Chapters summaries

Chapter 1: General introduction The general introduction presents the objectives of the book. Instead of trying to address all the aspects of sustainability, the book focuses on two of them: the trade-off between environmental and economic issues, as well as intergenerational equity. While the usual literature examines what should be preserved for sustainability, the question addressed here is “what can we preserve for future generations?” The mathematical formalism used in the book is presented, along with the two benchmark models used to illustrate the general concepts studied: the cake-eating economy and the production-consumption economy with a nonrenewable resource. These models of nonrenewable resource use are interpreted in terms of sustainability, in view of the climate change issue. The outline of the books is given. Part I presents a selection of key results of the literature. Part II gathers personal works on sustainability and invariance.

Part I: The sustainability issue in the economic literature

Chapter 2: The sustainability issue and sustainability concepts This chapter presents the sustainability issue and the two main approaches that have been proposed to deal with the raising concerns for environmental degradations and intergenerational equity. The weak sustainability paradigm aims at defining an aggregate measure of the productive capacity of the economy, giving a value to all productive capital stocks (including natural assets). It is based on “prices”. The strong sustainability paradigm aims at preserving specific critical natural resources. It is based on “quantities”. Even if the nature of what should be conserved for future generations is different in the two approaches, they define a “capital” to be bequeathed to future generations.

Chapter 3: The economics of intertemporal decisions The capital that is bequeathed to future generations depends on present choices of consumption, investment, and natural asset depreciation. This chapter presents the drivers of intertemporal choice in economics, and how the preference for the present, the aversion to intertemporal inequalities, as well as the productivity of investment influence the pattern of consumption and investment, and thus the growth of the economy. The traditional criterion used to define optimal growth is discounted utility. This criterion, however, does not treat all generations with anonymity, and favors short term and present generation. It may result in non sustainable development paths. Economists have thus searched for alternative sustainability criteria.

Chapter 4: The emergence of sustainability criteria Defining a criterion which is inter-generationally equitable is a difficult task. This chapter presents some of the candidates discussed in the literature: Discounted utility, undiscounted utility, the maximin, the green golden rule, Chichilnisky’s criterion, and the mixed Bentham-Rawls criterion. Each criterion has its pros and cons. Each defines a particular “optimal” consumption and investment path, and thus what is conserved for future generations. If the willingness to save, broadly speaking, is high enough, the path can exhibit a non-declining utility. Otherwise, present consumption is favored over development or sustainability. The rule of “nil net investment," requiring compensating for natural assets depreciation by investment in reproducible capital, plays a crucial role in this respect.

Chapter 5: Some comments on key results… and misleading interpretations The concept of genuine savings is based on the idea that if aggregate investment (including resource depreciation) preserves the economy’s productive capacity, a constant level of consumption is sustainable. This provides the main indicator of weak sustainability. This chapter examines to which extent a non negative net investment makes it possible to sustain current utility. It is emphasized that positive genuine savings can indicate sustainable utility only if prices are intertemporally efficient forever (in particular, the markets must be perfectly forward looking) and if the accounting prices reflect sustainable preferences. If this is not the case, non-negative net investment accounted at wrong prices may induce a diminution of the productive capacity of the economy and non-sustainability.

Chapter 6: What can we preserve for future generations? This chapter summarizes the results presented in the first part of the book. It emphasizes the fact that the choice of a sustainability criterion defines an optimal development path, with implications on the trade-off between consumption and environmental preservation, as well as on intergenerational equity. Whatever the criterion applied, it defines what should be conserved for future generations. The second part of the book adopts a quite different approach, and tries to define what could be preserved for future generations. If something is preserved over time, this means that there are invariant quantities conserved along development paths. Invariance theories make it possible to exhibit such quantities bequeathed to future generations.

Part II: Invariance Theories and Sustainable Development

Chapter 7: Invariance in growth theory Sustainability requires preserving something for future generations. There is, however, no reason to define what has to be preserved a priori. A criterion proposed to cope with the sustainability issue can be discussed with respect to all the quantities that are conserved along the optimal trajectory it defines. In this chapter, the economic conservation laws of optimal growth paths are exhibited using invariance theory tools. It is shown that some quantities are conserved along optimal growth paths only under quite restrictive conditions on the time preferences and technological progress of the economy. In any case, what is conserved is related to the net production of the economy, and does not necessarily entail intergenerational equity. Requiring that some quantities are strictly invariant over time is thus too restrictive to define sustainability.

Chapter 8: Weak Invariance: the viability approach In practice, policy makers use sustainability indicators to measure the performance of the economy with respect to the various sustainability issues, and compare these indicators to thresholds indicating the sustainability of the economy. Departing from the optimality approach of sustainability criteria, this chapter examines how to satisfy sustainability constraints over time. The viability approach is used to determine the economic conditions under which an economic dynamics is consistent with sustainability constraints to be satisfied over time. In this feasibility approach, there is no trade-off between the sustainability objectives as they all have to be achieved. All generations are treated with anonymity as the constraints have to be satisfied at all times.

Chapter 9: What we can preserve for future generations How should we go about defining the sustainability thresholds characterizing the sustainability constraints? Such a choice must account for the difficulty to achieve all the objectives at all times. Inverse viability makes it possible to describe the necessary trade-offs between conflicting issues. Choosing a feasible set of objectives implies underlying preferences among conflicting aspects of sustainability. The approach described in this chapter amounts to define minimal rights to be guaranteed to all generations. As this choice can be formalized as an optimization problem, it is related to a concept of value and to prices reflecting the difficulty of satisfying all the sustainability constraints at all times. Ultimately, the approaches to sustainability based on “prices" and “quantities" are linked.

Chapter 10: General Conclusion Different approaches to sustainability, or different criteria, lead to different results. The choice of a framework strongly influences what is conserved for future generations. In this investigation, I have described what is conserved according to various approaches, discussing their advantages and drawbacks. In an attempt to depart from the traditional normative approaches to sustainability, I have chosen to rely on invariance theories to describe what can be preserved for future generations. More specifically, the approaches developed describe the necessary trade-offs that must be arbitrated when addressing the issues of sustainability. This analysis may help decision-making meet the two main challenges of sustainability: accounting for conflicting issues and intergenerational equity.