Both a naive logistic model and a sophisticated age class model are used to investigate competitive equilibria for a renewable natural resource, A rational expectations model is presented and tested for Douglas Fir stumpage supply. Forest Service policy is discussed" It is concluded that explicit valuation of standing timber stock.for other than lumber purposes leads to a coherent forest policy consistent with the Multiple-Use Sustained Yield Act of 1960. Public ownership and government regulation are prevalent in the renewable natural resource field, Fish, lobsters and other valuable marine life are protected by a maze of catch limitations. Public ownership of timber lands is not uncommon in many countries. In the U.S. about one-third of all timber land is publicly owned, Government ownership and regulation makes the government responsible for deciding how much of these resources are used in the present and how much will be available in the future. Resources have two sources of value: the end products they produce are consumer (fish cakes, wood frame houses, lobster dinners) and the stock of the resource provides externalities by its very existence (forests provide recreation, fish provide food for other fish, etc.). The price consumers are willing to pay for a resource is an adequate measure of the resource's private value. The public value is admittedly much harder to measure. (What would the last Dodo bird or carrier pigeon have been worth?) The United States Forest Service appears to make its harvest decisions without placing any weight on prices. Below it is shown that a policy very like the one the Forest Service actually follows can be arrived at by maximizing the present discounted value of the timber stock for public (recreation of wildlife) purposes. Further, the analysis of present discounted value gives a proper criterion for judging forest improvement projects while the present analytical framework (Maximum Sustainable Yield) does not. The difficulty with present discounted value is that the future prices are unknown. Much of this thesis is devoted to building a rational expectations model to predict future prices. An outline of the sections of this paper follow. Section 1: Discusses the difference in growth functions between fish and trees. Develops the formula for an optimal policy for a present discounted value maximizing producer facing constant prices. Section 2: Uses a simple logistic model to discuss a renewable resource in a simple competitive world. The inclusion of a demand curve in the model causes there to be a smooth flow of the resource. If the initial stock of the resource is large compared to the eventual steady state stock, then the stock is slowly reduced to the steady state stock and, at the same time, prices are rising. The model is extended to include a nonrenewable resource; it is seen that the inclusion of the nonrenewable resource, in the case cited, can cause the extinction of the renewable one.
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