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Article Excerpt
Abstract Global warming (GW) is now recognized as a significant threat to sustainable development on an international scale. After providing some introductory background material, we introduce a benchmark dynamic game within which to study the GW problem. The model allows for population growth and is subsequently generalized to allow for changes in technology. In each case, a benchmark "Business as Usual" (BAU) equilibrium is analyzed and contrasted with the efficient solution. Furthermore, a complete characterization is provided in the benchmark model of the entire subgame perfect equilibrium value correspondence.
Keywords Global warming * Population growth * Dynamic game * Subgame perfect equilibrium
JEL Classification Q54 * D99 * O12
1 Introduction
Here are four facts related to global warming (GW):
1. Average global surface temperatures have risen by 0.6[degrees]C in the last 140 years.
2. Every one of the 10 warmest years in recorded history have occurred since 1990, including each year since 1997.
3. The intergovernmental panel on climate change (IPCC) predicts that if we go on as we are, by 2100 global sea levels will probably have risen by 9-88 cm and average temperatures by between 1.5 and 5.5[degrees]C.
The most frequently cited cause for this warming is the greenhouse effect--the increase in greenhouse gases (GHGs), especially C[O.sub.2], generated through the burning of fossil fuels. (1) Note,
4. Before the Industrial Revolution, atmospheric C[O.sub.2] concentrations were about 270-280 parts per million (ppm). They now stand at almost 380 ppm, and have been rising at about 1.5 ppm annually. (2)
The dramatic rise of the world's population in the last three centuries, coupled with an even more dramatic acceleration of economic development in some parts of the world, has led to a transformation of the natural environment by humans that is unprecedented in its scale. In particular, on account of the greenhouse effect, the threat of GW has emerged as a serious world-wide problem.
The present paper is part of an ongoing research project in which we have addressed certain elements of the GW problem from a strategic and economic perspective. In particular, our focus is on the economic costs of warming and the countervailing benefits foregone in containing the greenhouse effect. Our research is also the first to take a fully strategic approach to the problem. The strategic approach is necessary in our view because the problem is a transnational one and, in the absence of a global government, the only implementable treaties are likely to be agreements that are incentive-compatible for the signatories. (For other studies in the current project, see Dutta and Radner (2004a,b,c). For other studies that take a strategic, though static, view of global warming, see Barrett (2003) and Finus (2001).)
The present paper has three main parts:
1. Background material on the GW problem and a general discussion of the theoretical issues that need to be faced in the analysis of the control of GW. (Section 2). In turn that leads us to formulate a bench-mark model (Section 3); this model allows population growth and in doing that generalizes a model analyzed in detail elsewhere (Dutta and Radner 2004a).
2. In the benchmark model we establish a series of results on the tragedy of the common and the population effects on emissions. We also provide a complete characterization of the entire set of subgame perfect equilibria (SPE) of the model (Section 3).
3. We then study the implications of the arrival of new technology for the reduction of emissions (Section 4).
2 Background and theoretical issues
2.1 Global warming: a background
Carbon dioxide (C[O.sub.2]) is by far the most important of the "GHGs". It is produced by the metabolism of living organisms, and by other activities of humans. Currently, the burning of fossil fuels accounts for most of the carbon emissions actually produced by humans. On the other hand, C[O.sub.2] is broken down by photosynthesis in plants. However, the destruction of forests and other changes in land use have reduced the rate of global photosynthesis. Also, as the concentration of C[O.sub.2] in the atmosphere increases, the oceans recapture some of it, but very slowly. The net result of these activities is a net emission rate of C[O.sub.2]. Fossil-fuel use currently accounts for more than two-thirds of the (net) emissions, with changes in forest and land use accounting for most of the rest.
Almost all of the burning of fossil fuels is done for the purpose of producing energy. North America currently produces about 27% of such emissions, with the bulk of this coming from the US. The current share of Asia (not including Japan) is double its cumulative share since 1800, reflecting its recent spurt in economic development; Asia currently ranks second amongst the various regions. Furthermore, given the large population of Asia, and its rate of population growth, if per capita carbon emissions in Asia were to increase to North American and Western European levels, the total emissions from Asia would increase enormously.
Over time technology changes and typically this leads to a progressive "decarbonization" of energy production. For example this has coincided with the movement from coal to oil and natural gas. Another technological change--and source of decarbonization--is increased efficiency in the utilization of energy.
The costs and benefits of GW are subject to considerable uncertainty and debate. Roughly speaking, the costs and benefits of GW are themselves the results of two primary effects: (1) a rise in the sea level, and (2) climate changes. The rise in the sea level is caused by melting of glacial ice, especially at the poles, and to some extent by the thermal expansion of the sea water. The rise in the sea level would damage, and even eliminate, many coastlines, and would be particularly costly to low-lying areas, such as Bangladesh, The Netherlands, and the eastern seaboard of the US. (for example). Climate changes are more complex. In some parts of the world, like the northern latitudes of North America, the warming would be accompanied by higher rainfall. This, with the lengthening of the summer growing period, would increase the agricultural productivity of such areas, benefiting Canada, the U.S., and Russia. Other parts of the world, such as Sub-Saharan Africa, would probably become more arid and less productive agriculturally. Other effects would include:
(a) Increased energy requirements for air-conditioning, only partially offset by reduced heating costs.
(b) Lesser runoff in water basins, curtailing water supplies.
(c) Increased urban air pollution (tropospheric ozone).
(d) Increased hurricane and fire damage.
Damages are likely to be nonlinear in the amount of warming. For example, "in the initial range, the Antarctic does not contribute to sea-level rise, because temperature is in a low range where increased melting is more than offset by increased snow carried by air with more moisture. On the scale of 10 degrees warming, however, the Antarctic would likely become a major source of sea-level rise, especially if the West Antarctic ice shelf should disintegrate (Cline 1992, p. 6)."
The efforts to avoid GW will, of course, be costly as well. Immediate costs would be incurred if economies were forced to substitute more expensive but less carbon intensive technologies for producing...
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