UBC Theses and Dissertations
Essays on the qualitative theory of forest economics Heaps, Terry
This thesis is concerned with questions relating to the optimal regulation of logging in a solely owned forest. Optimal is taken to mean maximizing the present value of net revenues obtainable from growing and harvesting an infinite sequence of crops on a piece of forest land. Discussions of optimal harvesting usually assume there is no advantage to changing the age distribution of a forest. This is also the assumption of Chapter I. In this case, trees are cut when their age reaches the rotation period which is determined from what is called the Faustmann formula. Chapter I looks at the comparative statics of these rotation periods. The effect of a change in an exogenous parameter on the rotation period is shown to depend on how certain elasticities are changed. It is then shown that there are conditions under which these results extend to a more complex forestry model where the manager chooses the level of effort to be expended on regeneration and silvicultural activities. The techniques used are drawn from optimal control theory. Chapter II introduces considerations which may make it advantageous to alter the age structure of a forest while logging it. In particular, a variable average cost of harvesting function is allowed for. A forestry maximum principle is derived which determines the dynamics of optimal harvesting. This is similar to the maximum principle for processes incorporating a delay (the time between planting and harvesting). The usual growth theory questions are then asked. In the variable average cost case, the "steady state" age distributions turn out to be "normal" forests with the time between harvests being determined by a Faustmann formula Global asymptotic stability is not proven but is shown to be likely. Finally, Chapter III applies the forestry maximum principle to a problem of determining an optimal harvesting policy for a group of forests subject to a sustained yield constraint. Assuming stability and with a few additional restrictions, it is shown that the optimal long run policy is to convert each separate forest to a "normal" forest. The Faustmann formula determines the number of age classes in each forest.
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