OPTIMAL ECONOMIC GROWTH WITH UNCERTAIN EXHAUSTIBLE RESOURCE STOCKS

This dissertation examines basic theoretical properties of an optimal growth model with capital and an uncertain exhaustible resource stock and then applies some of the theoretical results to a consideration of efficient offshore oil development in the United States.;In the examination of efficient offshore oil development programs, a market valuation characterization of the utility function (based on the value of consumers' and producers' surplus) is developed and an optimal resource depletion program based on estimates of offshore oil exploration and development costs and United States Geological Survey estimates of the probability distribution of undiscovered offshore oil resources is calculated using numerical methods to solve the differential equations characterizing the efficient program. Among the results is the finding that an increase in the discount rate retards the efficient rate of reserve development, in contrast to the result for simple exhaustible resource models in which an increase in the discount rate hastens the depletion of the resource. This seemingly anomolous result arises from the peculiar technological features of petroleum development. Furthermore, taking into account information about the probability distribution of undiscovered recoverable resources is found to increase the expected value of the efficient program compared to a program based on information about mean resource availability alone.;In the theoretical model, utility is derived from two types of consumption, general consumption produced using capital in a conventional neoclassical growth model and resource consumption proportional to the rate of depletion of an exhaustible resource stock. Two types of uncertainty are examined: development uncertainty, which is uncertainty about the size of the recoverable resource stock that can only be resolved by actually depleting the resource, and exploration uncertainty, which is uncertainty about the success of exploration efforts aimed at discovering additional resources. Properties of the optimal resource depletion and capital accumulation programs under the different assumptions about uncertainty differ from each other and from the programs characterizing resource depletion and capital accumulation in simple models with no uncertainty. The sensitivity of results to different assumptions about the "essentiality" of the resource, i. e., whether general consumption can continue following the depletion of the resource, and to whether future utilities are discounted or not is also examined.