The welfare effects of a market allocation of an exhaustible resource
Date
1977
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Abstract
In recent years, cost-benefit theorists have developed “net benefit" measures of welfare change attributable to shifts in the allocation of flow resources. Presumably, such welfare-change measures have been developed as an attempt to minimize the wastage of resources on unsound projects. However, to the author's knowledge, no such welfare-change measure has been developed to rank alternative allocations of an exhaustible resource. This dissertation attempts to devise such a measure. The measure is developed in three steps. The first step (Chapter two) is an explanation of how a free market allocates the exhaustible resource over time. Inquiry is made as to how the time path of extraction is affected by changes in (1) production costs, (2) total known supply, (3) the costs of a substitute techno1ogy, and (4) the discount rate. Knowledge of the allocation explored in this step is important, because, once determined, the market outcome can be compared to some appropriately-defined efficiency norm. The second step (Chapter three) develops an efficiency norm as a basis for determining whether the market depletes the exhaustible resource too quickly, too slowly, or at the right rate. The third step (Chapter four) of this dissertation is an attempt to develop a measure which quantifies how well the market's time-use of the mineral approaches an efficient allocation. The methodology used is the development of a measure of welfare change. Specifically, this measure is designed to ascertain the net change in benefits attributable to changes in either of two generalized distortions relevant to the market for an exhaustible resource. At all three steps, this dissertation draws from and extends the theory of exhaustible resources. The first step is an extension and refinement of the comparative statics of competitive mining theory. At the second step, the optimality properties of a market allocation over time are examined. At the third step, the degree to which the market breaks down is the subject of concern. Specifically, an extension of currently-accepted welfare-loss theory is developed and made applicable to the exhaustible resources sector. The results of this dissertation are that, indeed, such a welfare-loss measure can be quantified. By incorporating (1) the effect of a change in a market distortion on the private profit-maximizing output path of each of n mining firms, and (2) the effect of these n output path changes on aggregate total discounted net benefits, a welfare-loss measure is developed. The measure can, in principle, rank alternative allocations of an exhaustible resource on the basis of the net size of two generalized distortions, the values of which would depend on the size of the policy variable under consideration.