Departing from Hotelling's assumption of fixed and known reserves, in this paper I develop an economic model of additions to proven reserves that explicitly incorporates the effects of expected resource price, cumulative reserves development, and technological progress on reserves additions. The model treats additions to proven oil reserves as output of a production process in which drilling wells is a primary input to transform some of the oil-in-place into the economic category of proven reserves. Application of the model to U.S. data for the 1950-1995 period provides strong statistical support for the existence of all the three salient effects. I obtain an estimate of the price elasticity of reserves additions (absent from previous studies) which, although statistically highly significant, is small in magnitude. Using this price elasticity estimate, I show that if in the face of steady economic growth, and hence oil consumption, U.S. dependence on foreign oil is to be kept from rising in the future, ceteris paribus, a steady oil price increase in the range of 1.5 to 4.5 percent a year is essential.