The origins of this volume can be traced back to a conference on "Ethics, Economic and Business" organized by Columbia Busi ness School in March of 1993, and held in the splendid facilities of Columbia's Casa Italiana. Preliminary versions of several of the papers were presented at that meeting. In July 1994 the Fields Institute of Mathematical Sciences sponsored a workshop on "Geometry, Topology and Markets" additional papers and more refined versions of the original papers were presented there. They were published in their present versions in Social Choice and Wel fare, volume 14, number 2, 1997. The common aim of these workshops and this volume is to crystallize research in an area which has emerged rapidly in the last fifteen years, the area of topological approaches to social choice and the theory of games. The area is attracting increasing interest from social choice theorists, game theorists, mathematical econ omists and mathematicians, yet there is no authoritative collection of papers in the area. Nor is there any surveyor book to give a perspective and act as a guide to the issues in and contributions to this new area. One of the two aims of this volume is in some measure to play this role: the other aim is of course to present interesting and surprising new results."

of ecological (also biological) variables b which interact in their dynamic t evolution: det dbt dt = f (et, bt)' dt = 9 (et, bt)* Among the solution paths to this interaction between economic and ecologi cal variables, we look for those which are sustainable. Sustainable paths are typically those along which the values of certain key stocks are always pos itive, these key stocks being important environmental resources. The types of paths on which certain variables can be positive forever include station ary solutions with appropriate positivity conditions, or limit cycles or chaotic attractors satisfying the same positivity conditions. These paths, and the paths which approach them, constitute the set of sustainable paths. From amongst these we have to choose one or more which are in some sense the best. Note that rather than imposing positivity of certain stocks in the long run as a condition for sustainability, we would prefer to derive this as a characteristic of optimal solutions from more fundamental judgements about the valuation of stocks and flows: this is the route pursued by the papers in this volume. The introductory paper by Heal in Section I reviews these matters in gen eral terms, not going into technical details: it discusses the precedents for a concept of sustainability in welfare economics, and reviews alternative opti mality concepts and their connection to sustainability.

In the decades since Geoffrey Heal began his field-defining work in environmental economics, one central question has animated his research: "Can we save our environment and grow our economy?" This issue has become only more urgent in recent years with the threat of climate change, the accelerating loss of ecosystems, and the rapid industrialization of the developing world. Reflecting on a lifetime of experience not only as a leading voice in the field, but as a green entrepreneur, activist, and advisor to governments and global organizations, Heal clearly and passionately demonstrates that the only way to achieve long-term economic growth is to protect our environment. Writing both to those conversant in economics and to those encountering these ideas for the first time, Heal begins with familiar concepts, like the tragedy of the commons and unregulated pollution, to demonstrate the underlying tensions that have compromised our planet, damaging and in many cases devastating our natural world. Such destruction has dire consequences not only for us and the environment but also for businesses, which often vastly underestimate their reliance on unpriced natural benefits like pollination, the water cycle, marine and forest ecosystems, and more. After painting a stark and unsettling picture of our current quandary, Heal outlines simple solutions that have already proven effective in conserving nature and boosting economic growth. In order to ensure a prosperous future for humanity, we must understand how environment and economy interact and how they can work in harmony-lest we permanently harm both.

With issues like global warming and the loss of biodiversity becoming increasingly important to policymakers and scientists worldwide, the issue of sustainability cannot be ignored as we move toward the twenty-first century.

Not surprisingly, the sustainable management of the biosphere has in recent years been the subject of much attention among ecologists, environmental engineers, and other members of the scientific community. Yet although these issues are clearly rooted in economic behavior and organization, the question of sustainability is not one that has been addressed directly by economists. Now, with "Valuing the Future, " economist Geoffrey Heal presents a coherent framework for understanding the earth's future from an economic perspective.

Heal's model begins with a reconciliation of the economist's and environmentalist's time horizon: in economics, discussions of "the long run" generally refer to a much shorter timeline than do those of the earth sciences. The book shows the benefits of viewing the environment as an economic asset that should be understood as a part of a nation's income and explains how this approach can lead to more conservative patterns of resource use.

Stepping beyond merely theoretical generalities, "Valuing the Future" offers a dynamic new blueprint for comprehending sustainability. Chapters provide complete mathematical templates for the valuation of a depletable stock and of renewable resources, the proper calculation of national income, and the conduct of cost-benefit analysis. It will be of great value to economic theorists, environmental economists and policymakers, providing a powerful new model for scientists concerned with environmental sustainability.

Markets are increasingly central to the resolution of environmental problems. They played a critical role in implementing the 1990 Clean Air Act of the United States, which has been instrumental in reducing acid rain in a cost-effective manner. They are also central to the global strategy adopted for limiting the emissions of greenhouse gases under the 1997 Kyoto Protocol and are being used for resolving conflicts over the use of other environmental resources, particularly water.

"Environmental Markets: Equity and Efficiency" represents the first systematic and in-depth study of the economic issues raised by this growing use of environmental markets. Focusing on the relationship between equity and efficiency -- which is central to many of the debates between industrial and developing countries -- the book explores the underlying economics and the possibilities for win-win solutions that benefit all parties to the problems.

Graciela Chichilnisky and Geoffrey Heal have been instrumental in developing the economic understanding required for the operation of environmental markets and for promoting their use among policy makers leading to the Kyoto Protocol. Contributors to this volume include established experts from international organizations, nongovernmental organizations, and academia, including Ra?l Estrada-Oyuela, who chaired the negotiating committee of the Framework Convention on Climate Change and the 1997 Kyoto meetings.