efficiency rebounds or backfires. This article fills the gap by providing an analytical model of the rebound and backfire effects. We propose an optimal control framework of dynamic pricing and eco-efficiency investment, for which eco-efficiency reduces the unit production cost and boosts the demand of environmentally concerned consumers. Results, which hold with a general demand formulation, examine the analytic conditions for the rebound and backfire effects. They also highlight the possibility of a reverse rebound effect. Such results pave the way to sounder sustainability strategies.
Article
Full-text available
This paper investigates how current and future generations are affected by commitment-based Nash equilibrium environmental strategies when the environmental absorption efficiency is susceptible to switch from a pollution sink to a source. We formulate a two-player differential game model of transboundary pollution that includes the environmental absorption efficiency as a state variable that can be enhanced thanks to restoration efforts. Based on a logarithmic specification for the instantaneous revenue function, we characterize the cooperative solution and the commitment-based Nash equilibrium strategy, and examine their differences in terms of steady state and transient behavior. We notably show that a commitment-based Nash equilibrium strategy makes it possible to prevent a definitive switching of the environmental absorption efficiency from a pollution sink to a source but imposes greater economic sacrifices on current generations than on future generations. In comparison, the cooperative solution imposes greater sacrifices on current generations in terms of revenues but it imposes lower environmental costs on both current and future generations than commitment-based Nash equilibrium strategy.
Article
Full-text available
Numerous optimal control models analyzed in economics are formulated as discounted infinite time horizon problems, where the defining functions are nonlinear as well in the states as in the controls. As a consequence solutions can often only be found numerically. Moreover, the long run optimal solutions are mostly limit sets like equilibria or limit cycles. Using these specific solutions a BVP approach together with a continuation technique is used to calculate the parameter dependent dynamic structure of the optimal vector field. We use a one dimensional optimal control model of a fishery to exemplify the numerical techniques. But these methods are applicable to a much wider class of optimal control problems with a moderate number of state and control variables.
Article
Full-text available
We consider an optimal technology adoption AK model in line with Boucekkine Krawczyk and Vallée (2011): an economy, caring about consumption and pollution as well, starts with a given technological regime and may decide to switch at any moment to a cleaner technology at a given permanent or transitory output cost. At the same time, we posit that there exists a pollution threshold above which the assimilation capacity of Nature goes down, featuring a kind of irreversible ecological regime. We study how ecological irreversibility interacts with the ingredients of the latter optimal technological switch problem, with a special attention to induced capital-pollution relationship. We find that if a single technological switch is optimal, one recovers the Environmental Kuznets Curve provided initial pollution is high enough. If exceeding the ecological threshold is optimal, then the latter configuration is far from being the rule.
Article
Full-text available
Localized ecological systems are known to shift abruptly and irreversibly from one state to another when they are forced across critical thresholds. Here we review evidence that the global ecosystem as a whole can react in the same way and is approaching a planetary-scale critical transition as a result of human influence. The plausibility of a planetary-scale ‘tipping point’ highlights the need to improve biological forecasting by detecting early warning signs of critical transitions on global as well as local scales, and by detecting feedbacks that promote such transitions. It is also necessary to address root causes of how humans are forcing biological changes.
Book
Full-text available
The goal of this book is to prepare readers to apply the optimal control theory to nonlinear processes beyond the standard applications. The examples investigated in depth are drawn from drug policy, corruption, and counter-terror, so this book will be of particular interest to economists, epidemiologists, and other scholars interested in the economics of crime, health, and violence. However, the book is designed to simultaneously appeal to an even larger audience of students in mathematics, economics, biosciences, and operations research for whom it fills a gap in the literature between “cookbooks,” that give recipes but not deeper understanding, and more formal mathematical textbooks that do not explain how to apply the theory to practical problems.
Article
Full-text available
A coupled physical-biogeochemical climate model that includes a dynamic global vegetation model and a representation of a coupled atmosphere-ocean general circulation model is driven by the nonintervention emission scenarios recently developed by the Intergovernmental Panel on Climate Change (IPCC). Atmospheric CO 2 , carbon sinks, radiative forcing by greenhouse gases (GHGs) and aerosols, changes in the fields of surface-air temperature, precipitation, cloud cover, ocean thermal expansion, and vegetation structure are projected. Up to 2100, atmospheric CO 2 increases to 540 ppm for the lowest and to 960 ppm for the highest emission scenario analyzed. Sensitivity analyses suggest an uncertainty in these projections of À10 to +30% for a given emission scenario. Radiative forcing is estimated to increase between 3 and 8 W m -2 between now and 2100. Simulated warmer conditions in North America and Eurasia affect ecosystem structure: boreal trees expand poleward in high latitudes and are partly replaced by temperate trees and grasses at lower latitudes. The consequences for terrestrial carbon storage depend on the assumed sensitivity of climate to radiative forcing, the sensitivity of soil respiration to temperature, and the rate of increase in radiative forcing by both CO 2 and other GHGs. In the most extreme cases, the terrestrial biosphere becomes a source of carbon during the second half of the century. High GHG emissions and high contributions of non-CO 2 agents to radiative forcing favor a transient terrestrial carbon source by enhancing warming and the associated release of soil carbon.
Article
Full-text available
This study investigates commonalities and differences in projected land biosphere carbon storage among climate change projections derived from one emission scenario by five different general circulation models (GCMs). Carbon storage is studied using a global biogeochemical process model of vegetation and soil that includes dynamic treatment of changes in vegetation composition, a recently enhanced version of the Lund-Potsdam-Jena Dynamic Global Vegetation Model (LPJ-DGVM). Uncertainty in future terrestrial carbon storage due to differences in the climate projections is large. Changes by the end of the century range from −106 to +201 PgC, thus, even the sign of the response whether source or sink, is uncertain. Three out of five climate projections produce a land carbon source by the year 2100, one is approximately neutral and one a sink. A regional breakdown shows some robust qualitative features. Large areas of the boreal forest are shown as a future CO2 source, while a sink appears in the arctic. The sign of the response in tropical and sub-tropical ecosystems differs among models, due to the large variations in simulated precipitation patterns. The largest uncertainty is in the response of tropical rainforests of South America and Central Africa.
Article
Full-text available
A new Earth system model, GENIE-1, is presented which comprises a 3-D frictional geostrophic ocean, phosphate-restoring marine biogeochemistry, dynamic and thermodynamic sea-ice, land surface physics and carbon cycling, and a seasonal 2-D energy-moisture balance atmosphere. Three sets of model climate parameters are used to explore the robustness of the results and for traceability to earlier work. The model versions have climate sensitivity of 2.8–3.3°C and predict atmospheric CO2 close to present observations. Six idealized total fossil fuel CO2 emissions scenarios are used to explore a range of 1,100–15,000 GtC total emissions and the effect of rate of emissions. Atmospheric CO2 approaches equilibrium in year 3000at 420–5,660ppmv, giving 1.5–12.5°C global warming. The ocean is a robust carbon sink of up to 6.5GtCyear−1. Under ‘business as usual’, the land becomes a carbon source around year 2100 which peaks at up to 2.5GtCyear−1. Soil carbon is lost globally, boreal vegetation generally increases, whilst under extreme forcing, dieback of some tropical and sub-tropical vegetation occurs. Average ocean surface pH drops by up to 1.15 units. A Greenland ice sheet melt threshold of 2.6°C local warming is only briefly exceeded if total emissions are limited to 1,100GtC, whilst 15,000GtC emissions cause complete Greenland melt by year 3000, contributing 7m to sea level rise. Total sea-level rise, including thermal expansion, is 0.4–10m in year 3000 and ongoing. The Atlantic meridional overturning circulation shuts down in two out of three model versions, but only under extreme emissions including exotic fossil fuel resources.
Article
Full-text available
Localized ecological systems are known to shift abruptly and irreversibly from one state to another when they are forced across critical thresholds. Here we review evidence that the global ecosystem as a whole can react in the same way and is approaching a planetary-scale critical transition as a result of human influence. The plausibility of a planetary-scale 'tipping point' highlights the need to improve biological forecasting by detecting early warning signs of critical transitions on global as well as local scales, and by detecting feedbacks that promote such transitions. It is also necessary to address root causes of how humans are forcing biological changes.
Article
Full-text available
The terrestrial carbon sink has been large in recent decades, but its size and location remain uncertain. Using forest inventory data and long-term ecosystem carbon studies, we estimate a total forest sink of 2.4 ± 0.4 petagrams of carbon per year (Pg C year–1) globally for 1990 to 2007. We also estimate a source of 1.3 ± 0.7 Pg C year–1 from tropical land-use change, consisting of a gross tropical deforestation emission of 2.9 ± 0.5 Pg C year–1 partially compensated by a carbon sink in tropical forest regrowth of 1.6 ± 0.5 Pg C year–1. Together, the fluxes comprise a net global forest sink of 1.1 ± 0.8 Pg C year–1, with tropical estimates having the largest uncertainties. Our total forest sink estimate is equivalent in magnitude to the terrestrial sink deduced from fossil fuel emissions and land-use change sources minus ocean and atmospheric sinks.
Article
Full-text available
The terrestrial carbon sink has been large in recent decades, but its size and location remain uncertain. Using forest inventory data and long-term ecosystem carbon studies, we estimate a total forest sink of 2.4 ± 0.4 petagrams of carbon per year (Pg C year–1) globally for 1990 to 2007. We also estimate a source of 1.3 ± 0.7 Pg C year–1 from tropical land-use change, consisting of a gross tropical deforestation emission of 2.9 ± 0.5 Pg C year–1 partially compensated by a carbon sink in tropical forest regrowth of 1.6 ± 0.5 Pg C year–1. Together, the fluxes comprise a net global forest sink of 1.1 ± 0.8 Pg C year–1, with tropical estimates having the largest uncertainties. Our total forest sink estimate is equivalent in magnitude to the terrestrial sink deduced from fossil fuel emissions and land-use change sources minus ocean and atmospheric sinks.
Article
Full-text available
The continued increase in the atmospheric concentration of carbon dioxide due to anthropogenic emissions is predicted to lead to significant changes in climate. About half of the current emissions are being absorbed by the ocean and by land ecosystems, but this absorption is sensitive to climate as well as to atmospheric carbon dioxide concentrations, creating a feedback loop. General circulation models have generally excluded the feedback between climate and the biosphere, using static vegetation distributions and CO2 concentrations from simple carbon-cycle models that do not include climate change. Here we present results from a fully coupled, three-dimensional carbon-climate model, indicating that carbon-cycle feedbacks could significantly accelerate climate change over the twenty-first century. We find that under a 'business as usual' scenario, the terrestrial biosphere acts as an overall carbon sink until about 2050, but turns into a source thereafter. By 2100, the ocean uptake rate of 5 Gt C yr(-1) is balanced by the terrestrial carbon source, and atmospheric CO2 concentrations are 250 p.p.m.v. higher in our fully coupled simulation than in uncoupled carbon models, resulting in a global-mean warming of 5.5 K, as compared to 4 K without the carbon-cycle feedback.
Article
Full-text available
The continued increase in the atmospheric concentration of carbon dioxide due to anthropogenic emissions is predicted to lead to significant changes in climate. About half of the current emissions are being absorbed by the ocean and by land ecosystems, but this absorption is sensitive to climate as well as to atmospheric carbon dioxide concentrations, creating a feedback loop. General circulation models have generally excluded the feedback between climate and the biosphere, using static vegetation distributions and CO2 concentrations from simple carbon-cycle models that do not include climate change. Here we present results from a fully coupled, three-dimensional carbon-climate model, indicating that carbon-cycle feedbacks could significantly accelerate climate change over the twenty-first century. We find that under a 'business as usual' scenario, the terrestrial biosphere acts as an overall carbon sink until about 2050, but turns into a source thereafter. By 2100, the ocean uptake rate of 5 Gt C yr(-1) is balanced by the terrestrial carbon source, and atmospheric CO2 concentrations are 250 p.p.m.v. higher in our fully coupled simulation than in uncoupled carbon models, resulting in a global-mean warming of 5.5 K, as compared to 4 K without the carbon-cycle feedback.
Article
Full-text available
The growth rate of atmospheric carbon dioxide (CO(2)), the largest human contributor to human-induced climate change, is increasing rapidly. Three processes contribute to this rapid increase. Two of these processes concern emissions. Recent growth of the world economy combined with an increase in its carbon intensity have led to rapid growth in fossil fuel CO(2) emissions since 2000: comparing the 1990s with 2000-2006, the emissions growth rate increased from 1.3% to 3.3% y(-1). The third process is indicated by increasing evidence (P = 0.89) for a long-term (50-year) increase in the airborne fraction (AF) of CO(2) emissions, implying a decline in the efficiency of CO(2) sinks on land and oceans in absorbing anthropogenic emissions. Since 2000, the contributions of these three factors to the increase in the atmospheric CO(2) growth rate have been approximately 65 +/- 16% from increasing global economic activity, 17 +/- 6% from the increasing carbon intensity of the global economy, and 18 +/- 15% from the increase in AF. An increasing AF is consistent with results of climate-carbon cycle models, but the magnitude of the observed signal appears larger than that estimated by models. All of these changes characterize a carbon cycle that is generating stronger-than-expected and sooner-than-expected climate forcing.
Article
Full-text available
The carbon balance of terrestrial ecosystems is particularly sensitive to climatic changes in autumn and spring, with spring and autumn temperatures over northern latitudes having risen by about 1.1 degrees C and 0.8 degrees C, respectively, over the past two decades. A simultaneous greening trend has also been observed, characterized by a longer growing season and greater photosynthetic activity. These observations have led to speculation that spring and autumn warming could enhance carbon sequestration and extend the period of net carbon uptake in the future. Here we analyse interannual variations in atmospheric carbon dioxide concentration data and ecosystem carbon dioxide fluxes. We find that atmospheric records from the past 20 years show a trend towards an earlier autumn-to-winter carbon dioxide build-up, suggesting a shorter net carbon uptake period. This trend cannot be explained by changes in atmospheric transport alone and, together with the ecosystem flux data, suggest increasing carbon losses in autumn. We use a process-based terrestrial biosphere model and satellite vegetation greenness index observations to investigate further the observed seasonal response of northern ecosystems to autumnal warming. We find that both photosynthesis and respiration increase during autumn warming, but the increase in respiration is greater. In contrast, warming increases photosynthesis more than respiration in spring. Our simulations and observations indicate that northern terrestrial ecosystems may currently lose carbon dioxide in response to autumn warming, with a sensitivity of about 0.2 PgC degrees C(-1), offsetting 90% of the increased carbon dioxide uptake during spring. If future autumn warming occurs at a faster rate than in spring, the ability of northern ecosystems to sequester carbon may be diminished earlier than previously suggested.
Article
Full-text available
This paper presents an optimal endogenous growth model with pollutionaccumulation and abatement activities which analyzes the implications ofpollution accumulation irreversibility on the existence of sustainablegrowth paths. This model studies different pollution-decay functions whichpresent, among others, the feature that a sufficiently high pollution stocklevel can reduce the rate of decay to zero. This study shows that this newfeature, which gains support for the biological literature, significantlyalters the traditional results on the properties of sustainable endogenousgrowth by reducing the field of existence and strengthening the role ofindividual preferences. Copyright Kluwer Academic Publishers 2000
Article
We consider an optimal consumption and pollution problem that has two important features. Environmental damages due to economic activities may be irreversible and the level at which the degradation becomes irreversible is unknown. Particular attention is paid to the situation where agents are relatively impatient and/or do not care a lot about the environment and/or Nature regenerates at low rate. We show that the optimal policy of the uncertain problem drives the economy in the long run toward a steady state while, when ignoring irreversibility, the economy follows a balanced growth path accompanied by a perpetual decrease in environmental quality and consumption, both asymptotically converging toward zero. Therefore, accounting for the risk of irreversibility induces more conservative decisions regarding consumption and polluting emissions. In general, however, we cannot rule out situations where the economy will optimally follow an irreversible path and consequently, will also be left, in the long run, with an irreversibly degraded environment.
Article
We consider the effect of an increase in the risk from pollution. We show that in the case of a flow pollution, when the number of players is sufficiently large, the result of Bramoulle and Treich [ Journal of the European Economic Association , 2009], showing that a marginal increase of risk in the neighborhood of a risk-free world is welfare-improving, holds even when we consider non-marginal increases in risk and for any initial values of the risk. By contrast, in the case of a stock pollutant, we show that starting in a risk-free world a marginal increase in risk is always welfare reducing. However if the initial value of the risk is sufficiently large, the impact of an increase in risk depends on the level of the stock pollutant. In this non-negligible risk case, it is only for values of the stock of pollution that are below a certain threshold that an increase in risk can mitigate the failure from cooperation over emissions and increase welfare.
Article
We consider a general control problem with two types of optimal regime switch. The first one concerns technological and/or institutional regimes indexed by a finite number of discrete parameter values, and the second features regimes relying on given threshold values for given state variables. We propose a general optimal control framework allowing to derive the first-order optimality conditions and in particular to characterize the geometry of the shadow prices at optimal switching times (if any). We apply this new optimal control material to address the problem of the optimal management of natural resources under ecological irreversibility, and with the possibility to switch to a backstop technology.
Article
Multi-stage modeling provides powerful tools to study optimal switches between different technologies. In most of the related literature, however, it is assumed that the number of switches is a-priori fixed. In the present paper we allow for multiple optimally determined switches. Consequently, we are able to locate solution paths that not only lead to different long-run outcomes but also differ in the number of switches along these paths. We present a simple production-pollution model in which a representative firm wants to maximize the profit gained out of production which, however, causes harmful pollution as by-product. The firm has the choice between two different technologies, one which is efficient in production but pollutive, and another one which is less efficient but environmentally friendly. With this two stage-model we focus on the numerical investigation of the conditions determining when and how often it is optimal for the firm to switch between these different technologies. We show that for certain parameters even several switches can be optimal and that the height of the switching costs crucially influences the long-run outcome. In the course of these investigations, we discuss two different economic mechanisms related to the harm due to pollution which lead to the occurrence of multiple equilibria, history-dependence and so-called Skiba points.
Article
This pollution accumulation model shows that the environmental absorption capacity is impacted by economic activity. The resulting optimal control problem has two inter-related state variables: the stock of pollution and the absorption capacity of the environment. The stock of pollution decreases with environmental absorption capacity and increases with the rate of current emissions, which is controlled by a production level as well as an emissions reduction effort. However, the environmental absorption capacity is positively affected by an absorption development effort, and negatively impacted by the stock of pollution. Under specific conditions, it is shown that an optimal path, which can be either monotonic or following transient oscillations, leads to a (nontrivial) saddle-point characterized by a positive environmental absorption capacity.
Article
THIS REVIEW EXPLORES BOTH ECOLOGICAL THEORY AND THE BEHAVIOR OF NATURAL SYSTEMS TO SEE IF DIFFERENT PERSPECTIVES OF THEIR BEHAVIOR CAN YIELD DIFFERENT INSIGHTS THAT ARE USEFUL FOR BOTH THEORY AND PRACTICE. THE RESILIENCE AND STABILITY VIEWPOINTS OF THE BEHAVIOR OF ECOLOGICAL SYSTEMS CAN YIELD VERY DIFFERENT APPROACHES TO THE MANAGEMENT OF RESOURCES. THE STABILITY VIEW EMPHASIZES THE EQUILIBRIUM, THE MAINTENANCE OF A PREDICTABLE WORLD, AND THE HARVESTING OF NATURE'S EXCESS PRODUCTION WITH AS LITTLE FLUCTUATION AS POSSIBLE. THE RESILIENCE VIEW EMPHASIZES DOMAINS OF ATTRACTION AND THE NEED FOR PERSISTENCE. BUT EXTINCTION IS NOT PURELY A RANDOM EVENT: IT RESULTS FROM THE INTERACTION OF RANDOM EVENTS WITH THOSE DETERMINISTIC FORCES THAT DEFINE THE SHAPE, SIZE AND CHARACTERISTICS OF THE DOMAIN OF ATTRACTION. THE VERY APPROACH, THEREFORE, THAT ASSURES A STABLE MAXIMUM SUSTAINED YIELD OF A RENEWABLE RESOURCE, MIGHT SO CHANGE THESE CONDITIONS THAT THE RESILIENCE IS LOST OR IS REDUCED SO THAT A CHANCE AND RARE EVENT THAT PREVIOUSLY COULD BE ABSORBED CAN TRIGGER A SUDDEN DRAMATIC CHANGE AND LOSS OF STRUCTURAL INTEGRITY OF THE SYSTEM. A MANAGEMENT APPROACH BASED ON RESILIENCE, ON THE OTHER HAND, WOULD EMPHASIZE THE NEED TO KEEP OPTIONS OPEN, THE NEED TO VIEW EVENTS IN A REGIONAL RATHER THAN A LOCAL CONTEXT, AND THE NEED TO EMPHASIZE HETEROGENEITY. THE RESILIENCE FRAMEWORK DOES NOT REQUIRE A PRECISE CAPACITY TO PREDICT THE FUTURE BUT ONLY A QUALITATIVE CAPACITY TO DEVISE SYSTEMS THAT CAN ABSORB AND ACCOMMODATE FUTURE EVENTS IN WHATEVER UNEXPECTED FORM THEY MAY TAKE.
Article
The possible responses of ecosystem processes to rising atmospheric CO2 concentration and climate change are illustrated using six dynamic global vegetation models that explicitly represent the interactions of ecosystem carbon and water exchanges with vegetation dynamics. The models are driven by the IPCC IS92a scenario of rising CO2 (Wigley et al. 1991), and by climate changes resulting from effective CO2 concentrations corresponding to IS92a, simulated by the coupled ocean atmosphere model HadCM2-SUL. Simulations with changing CO2 alone show a widely distributed terrestrial carbon sink of 1.4–3.8 Pg C y−1 during the 1990s, rising to 3.7–8.6 Pg C y−1 a century later. Simulations including climate change show a reduced sink both today (0.6–3.0 Pg C y−1) and a century later (0.3–6.6 Pg C y−1) as a result of the impacts of climate change on NEP of tropical and southern hemisphere ecosystems. In all models, the rate of increase of NEP begins to level off around 2030 as a consequence of the ‘diminishing return’ of physiological CO2 effects at high CO2 concentrations. Four out of the six models show a further, climate-induced decline in NEP resulting from increased heterotrophic respiration and declining tropical NPP after 2050. Changes in vegetation structure influence the magnitude and spatial pattern of the carbon sink and, in combination with changing climate, also freshwater availability (runoff). It is shown that these changes, once set in motion, would continue to evolve for at least a century even if atmospheric CO2 concentration and climate could be instantaneously stabilized. The results should be considered illustrative in the sense that the choice of CO2 concentration scenario was arbitrary and only one climate model scenario was used. However, the results serve to indicate a range of possible biospheric responses to CO2 and climate change. They reveal major uncertainties about the response of NEP to climate change resulting, primarily, from differences in the way that modelled global NPP responds to a changing climate. The simulations illustrate, however, that the magnitude of possible biospheric influences on the carbon balance requires that this factor is taken into account for future scenarios of atmospheric CO2 and climate change.
Article
We consider an optimal consumption and pollution problem that has two important features. Environmental damages due to economic activities may be irreversible and the level at which the degradation becomes irreversible is unknown. Particular attention is paid to the situation where agents are relatively impatient and/or do not care a lot about the environment and/or Nature regenerates at low rate. We show that the optimal policy of the uncertain problem drives the economy in the long run toward a steady state while, when ignoring irreversibility, the economy follows a balanced growth path accompanied by a perpetual decrease in environmental quality and consumption, both asymptotically converging toward zero. Therefore, accounting for the risk of irreversibility induces more conservative decisions regarding consumption and polluting emissions. In general, however, we cannot rule out situations where the economy will optimally follow an irreversible path and consequently, will also be left, in the long run, with an irreversibly degraded environment.
Article
This paper extends the classical exhaustible-resource/stock-pollution model with the irreversibility of pollution decay. Within this framework, we answer the question how the potential irreversibility of pollution affects the extraction path. We investigate the conditions under which the economy will optimally adopt a reversible policy, and when it is optimal to enter the irreversible region. In the case of irreversibility it may be optimal to leave a positive amount of resource in the ground forever. As far the optimal extraction/emission policy is concerned, several types of solutions may arise, including solutions where the economy stays at the threshold for a while. Given that different programs may satisfy the first order conditions for optimality, we further investigate when each of these is optimal. The analysis is illustrated by means of a numerical example. To sum up, for any pollution level, we can identify a critical resource stock such that there exist multiple optima i.e. a reversible and an irreversible policy that yield exactly the same present value. For any resource stock below this critical value, the optimal policy is reversible whereas with large enough resource, irreversible policies outperform reversible programs. Finally, the comparison between irreversible policies reveals that it is never optimal for the economy to stay at the threshold for a while before entering the irreversible region.
Article
This paper considers optimal pollution accumulation when the decay function has an inverted-U shape. Such decay functions have empirical relevance but they lead to nonconvexities in dynamic optimization. The nonconvexity problem is handled here by applying a two-stage optimization procedure. The analysis shows that two qualitatively different optimality candidates may exist simultaneously. We identify cases where the choice can be made on a priori grounds and cases where it requires computation of the present values of both optimality candidates. An optimal emission trajectory leading to irreversible pollution is typically nonmonotonic.
Article
Underlying some of the most pressing environmental problems are the interlinked resource and environmental stock externalities with threshold effects. Using a simple dynamic model, it is shown how in the face of such externalities the static market-based policy instruments such as Pigouvian taxes should be modified. It is shown that even if for an initial period there is going to be no pollution stock damage, the optimal policy still requires that abatement begins immediately and at increasing rates. Simulation of the model for the case of fossil fuel burning and the consequent global warming shows that the optimal carbon tax, and therefore the optimal control strategy, is particularly sensitive to changes in the marginal abatement cost and the level of fossil fuel demand. Policy simulations contrast the optimal control policy with, and estimate the welfare losses from, alternative policies deriving from arbitrary tax paths. The latter include: (i) a no-tax policy, (ii) a constant carbon tax rate, (iii) the European Community's proposed carbon tax path, and (iv) a delayed optimal tax path.
Article
Terrestrial net primary production (NPP) quantifies the amount of atmospheric carbon fixed by plants and accumulated as biomass. Previous studies have shown that climate constraints were relaxing with increasing temperature and solar radiation, allowing an upward trend in NPP from 1982 through 1999. The past decade (2000 to 2009) has been the warmest since instrumental measurements began, which could imply continued increases in NPP; however, our estimates suggest a reduction in the global NPP of 0.55 petagrams of carbon. Large-scale droughts have reduced regional NPP, and a drying trend in the Southern Hemisphere has decreased NPP in that area, counteracting the increased NPP over the Northern Hemisphere. A continued decline in NPP would not only weaken the terrestrial carbon sink, but it would also intensify future competition between food demand and proposed biofuel production.
Article
The purpose of this paper is to derive conditions for the optimality of a limit cycle in a dynamic economic system and to interpret them economically. A fairly general two-state continuous-time nonlinear optimal control problem is considered. It turns out that for this class of models three different economic mechanisms can be identified as the possible source of limit cycles. One relates to an intertemporal substitution effect expressed in terms of complementarity over time, the second one is a dominating cross effect between the state variables of the system (i.e., the capital stocks in our model), and the third one is positive growth at the equilibrium.
Article
Forests currently absorb billions of tons of CO2 globally every year, an economic subsidy worth hundreds of billions of dollars if an equivalent sink had to be created in other ways. Concerns about the permanency of forest carbon stocks, difficulties in quantifying stock changes, and the threat of environmental and socioeconomic impacts of large-scale reforestation programs have limited the uptake of forestry activities in climate policies. With political will and the involvement of tropical regions, forests can contribute to climate change protection through carbon sequestration as well as offering economic, environmental, and sociocultural benefits. A key opportunity in tropical regions is the reduction of carbon emissions from deforestation and degradation.
Article
Endogenous growth is generally built on a positive externality hypothesis which is the opposite of a negative externality caused by pollution. We study a linear technology with simple assumption: an aggregate capital stock which represents a learning by doing effect and a pollution flow proportional to production. In this framework, we analyse the precise effects on growth of the disutility of pollution and its interaction with the utility of consumption in an economy without abatement technology. The decentralized equilibrium always leads to unlimited growth, but optimal growth is often limited (the negative effect of pollution dominating the positive effect of learning by doing). In this case, the optimal policy which leads the decentralized economy to follow the optimal growth path is to tax capital; in contrast with the optimal subsidy policy in an economy without pollution. When an abatement technology is introduced, the optimal solution can lead the economy to unlimited growth, whatever the form of the utility function. Copyright Kluwer Academic Publishers 1995
Article
We develop an overlapping generations model where consumption is the source of polluting emissions. Pollution stock accumulates with emissions but is partially assimilated by nature at each period. The assimilation capacity of nature is limited and vanishes beyond a critical level of pollution. We first show that multiple equilibria exist. More importantly, some exhibit irreversible pollution levels although an abatement activity is operative. Thus, the simple engagement of maintenance does not necessarily suffice to protect an economy against convergence toward a steady state having the properties of an ecological and economic poverty trap. In contrast with earlier related studies, the emergence of the environmental Kuznets curve is no longer the rule. Instead, we detect a sort of degenerated Environmental Kuznets Curve that corresponds to the equilibrium trajectory leading to the irreversible solution.
Local stability in optimal control problems with two state variables
  • E Dockner
New efforts to quantify ‘social cost’ of pollution
  • M L Wald
Acceleration of global warming due to carbon-cycle feedbacks in a coupled climate model
  • P M Cox
  • R A Betts
  • C Jones
  • S A Spall
  • I Totterdell
  • PM Cox