Capacity constraints and the production of nonrenewable resources: OIES paper: EE5

Abstract

This paper examines the extent to which the use of a fixed input in the extraction process for a nonrenewable resource affects a number of common results in depletion theory. A multi-deposit model is constructed where the extraction technology requires capital equipment that is deposit-specific and has no resale value once installed. It is shown that for each deposit there is an equilibrium capacity level, which is built up all at once or gradually, depending on the adjustment costs associated with installing the equipment and the heterogeneity of deposits. The aggregate extraction rate is constant over an initial period of time. The paper goes on to derive a number of results for this model. Firstly, different quality deposits are always exploited simultaneously, although better quality deposits are exhausted first. Secondly, higher discount rates entail quicker depletion only if the resource is sufficiently scarce relative to capital equipment. Thirdly, a programme that is optimal from a social viewpoint can in principle be reproduced without intervention in a perfectly competitive market. Fourthly, fiscal instruments generally discourage investment, and consequently overconserve the resource, unless tax writeoff provisions or depletion allowances are in force. Fiftly, exploitation under monopoly and symmetrically placed Cournot-Nash producers is generally more conservationist than the social optimum, but the distortion is negligible if the number of producers is sufficiently large. Finally, allowing for a variable input in the extraction process or a positive rate of depreciation for capital equipment is shown to quality the results by restoring the more common results that the aggregate extraction rate is always a strictly declining function of time