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Optimal Rangeland Management of Great Basin in the Presence of a Reversible Threshold
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This research attempts to determine the optimal treatment level and herd size of the rangeland area of Great Basin along the planning period in the presence of cheatgrass expansion and a reversible ecological threshold. A modified optimal control model is developed to deal with the dynamic optimization problem with a threshold, control space constraints and state space constraints together. Phase diagram and steady state analysis are employed to describe the potential optimal paths. It has been shown that the existence of a threshold implies discontinuities in the control variables, the control variables constraints could lead to corner solutions and state space constraints implies that under certain conditions it is potentially optimal that the state variable trajectory reaches the boundary and stays there forever. In addition, it has been shown that different relative values of parameters determine different candidates for optimal path. This study presents four parameters conditions that may result in the candidate paths of interest to policy makers. The potential optimal paths for each of the above four parameter conditions are described qualitatively through phase diagram analysis. It is found that there are multiple candidate paths for optimality in each of these four parameter conditions, and which of these candidates is optimal relies on the relative values of parameters within the scope of each of those four parameter conditions. And numerical simulation and comparative statics need to be implemented to yield the optimal path.