The Optimal Depletion of Exhaustible Resource under Different Commitment

There are few papers in the literature focusing on the issue of the optimal depletion of exhaustible resources in the framework of variable time preference. This paper attempts to analyze the pure consumption of exhaustible resource under hyperbolic time preference, and to discuss the optimal depletion rate and the effect of the protection of the exhaustible resource under different commitment abilities. The results of model show that the case of the hyperbolic discount with the full commitment of the government is equivalent to the case of constant discount of the social planner problem. In that case, the optimal depletion rate and the initial consumption of exhaustible resource are the slowest. On the contrary, they are the highest and the myopic behaviors lead to excessive consumption of exhaustible resources inevitably without commitment. Otherwise, in the case of partial commitment, the results are between the cases of full commitment and of no commitment. Therefore, with the hyperbolic time preference, the optimal depletion rate of resource depends on the commitment ability. Higher commitment ability leads to lower effective rate of time preference, and consequently, lower depletion rate and lower initial depletion value. The improvement of commitment ability can decrease the impatience and myopia behaviors, and contribute to the protection of the exhaustible resources.