The Optimal Extraction Path of Exhaustible Resource with Environment Cost

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Assuming in the perfectly competitive market, using the optimal control theory and making the social welfare as the maximization target, the paper studies on environment cost which impacts the optimal extraction path of exhaustible resource. The special case result shows that: the time of optimal exhaustion increases with the addition of marginal environmental cost, the price has negative linear correlation with the marginal environmental cost, and the optimal extraction has positive linear correlation with the marginal environmental cost.