Edited by Jeroen C.J.M. van den Bergh
Chapter 3: Optimal Extraction of Non-Renewable Resources
Cees Withagen 1. Introduction This chapter reviews the optimal exploitation of exhaustible resources. The literature on this subject is so huge that it is impossible to do justice to all the important contributions that have been made. We shall concentrate on theoretical issues of resource depletion under certainty, while some remarks about uncertainty will be made at the end of this chapter. We shall consider optimal depletion in a closed economy from the point of view of a social planner and compare the Rawlsian and the utilitarian outcomes. We shall not go into the question how the welfare qptimum can be implemented in a decentralized economy, nor shall we deal with matters such as imperfect competition. For these issues the reader is referred to other chapters of this handbook (see also Withagen, 1990). Since we are dealing with optimal exploitation over time, intergenerational welfare has to be given attention at the outset. An excellent introduction to the theory of intergenerational welfare is provided by Dasgupta and Heal (1 979). Here we shall restrict ourselves to a very brief statement of the questions involved. The number of people living at date t is denoted by L(t), where the the initial population, at t = 0, is normalized to unity. The growth rate of the population is given by T.As far as labour is an input in a production process, it is assumed throughout that this is a given constant fraction of the population. Without loss of generality it is assumed that...
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