Forests emit and absorb carbon. Although the portion of anthropic climate change that can be attributed to forestry activities and land use is small relative to the contribution of fossil fuels consumption, it is by no mean negligible. The role that the forest may play as a sink or a source of greenhouse gases (GHG) has been recognized in the process leading to the Kyoto agreement and the necessity to encourage improvements in that respect has also been stressed. In countries such as Canada, for example, forests have been a net sink to the tune of about 70 Million t per year for the best part of the century, but various factors made it a net source in the late 1980's. Rough calculations based on Winjum (1998) indicate that changes that would reduce by one third the sources associated with wood harvest only (twigs, branches, tops, and stumps left to be burned or to decompose) could contribute almost a fifth of Canada's Kyoto commitment. Many other factors have been identified as potentially significant contributors to a forest's GHG emission balance. Human factors are crucial in that respect. They can be decomposed into three major components that need to be investigated from a theoretical point of view before their impact can be appraised, and before behaviors can be targeted from a policy point of view. The first factor is forest management; the second factor is the mix and use of forest products; the third element is forest area. Our paper is part of a research program which addresses all three factors. It deals with the first factor: forest management. Although externalities have been added to old and new formulations of the tree cutting problem, the GHG externality turns out to be special. It results in a positive flow during growth; it becomes insignificant when net growth is over; harvest releases part of the carbon locked into wood back into the atmosphere but also allows the beginning of a new carbon locking rotation; meanwhile the carbon contained in harvested wood products is released into the atmosphere at rates that are highly dependent on the type of product (fire wood, paper, construction wood, etc.). Our paper provides a theoretical analysis of the socially optimal harvesting decision when society attributes value to carbon being locked into wood and when wood prices evolve randomly as in Reed and Clarke (1990). We provide results and comparative statics results on optimum cutting age and carbon emissions under socially optimal, versus private, management. In the process we also provide the forest value function relevant to the decision whether to devote land to forestry or to alternative uses. This is the central element necessary to address the third component of our research program: the determination of forest area and its impact on GHG emissions.
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