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ABSTRACT This article uses the forest management problem under uncertainty to derive the optimal reservation price when a standing timber is to be auctioned. Introduction In forestry, the selling of standing timber is conducted either through direct negotiation between the forest owner and the exploiting firm or by auctions.
Over the past decade, theoretical and empirical works have focused intensively on these two auction formats by analysing the binding behaviour and the minimum price that must be bid optimally the optimal reservation price under various assumptions.
This result is not suitable in forestry, where the valuation of a bidder depends on the optimal harvest time of trees namely, the optimal rotation which is the central problem in the management of forest resources.
This article combines both the auctions and the forest management problem to derive theoretically the optimal reservation price in forestry when the forest owner sells its timber through auctions under uncertainty regarding the stumpage price of timber1.
Thus, the fixation of a reservation price must take into account the harvesting decision. In the forest management problem under uncertainty,  -  showed numerically that, when the stumpage price of timber is uncertain but stationary, the optimal rotation follows a reservation price policy in which the tree is harvested when the current market price of timber is above the historical average or a determined reservation price.
Others studies, such as  -  considered the case of non-stationary price process geometric Brownian motion.
They showed that a reservation price is relevant only if there are fixed costs. All of these studies have implicitly assumed that the forest owner harvests the forest himself by focusing their attention only on the optimal cutting age.
In that setting, the reservation price specifies when the forest stand shall be cut or postponed. This article, in addition to the harvesting problem, considers the case where the timber stand is to be auctioned as described above. The participant in the auction must submit a bid higher than the specifying reservation price.
The reservation price is set to maximize the expected profit of the forest owner from planting to harvesting. The stumpage prices are assumed to follow a stationary autoregressive process. A stationary autoregressive process has the feature that it is attracted by the long-run mean price mean-reverting.
Therefore, a current market price above the long-run mean price gives higher incentive to the forest owner to harvest the trees earlier.
This article contributes theoretically to the literature of forest auctions by extending the results of Laffont and Maskin as well as Riley and Samuelson in the context of forestry management.
The article is organized as follows. In Section 2, I first present the theoretical model that combines auctions and the forest management problem under uncertainty when stumpage prices follow an autoregressive process. Section 3 then determines the optimal bidding strategies, the optimal cutting age and the optimal reservation price.
Finally, Section 4 concludes the article. Optimal Mechanism In this section, I use the forest management framework under uncertainty to derive the theoretical optimal mechanism when a standing timber is sold through auctions.
The optimal mechanism consists of the optimal bidding strategy, the optimal cutting age optimal rotationand the optimal reservation price. I assume that the forest owner cannot harvest the forest himself, as the forest land is publicly owned.
The first price sealed-bid auctions and the ascending auctions are used to model the problem because both auction formats are used by USFS for the sale of standing timber.
In the US, the forest owner sells only the rights to cut the standing timber, not the forest land itself. In addition, the identity of the winning firm can be different at each harvesting time.
Therefore, the best way to address the forest management problem in this situation is the use of the single rotation. This will be assumed in this article.
The Model Consider a stand of trees with one species. The trees can be the same age or different ages. Let t be the current period, and the planting time of a tree.
The age of the tree at time t is then. The timber growth function denoted by is assumed to be deterministic and depends only on the age of the tree. It is also assumed that satisfies the following assumptions:Online Consumer Herding Behaviors in the Hotel Industry Jun Mo Kwon Department of Nutrition, Hospitality, and Retailing Many online room reservation companies provide Theoretical Framework Positive intention .
Framework, by Barry R. Chiswick 5. Human Capital, 2nd Edition, by Gary S. Becker The object of the National Bureau of Economic Research is to ascertain and to present to such memorandum of dissent or reservation shall be published with the manuscript if he so desires.
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