A mathematical model, with 86% accuracy, has been developed to explain discoveries or additions to proven petroleum reserves. In the model, the quantity of petroleum discovered directly depends on property acquisition, exploration, and development expenditures. Also, petroleum discoveries indirectly depend on the petroleum stock remaining to be discovered. The empirical data base is a survey of corporate expenditure data for the years 1979-82. Unlike most previous models in this field, this model is based on economic theory and economic production-function mathematics. Allowing a dual application of the model, not only is it useful for forecasting petroleum additions, but it also addresses some fundamental questions concerning petroleum exploration and discovery. Five pri ary questions concerning the structure of the American petroleum industry are: (1) Which firms are more efficient in petroleum exploration and discovery, large or small? (2) Are governmental lease policies efficient? (3) How should a firm optimally allocate its resources to maximize petroleum discoveries? (4) In what ways does a declining stock affect discoveries? (5) Have increasing prices effected a structural change in the petroleum exploration industry? The dual nature of the model, the explanatory accuracy, and the one-equation simplicity, all encourage increased application of this type of analysis to the natural-resource industries.

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