Optimal Depletion Of Exhaustible Resource Research Articles

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 hy- perbolic 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 govemment 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 commit- ment, 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.

The optimal depletion of exhaustible resources: A complete characterization

Abstract We provide the closed form solution to the Dasgupta–Heal–Solow–Stiglitz (DHSS) model. The DHSS model is based on the seminal articles Dasgupta and Heal (1974); Solow (1974) and Stiglitz (1974) and describes an economy with two assets, man-made capital and a nonrenewable resource stock. We explicitly characterize, for such an economy, the dynamics along the optimal trajectory of all the variables in the model and from all possible initial values of the stocks. We use the analytical solution to prove several properties of the optimal consumption path. In particular, we show that the initial consumption under a utilitarian criterion starts below the maximin rate of consumption if and only the resource is abundant enough and that under a utilitarian criterion, it is not necessarily the present generation that benefits most from a windfall of resources.

Effects of resource assessments on optimal depletion estimates

Optimal depletion of exhaustible resources has become part of resource economics textbooks. In this paper the author explores the possible policy relevance of some simple abstract models. It is shown that optimal depletion of an exhaustible resource of constant cost and a hyperbolic demand curve is compatible with Marchetti's logistic substitution model. Optimal depletion trajectories for an exhaustible resource which has a linear demand curve, for which cost increases linearly with cumulated use, are described by the analogue of a damped oscillator. Combining this model with resource supply curves as derived from the crustal abundance geostatistical model provides a tool to relate the resource economic notions of maximizing social welfare, price elasticity of demand and resource base estimates for a given set of planning parameters.

A Note on "The Optimal Depletion of Exhaustible Resources"

Consequently, the possibility of an inflection point in the optimal resource utilization time profile (Figure 4, page 18) arises only if q 1), or even if it is unbounded but q7 > a, Rt > 0 for all t '0 and the Rt profile cannot display an inflection point; under these assumptions, it is rendered similar, qualitatively, to the optimal resource consumption profile obtained in the simple cake-eating context (Proposition 3, Figure 1, page 7).

Some Results on the Optimal Depletion of Exhaustible Resources Under Negative Discounting

Some Results on the Optimal Depletion of Exhaustible Resources Under Negative Discounting

On Optimal Depletion of Exhaustible Resources: Existence and Characterization Results

IN RECENT YEARS, there has developed a significant literature on the economics of natural resources. A part of this literature is concerned with finding the characteristics of optimal programs for economies with exhaustible resource constraints; that is, of jointly determining the optimal depletion of such resources, and optimal investment in augmentable capital goods. It should be noted that the theory of optimal economic growth, in the form given it by Ramsey [17], and extensively developed by many others, had been primarily concerned with the latter problem. Natural resources were often assumed to be supplied exogenously in given amounts in each period, an approach clearly unsuitable for capturing the essence of problems associated with the optimal use of exhaustible resources. The more recent literature derives its inspiration from Hotelling's classic paper [8], stressing the increasing significance of such resources in production, as they are irrevocably run down. I shall consider, in this paper, a model of intertemporal allocation in which there is a produced good (which can be used for consumption or for further production), and an exhaustible resource (which is essential for production), the total initial stock of which is given. The use of the resource over the (infinite) planning horizon must not exceed this available stock. A planner is assumed to evaluate consumption in each period, in terms of a utility function, and to "maximize" the undiscounted sum of these one-period utilities, to obtain, simultaneously, the optimal depletion of the exhaustible resource, and the optimal investment 2 pattern. This model resembles, in some aspect or other, the frameworks examined by Dasgupta [3], Dasgupta and Heal [4, 5], Solow [18], and Stiglitz [19], to mention only a few. I will address three sets of issues in this framework. First, an interesting problem in the theory of optimal economic growth is to find suitable conditions under which a competitive program is optimal. I will show that a feasible program is optimal if and only if (a) it is competitive,3 and (b) it satisfies the transversality condition, that the value of the capital and resource stocks, at the competitive prices, converges to zero (Theorem 3.1). It follows from this result, that a competitive program is optimal if and only if it satisfies the above-mentioned transversality condition. It should be noted that in traditional models of optimal growth (in which exhaustible resources do not appear as essential factors of production), a feasible program, under certain technological curvature conditions, is shown to be optimal if and only if it is competitive, and the value of input